Model Predictive Control
Abstract
From power plants to sugar refining, model predictive control (MPC) schemes have established themselves as the preferred control strategies for a wide variety of processes.
The second edition of Model Predictive Control provides a thorough introduction to theoretical and practical aspects of the most commonly used MPC strategies. It bridges the gap between the powerful but often abstract techniques of control researchers and the more empirical approach of practitioners. Model Predictive Control demonstrates that a powerful technique does not always require complex control algorithms.
The text features material on the following subjects:
general MPC elements and algorithms;
commercial MPC schemes;
generalized predictive control
multivariable, robust, constrained nonlinear and hybrid MPC;
fast methods for MPC implementation;
applications.
All of the material is thoroughly updated for the second edition with the chapters on nonlinear MPC, MPC and hybrid systems and MPC implementation being entirely new. Many new exercises and examples have also have also been added throughout and Matlab® programs to aid in their solution can be downloaded from the authors' website at http://www.esi.us.es/MPCBOOK. The text is an excellent aid for graduate and advanced undergraduate students and will also be of use to researchers and industrial practitioners wishing to keep abreast of a fast-moving field.
Chapters (10)
Model Predictive Control (MPC) originated in the late seventies and has developed considerably since then. The term Model Predictive Control does not designate a specific control strategy but rather an ample range of control methods which make explicit use of a model of the process to obtain the control signal by minimizing an objective function. These design methods lead to controllers which have practically the same structure and present adequate degrees of freedom. The ideas, appearing in greater or lesser degree in the predictive control family, are basically: explicit use of a model to predict the process output at future time instants (horizon); calculation of a control sequence minimizing an objective function; and receding strategy, so that at each instant the horizon is displaced towards the future, which involves the application of the first control signal of the sequence calculated at each step.
As has been shown in previous chapters, there is a wide family of predictive controllers, each member of which is defined by the choice of the common elements such as the prediction model, the objective function and obtaining the control law.
This chapter describes one of the most popular predictive control algorithms: Generalized Predictive Control (GPC). The method is developed in detail, showing the general procedure to obtain the control law and its most outstanding characteristics. The original algorithm is extended to include the cases of measurable disturbances and change in the predictor. Close derivations of this controller such as CRHPC and Stable GPC are also treated here, illustrating the way they can be implemented.
One of the reasons for the success of the traditional PID controllers in industry is that PID are very easy to implement and tune using heuristic tuning rules such as the Ziegler-Nichols rules frequently used in practice. A Generalized Predictive Controller, as shown in the previous chapter, results in a linear control law which is very easy to implement once the controller parameters are known. The derivation of the GPC parameters requires, however, some mathematical complexities such as recursively solving the Diophantine equation, forming the matrices G, G′ and f and then solving a set of linear equations. Although this is not a problem for people in the research control community where mathematical packages are normally available, it may be discouraging for practitioners used to much simpler ways of implementing and tuning controllers.
Most industrial plants have many variables that have to be controlled (outputs) and many manipulated variables or variables used to control the plant (inputs). In certain cases a change in one of the manipulated variables mainly affects the corresponding controlled variable, and each the input-output pair can be considered as a single-input single-output (SISO) plant and controlled by independent loops. In many cases, when one of the manipulated variables is changed, it not only affects the corresponding controlled variable but also upsets the other controlled variables. These interactions between process variables may result in poor performance of the control process or even instability. When the interactions are not negligible, the plant must be considered to be a process with multiple inputs and outputs (MIMO) instead of a set of SISO processes. The control of MIMO processes has been extensively treated in literature; perhaps the most popular way of controlling MIMO processes is by designing decoupling compensators to suppress or diminish the interactions and then designing multiple SISO controllers. This requires first determining how to pair the input and output variables, that is, which manipulated variable will be used to control which output variables, and that the plant have the same number of manipulated and controlled variables. Total decoupling is very difficult to achieve for processes with complex dynamics or exhibiting dead times.
The control problem was formulated in the previous chapters considering all signals to possess an unlimited range. This is not very realistic because in practice all processes are subject to constraints. Actuators have a limited range of action and a limited slew rate, as is the case of control valves limited by a fully closed and fully open position and a maximum slew rate. Constructive or safety reasons, as well as sensor range, cause bounds in process variables, as in the case of levels in tanks, flows in pipes, and pressures in deposits. Furthermore, in practice, the operating points of plants are determined to satisfy economic goals and lie at the intersection of certain constraints. The control system normally operates close to the limits and constraint violations are likely to occur. The control system, especially for longrange predictive control, has to anticipate constraint violations and correct them in an appropriate way. Although input and output constraints are basically treated in the same way, as is shown in this chapter, the implications of the constraints differ. Output constraints are mainly due to safety reasons and must be controlled in advance because output variables are affected by process dynamics. Input (or manipulated) variables can always be kept in bound by the controller by clipping the control action to a value satisfying amplitude and slew rate constraints.
In general, industrial processes are nonlinear, but, as has been shown in this book, most MPC applications are based on the use of linear models. There are two main reasons for this: on one hand, the identification of a linear model based on process data is relatively easy and, on the other hand, linear models provide good results when the plant is operating in the neighbourhood of the operating point. In the process industries, where linear MPC is widespread, the objective is to keep the process around the stationary state rather than perform frequent changes from one operation point to another and, therefore, a precise linear model is enough. Besides, the use of a linear model together with a quadratic objective function gives rise to a convex problem (Quadratic Programming) whose solution is well studied with many commercial products available. The existence of algorithms that can guarantee a convergent solution in a time shorter than the sampling time is crucial in processes where a great number of variables appear.
In most processes there are not only continuous variables but also variables that have a discrete nature. For a long time, the control of processes with discrete variables and the control of processes with continuous variables were considered to be two completely different things. On the one hand, the theories of finite state machines were used to control processes with discrete variables, and on the other hand, linear and nonlinear control theory was used for the control of continuous variables. The techniques for modelling and analysis of these types of systems are different. In the case of continuous systems, differential equations, transfer functions, etc., are used as modelling tools, while in the discrete counterpart, state transition graphs, Petri Nets, etc., are employed (see ). From the beginning of the 1990s there has been great interest in processes that have both discrete and continuous parts. Hybrid systems are dynamic systems with both continuous-state and discrete-state and event variables. That is, the plant has time-driven and event-driven dynamics, the controller affects both time-driven and event-driven components, and it may deal with continuous and/or discrete signals.
One of the disadvantages of MPC is that the computation time required in some cases considerably limits the bandwidth of processes to which it can be applied. This is the case of MPC in the presence of constraints, adaptive MPC, robust MPC and MPC of nonlinear processes. This chapter is devoted to explaining some of the procedures used to reduce the amount of computation needed for the implementation of MPC. All of these procedures are based on doing most of the required computation off-line, leaving only part of the computation for the online part of the implementation.
This chapter is dedicated to presenting some MPC applications to the control of different real and simulated processes. The first application presented corresponds to a self-tuning and a gain scheduling GPC for a distributed collector field of a solar power plant. In order to illustrate how easily the control scheme shown in Chapter 5 can be used in any commercial control system, some applications concerning the control of typical variables such as flows, temperatures and levels of different processes of a pilot plant are presented. The description of two applications in the food industry (a sugar refinery and an olive oil mill) are included. Finally the application of an MPC to a highly nonlinear process (a mobile robot) is also described.
... Generalized Predictive Control (GPC) is a widely used model predictive control algorithm recognized for its versatility in handling various prediction models [1]. Its primary strength lies in its robustness to model uncertainties, achieved by incorporating historical control actions and error values. ...
... Its primary strength lies in its robustness to model uncertainties, achieved by incorporating historical control actions and error values. This adaptability to changing system behavior ensures consistent control performance [1]- [3]. This makes GPC particularly effective for complex, nonlinear, and non-minimum phase systems. ...
... According to the operating principle of the GPC controller, the system model is represented using the integrated Auto-Regressive Moving-Average (CARIMA) model, defined by [1]: ...
... Motivated by the previously described advantages and existing gap in the techniques using MPC, in this article a predictive control system for drug co-administration (MISO case) with event-based capabilities is proposed and evaluated. The developed controller uses a generalized predictive controller (GPC) 27 and the control architecture is built using a nonlinear pharmacokinetic/pharmacodynamic (PK/PD) patient model. This model has the MISO configuration, where the infusions of propofol and remifentanil are the control variables and the BIS signal, representing the DoH level, is the controlled variable. ...
... The proposed event-based architecture uses the GPC algorithm 27 to compute a new control action when a new event is triggered. Due to the working principle introduced previously, it is necessary to implement a set of controllers where each of them corresponds to one sampling rate of the T f vector (the specific number of controllers is defined based on clinical requirements and limitations, as described in Section 4.4). ...
... The tuning parameters are the control horizon N f u p , the minimum N f 1 and maximum N f prediction horizons values, and the weighing factor f between the error and the future control moves. 27 Finally, the minimization of the cost function J is performed using quadratic programming (QP) optimization, where constraints related to the clinical requirements and process limitation are imposed in the control signal computation. In fact, the predictive controller computes the future control signal u f p (t), u f p (t + 1), … , u f p (t + N f u p − 1) that will keep the process output y f (t + j) around the provided reference w(t + j). ...
In this article, a predictive event‐based control architecture for multivariable drug infusion in the anesthesia process is presented. The control scheme considers a multiple‐input single‐output process, where the depth of hypnosis is the controlled variable and the infusion rates of propofol and remifentanil, which are co‐administered by imposing a fixed ratio between them, are the control variables. The control system is built on the top of a nonlinear pharmacokinetic/pharmacodynamic model for drug co‐administration that reflects the super‐additive effect of both drugs on the bispectral index scale (BIS), which is a measure of the hypnotic state of the patient. Further, in order to compensate the nonlinear behavior of the system, it exploits an external predictor that is designed to increase the robustness to inter‐/intra‐patient variability. The overall controller parameters are tuned by applying an optimization method on a representative set of virtual patients. The main feature of the proposed control algorithm consists in its asynchronous execution, which can be beneficial in reducing control signal changes due to the noisy measurements of the BIS. The evaluation of the analyzed control architecture through a simulation study reveals that control action variations can be reduced by about 48% on average with respect to its time‐based counterpart. This reduction is obtained at the expense of a lower control accuracy, resulting in a degradation of 18% in terms of integrated absolute error. Results are acceptable from a clinical practice perspective proving that the proposed approach is a feasible alternative to classical time‐based predictive controllers.
... As a consequence of the receding horizon paradigm, the control law u(kT s ) = u k = Δu k|k + u k−1 is applied at each sampling instant, and the entire optimization problem is repeated at k + 1 . The definition of the free response and future outputs for both GPC and DMC are widely explored in [8] and a quick review of its computation is available in "Appendices A and B". ...
... In general, e(kt s ) = Z −1 {E(z)} is assumed to be a white noise with null mean and T(z −1 ) may be used to modified the white noise properties.In this case, or simplywhere à (z −1 ) = A(z −1 )(1 − z −1 ), and ΔU(z) = (1 − z −1 )U(z) as discussed in . If T(z −1 ) ≠ I , then the GPC is commonly identified as GPC-T[8, Chapter 4]. Now assume that à (z −1 ) , B(z −1 ) , and T(z −1 ) are given by ...
This paper proposes a receptance-based linear model predictive control approach for time-varying reference tracking of multibody dynamical systems. Receptance-based Generalized Predictive Control and Dynamic Matrix Control are used to deal with the trajectory tracking of multibody control problems subject to time-varying targets. The reference tracking properties of the typical MPC strategies are analyzed with respect to the standard cost function. Furthermore, a modified receptance-based MPC approach is presented to reduce the tracking error sensitivity with respect to the MPC design parameters. Periodic references are considered to illustrate the benefits of the proposed modification. A case study based on a two link multibody system is presented to highlight the main properties of the new receptance based predictive control.
... MPC controllers require a model that describes the main dynamics of the plant system in the operating region [56]. For the control of nonlinear systems, the plant model can be linear or nonlinear; however, the use of a nonlinear model significantly increases the complexity and computational load of the controller. ...
... The MPC controller receives or estimates the current state of the plant and calculates the sequence of control actions that minimises a cost function over the horizon, solving a conditional optimisation problem [56,61]. The cost function, predefined in the Matlab MPC toolbox, was established by Equation (14). ...
Water heating is a significant part of households’ energy consumption, and tankless gas water heaters (TGWHs) are commonly used. One of the limitations of these devices is the difficulty of keeping hot water temperature setpoints when changes in water flow occur. As these changes are usually unexpected, the controllers typically used in these devices cannot anticipate them, strongly affecting the users’ comfort. Moreover, considerable water and energy waste are associated with the long-time response to cold starts. This work proposes the development of a model predictive control (MPC) to be deployed in low-cost hardware, such that the users’ thermal comfort and water savings can be improved. Matlab/Simulink were used to develop, validate and automatically generate C code for implementing the controller in microcontroller-based systems. Hardware-in-the-loop simulations were performed to evaluate the performance of the MPC algorithm in 8-bit and 32-bit microcontrollers. A 6.8% higher comfort index was obtained using the implementation on the 32-bit microcontroller compared to the current deployments; concerning the 8-bit microcontroller, a 4.2% higher comfort index was achieved. These applications in low-cost hardware highlight that users’ thermal comfort can be successfully enhanced while ensuring operation safety. Additionally, the environmental impact can be significantly reduced by decreasing water and energy consumption in cold starts of TGWHs.
... Within a set of constraints, the control aim is to track reference trajectories with the least amount of error and effort. The formulation of the cost function reflecting the control objective as follows [54] where ∈ ℝ 2×2 and ∈ ℝ 7×7 are the diagonal positive definite weighting matrices for the state and control input variables, and is the value of the prediction horizon at each th step. The TRMS control input vector at time is represented by ( ) = 0 ∈ ℝ 2 , and ̃∈ ℝ 7 , is different between the TRMS variables of predicted state of the system (̂) and its reference state ( * ) at each instant, as expressed: ...
Nowadays, controlling a Twin Rotor MIMO System (TRMS) is a considerable challenge for engineers due to its high non-linear attributes. The controller's design goals are to achieve the appropriate pitch and yaw angles when there is cross-coupling between its main and tail rotors while minimizing both the angular position error and controller effort. Performance measures can be utilized to evaluate the performance of the controller including integral square error, total variation, and integral absolute control action. In this paper, a Nonlinear Model Predictive Control (NMPC) is proposed to control TRMS rotors, which refer to the vertical and horizontal planes. Fick’s Law Algorithm (FLA) has been utilized to offline obtain the best selection for NMPC parameters. That includes best weighting matrices, shorter time steps, and shorter prediction horizons, by minimizing a novel penalty function called robust integral square error. FLA is used due to its flexibility, the ability to avoid suboptimal regions, and simplicity of implementation. The effectiveness of the proposed controller is examined using simulation-based tests conducted with MATLAB, which makes use of the CasADi Toolbox. In comparison to Cross Coupled PID (CC-PID) controller, the simulation results prove that FLA-based-NMPC has better performance and can track trajectories (step, square, and sine) even when there is ±30% in TRMS parameters perturbation. This work has come up with new contributions such as the new tuning strategy, extra state variable consideration, and a new FLA engineering application.
... Properly selecting the prediction horizon window is critical in MPC as it is fundamental to obtaining satisfactory system results. Readers can refer to [23,65] for theoretical support of the prediction horizon. Therefore, the influence of different prediction horizons (i.e., 8,12,16,20, and 24 hours) on the MG control during a one-year operation is analyzed. ...
Access to electricity is a fundamental key to developing countries' growth. Microgrids (MG) have become potential solutions to provide energy to isolated rural areas in a safe and environmentally friendly way. Therefore, proposals for alternative solutions to bridge the electrification gap in the Ecuadorian Amazon – which has the most significant percentage of its population without access to electricity – are of significant interest. Consequently, this paper presents the design of an Energy Management System (EMS) based on Model Predictive Control (MPC) for an isolated electro-thermal microgrid comprising a photovoltaic generator, a diesel generator, a lithium-ion battery Energy Storage System (ESS), electrical loads, and a domestic hot water system. The EMS aims to supply energy reliably and safely, minimize the MG's operation costs, and extend the ESS's useful life while satisfying the end users' comfort. This study includes an estimated degradation model for the ESS’s State of Health (SOH), an essential parameter contributing to reducing the microgrid's operating costs in the long term. Simulation results using one-year data present the influence of the prediction horizon on the MG’s scheduling. In addition, the benefits of the proposed EMS are highlighted by comparing it with the results achieved by a Unit Commitment approach, where it is demonstrated that the proposed EMS presents a reduction in MG operating costs and greenhouse gas emissions while maximizing the utilization of renewable energy and extending the lifespan of the ESS. Finally, an experimental validation, using a Typhoon Hardware-in-the-loop HIL-402 device in real-time operation, stands out the effectiveness and feasibility of the proposed MPC-based EMS.
... Real-time monitoring and prediction of system states, such as flow rate and water level, enable the ongoing operation of actuators to activate existing storage capacity. Typically, developing RTC strategies involves using rule-based control (RBC) or optimization-based algorithms to meet local or global control objectives (Camacho & Bordons, 2007;Jean et al., 2021;Lund et al., 2018;Maciejowski, 2001). Model predictive control (MPC), an advanced optimization-based RTC technique, incorporates rainfall forecasts into its analysis, facilitating a more effective global strategy for each actuator than the reactive "if-then-else" rules (Eggimann et al., 2017;García et al., 2015;Sun et al., 2023). ...
The integration of green‐gray infrastructures with advanced control approaches is revolutionizing the stormwater system retrofitting, emerging as an innovative strategy to mitigate urban flood risks. However, a major challenge lies in balancing the substantial investments of these infrastructure projects with their environmental benefits, such as reduced flooding volume and lower peak flow. Model predictive control (MPC), a dynamic and intelligent control approach, optimizes these environmental benefits but is underutilized in the system design phase for cost‐effectiveness analysis. This study introduces a multi‐scenario model framework that incorporates MPC and other control approaches into stormwater system designs, including the implementation of controlled storage tanks and green infrastructures. This framework provides comprehensive modeling tools for practitioners to evaluate the flood control benefits and costs across various infrastructure designs and control scenarios, ultimately identifying solutions that are both environmentally and economically viable. A case study conducted in a small urban catchment area in Shenzhen City, China, demonstrates the effectiveness of this framework. The results indicate that MPC outperforms other control scenarios, particularly under heavy or extreme rainfall conditions. Notably, MPC not only provides superior environmental benefits but also yields considerable cost savings, ranging from 1,787 to 9,371 USD per hectare compared to static control, equating to a 5% reduction in cost relative to rule‐based control. Such findings suggest that integrating MPC is a cost‐effective alternative to extensive infrastructure expansion for flood management, which significantly enhances the benefit contribution of controlled infrastructures without substantial additional expenses.
... The proposed CSTR model, shown in Figure 1, is described by the equations given below as found in [50]: ...
In the chemical and petrochemical industries, the Continuous Stirred Tank Reactor (CSTR) is, without doubt, one of the most popular processes. From a control point of view, the mathematical model describing the temporal evolution of the CSTR has a strongly nonlinear cross-coupled character. Moreover, modeling errors such as external disturbances, neglected dynamics, and parameter variations or uncertainties make its control task a very difficult challenge. This problem has been the subject of a wide number of control strategies. This article attempts to propose a viable, robust nonlinear decoupling control scheme. The idea behind the proposed approach lies in the design of two nested control loops. The inner loop is responsible for the compensation of the nominal model's nonlinear cross-coupled terms via a static nonlinear feedback; while the outer loop, designed around an Extended State Observer (ESO), which the additional state gathers the global effect of modeling errors, is charged with instantaneously estimating and then compensating the ESO extended state. This way, the CSTR complex dynamics are reduced to a series of decoupled linear subsystems easily controllable using a simple Proportional-Integral (PI) linear control to ensure the robust pursuit of reference signals respecting the desired performance. The presented control validation was performed numerically by an objective comparison to a classical PID controller.
... This paper takes as its context Model Predictive Control (MPC) [1][2][3][4][5][6][7][8]. There have been an enormous number of papers published in this area showing how MPC algorithms can be tailored to specific objectives and requirements (e.g., [9,10]), but in the main these approaches focus on algorithms that require substantial computational power. ...
A recent study demonstrated that the use of feedforward information with conventional Predictive Functional Control (PFC) leads to unexpected inconsistencies, with subsequent negative impacts on tuning and behaviour. A proposal was made to define the coincident point differently and shown to reduce the lag in the closed-loop PFC responses and applied to some systems with benign dynamics. Other recent work has looked at parameterisations of the future input to deal with challenging open-loop dynamics and significantly extended the range of problems for which PFC can be effective. This paper combines the two concepts, and thus proposes an algorithm that has both more effective and simple tuning than original PFC as well as being applicable to a range of challenging dynamics.
... MPC (Camacho & Bordons, 2007) is an advanced process control method used for controlling complex systems, while, at the same time, satisfying a set of constraints. MPC requires an iterative optimization procedure of a system model over a finite horizon (prediction horizon-T H ) which keeps being shifted forward with a certain step (T S ) such as = ⋅ with ∈ℕ . ...
This paper proposes a method for reducing the environmental impact of sewer network (SN) overflows. The main objective of the paper is to minimize the wastewater quantity and the pollutant loads that overflow from the SN. The proposed algorithm to achieve this goal is Model Predictive Control using Particle Swarm Optimization as optimization method. It was tested in simulation using a simplified model of the network based on Benchmark Simulation Modelsewer as prediction model, and a forecasted influent. Three cases have been considered: (a) the fitness function is defined as the global yearly overflow volume calculated using equal weights for each tank; (b) the fitness function uses different weights for each tank depending on the medium loads and (c) integrating a penalty term related to the system state at the end of the prediction horizon in the previous fitness function. The simplified model determined a significant reduction of the integration time minimizing the optimization time.
... Thereby, the optimization is performed in the next time step according to the updated predictions and the updated measured state. This can be understood as a feedback loop and makes MPC a closed-loop control in contrast to optimal control [30,31]. By repeating the optimization with new information, the 13 This preprint research paper has not been peer reviewed. ...
... MPC refers to a wide range of control methods that use a model to obtain the control signal by minimizing an objective function (Camacho and Bordons, 2007). Compared to PID, which is usually model-free, MPC is model-based and considers constraints. ...
Magnetically driven microrobots hold great potential to perform specific tasks more locally and less invasively in the human body. To reach the lesion area in vivo, microrobots should usually be navigated in flowing blood, which is much more complex than static liquid. Therefore, it is more challenging to design a corresponding precise control scheme. A considerable amount of work has been done regarding control of magnetic microrobots in a flow and the corresponding theories. In this paper, we review and summarize the state-of-the-art research progress concerning magnetic microrobots in blood flow, including the establishment of flow systems, dynamics modeling of motion, and control methods. In addition, current challenges and limitations are discussed. We hope this work can shed light on the efficient control of microrobots in complex flow environments and accelerate the study of microrobots for clinical use.
... The learned causal dynamics model plays a crucial role in improving policy learning. Based on the learned model, we employ the model predictive control (MPC) [1] as the planning algorithm. MPC is an iterative and model-based control approach. ...
Learning an accurate dynamics model is the key task for model-based reinforcement learning (MBRL). Most existing MBRL methods learn the dynamics model over states. But in most cases, the relationships among states are complex because the states are affected by the interaction of various factors in the environment. Recently some works are proposed to learn the dynamics model on latent representations space. But the learned model is dense and may contain spurious associations between latent representations. To deal with these problems, we introduce a latent causal dynamics model over latent representations and provide a learning method for MBRL. Specifically, we first learn the latent representations from the observed state space. Second, we learn a latent causal dynamics model among latent representations by a causal discovery method. Finally, the latent causal dynamics model is used to aid policy learning. The above steps are iterative to update the unified loss function until convergence. Experimental results on four tasks show that the performance of our proposed method benefits from the causality and the learned latent representations.
... Considering the dimension of searching space and the number of waypoints, it is impractical to solve for all waypoints in one optimization step. Lin et al. [16] introduced an approach inspired by MPC [28] to generate an efficient and time-optimal trajectory through many intermediate waypoints. Multiple waypoints can be divided into several batches. ...
... At present, the commonly used motion control algorithms in the field of unmanned driving include the pure pursuit algorithm [27], Stanley algorithm [28], linear quadratic regulator (LQR) algorithm [29] and model predictive control (MPC) algorithm [30]. Among them, the pure pursuit algorithm and Stanley algorithm are motion control algorithms based on vehicle kinematics which are applicable to low-speed vehicle motion control. ...
Driverless technology refers to the technology that vehicles use to drive independently with the help of driverless system under the condition of unmanned intervention. The working environment of construction machinery is bad, and the working conditions are complex. The use of driverless technology can greatly reduce the risk of driver operation, reduce labor costs and improve economic benefits.Aiming at the problem of the GPS positioning signal in the working environment of construction machinery being weak and not able to achieve accurate positioning, this paper uses the fusion SLAM algorithm based on improved NDT to realize the real-time positioning of the whole vehicle through reconstruction of the scene. Considering that the motion characteristics of crawler construction machinery are different from those of ordinary passenger cars, this paper improves the existing pure pursuit algorithm. Simulations and real vehicle tests show that the algorithm combined with the fusion SLAM algorithm can realize the motion control of driverless crawler construction machinery well, complete the tracking of the set trajectory perfectly and have high robustness. Considering that there is no mature walking method of driverless crawler construction machinery for reference, the research of this paper will lay a foundation for the development of driverless crawler construction machinery.
Optical systems, such as a mobile LiDAR system, encounter mechanical disturbances associated with the condition of the road, resulting in significant misalignments in the optical paths within the system. To address this issue, considerable time is dedicated to the realignment process to restart the system. A suggested approach to overcome this challenge involves the implementation of automatic realignment through the control of the motion of the steering mirrors using an advanced control technique known as Model Predictive Control (MPC). This technique, which is relatively new in the field of optics, is widely utilized in the industry due to its capability to manage and resolve a broad range of problems that are inherent to industrial systems, particularly, those that are subject to constraints or undergo disturbances during operation. In this study, we utilize MPC on the optical chain, specifically the LiDAR component, to regulate the beam and promptly rectify any flexure that occurs during both constant and variable trajectories, as well as in the presence of disturbances. A comparative analysis is conducted with the PID controller to evaluate the performance of the advanced technique proposed.
This research presents an experimental electric vehicle developed at the Tecnológico Nacional de México Celaya campus. It was decided to use a golf cart-type gasoline vehicle as a starting point. Initially, the body was removed, and the vehicle was electrified, meaning its engine was replaced with an electric one. Subsequently, sensors used to measure the vehicle states were placed, calibrated, and instrumented. Additionally, a mathematical model was developed along with a strategy for the parametric identification of this model. A communication scheme was implemented consisting of four slave devices responsible for controlling the accelerator, brake, steering wheel, and measuring the sensors related to odometry. The master device is responsible for communicating with the slaves, displaying information on a screen, creating a log, and implementing trajectory tracking techniques based on classical, geometric, and predictive control. Finally, the performance of the control algorithms implemented on the experimental prototype was compared in terms of tracking error and control input across three different types of trajectories: lane change, right-angle curve, and U-turn.
Based on the characteristics of individual collector units, a solar field has to be assembled which is sufficiently large to generate the required thermal power at a sufficiently high temperature. The heat transfer fluid is pumped through a solar field, transporting the heat from the collectors to the demand side heat exchanger or directly to the consumer. Additional optical losses may occur in a solar field due to mutual shading and blocking. Thermal losses, especially at nighttime, and hydraulic pressure losses to be overcome by pumping power, shall be minimized. Changes in the thermophysical properties of single-phase fluids as well as phase change of two-phase fluids have to be considered. The basics of solar thermal loop control are presented, boundary conditions for the operation and maintenance of the components are illustrated, and finally some line- and point-focusing systems are compared with respect to their operating characteristics.
In order to address the problem of the real-time scheduling and control of batch chemical systems, this work proposes a model predictive control method based on Petri nets. First, a method is presented to construct a batch chemical system’s timed Petri net model. Second, a control structure is designed to augment the Petri net model to control the valves. This results in timed Petri nets that formally represent the process specifications of a batch chemical system. Third, a model predictive control method is developed to schedule and control timed Petri nets, where a proposed heuristic function is utilized to perform the optimization computation. The model parameters are dynamically adjusted using online data, and both scheduling and valve control instructions are calculated in real time. Finally, a series of experiments is carried out in a beer canning plant to verify the proposed method. According to the experimental results, the scheduling and control problem can be solved in real time, where the online computations can be performed in milliseconds, and the resulting scheduling strategies are optimal or near-optimal.
Most manufactured electrical cables suffer from reductions in their physical, mechanical and electrical properties. These setbacks are mainly attributed to the improper control of wire tension during the cable manufacturing process. Hence, this paper systematically reviewed different control algorithms involved in controlling tension in moving webs, which include conventional control, advanced control, observer-based control, artificial intelligence-based control and hybrid control techniques. Thus, the review provided information about existing tension control techniques in moving webs, including their strengths and weaknesses. It was observed in this review that although a significant research effort has been made on web tension control systems, a thorough literature review is still lacking. It was concluded that controller optimisation using hybrid control algorithms is gaining popularity in web tension control due to their improved control response. Hence, its application in wire tension control can better help cable manufacturers improve the quality of manufactured cables.
This paper proposes modified model predictive control (MMPC) for coordinated signals, aiming to enhance a model’s fidelity to the realistic traffic environment by relaxing typical assumptions. We focus on the arterial, where every intersection is equipped with a dual-ring-barrier signal controller that complies with the standards of the National Electric Manufacturers Association. MMPC employs the store-and-forward model to describe traffic flow, thereby transforming the signal control problem into a model-based rolling-horizon optimization problem, in which the prediction horizon is composed of several future sample intervals, commonly equal to the cycle length. A radar detector is used to collect vehicle data upstream of the stop line at every sampling instant. The optimization problem is solved to minimize the number of vehicles within the prediction horizon, and the next timing plan is determined based on the optimization results. Constraints are added and modified in order to incorporate the typical relaxed assumptions in the optimization process. For this purpose, MMPC introduces a transition-free ring-barrier structure, vehicle distribution ratio, and percent arrival before the end of green. Simulation results indicate that coordination can be maintained by MMPC without the need for transitions, and the estimation of current and future traffic states can be improved with the assistance of modified constraints. Compared with benchmark techniques, MMPC offers superior vehicle progression for coordinated movement, and significant improvements in delays, number of stops, and total travel time from a system-wide perspective, with an acceptable small increase in runtime.
Ensuring nominal asymptotic stability of the nonlinear model predictive control (NMPC) controller is not trivial. Stabilizing ingredients such as terminal penalty term and Terminal Region (TR) are crucial in establishing the asymptotic stability. Approaches available in the literature provide limited degrees of freedom for the characterization of the TR for the discrete time quasi infinite horizon NMPC formulation. Current work presents alternate approaches namely arbitrary controller based approach and linear quadratic regulator (LQR) based approach, which provide larger degrees of freedom for enlarging the TR. Both the approaches are scalable to system of any dimension. Approach from the literature provides a scalar whereas proposed approaches provide two additive matrices as tuning parameters for shaping of the TR. Proposed approaches involve solving modified Lyapunov equations to compute terminal penalty term, followed by explicit characterization of the TR. Efficacy of the proposed approaches is demonstrated using benchmark two state system. TR obtained using the arbitrary controller based approach and LQR based approach are approximately 10.4723 and 9.5055 times larger by area measure when compared to the largest TR obtained using the approach from the literature. As a result, there is significant reduction in the prediction horizon length while retaining the feasibility of the controller.
Flap-based steering systems on blunt-body Mars entry vehicles may improve flight performance relative to existing bank-angle steering systems. Successful implementation of articulating aerodynamic flaps on a hypersonic entry vehicle requires an active control system to map angle of attack and sideslip angle commands to flap deflection commands. Here, a successive-linearization model predictive control algorithm, as well as a linear-quadratic regulator, are designed and assessed to address this multiple input multiple output control problem. These two control algorithms are assessed in the presence of uncertainty in Monte Carlo simulations for various flap configurations and command profiles. Results indicate that while both control algorithms provide successful command tracking in the presence of uncertainty, the model predictive controller provides tracking errors about half the value of those corresponding to the linear-quadratic regulator, indicating increased robustness. Comparison of several flap configurations shows the model predictive controller can be applied to various flap configurations successfully with only marginal performance differences between configurations.
This article applies novel results for infinite- and finite-horizon optimal control problems with nonlinear dynamics and constraints. We use the Valentine transformation to convert a constrained optimal control problem into an unconstrained one and show uniqueness of the value function to the corresponding Hamilton–Jacobi–Bellman (HJB) equation. From there, we show how to approximate the solution of the initial (in)finite-horizon problem with a family of solutions that is Γ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varGamma $$\end{document}-convergent. Optimal solutions are efficiently obtained via a solver based on Pontryagin’s Principle (PP). The proposed methodology is demonstrated on the path planning problem using the full nonlinear dynamics of an unmanned aerial vehicle (UAV) and autonomous underwater vehicle (AUV) involving state constraints in 3D environments with obstacles.
Model uncertainty creates a largely open challenge for industrial process control, which causes a trade-off between robustness and performance optimality. In such a case, we propose a generalized conditional feedback (GCF) system to largely eliminate conflicts between robustness and performance optimality. This approach leverages a nominal model to design an optimal control in the virtual domain and defines an ancillary feedback controller to drive the physical process to track the trajectory of the virtual domain. The effectiveness of the proposed GCF scheme is demonstrated in a simulation for six typical industrial processes and three model-based control methods, and in a half-quadrotor system control test. Furthermore, the GCF scheme is open to existing optimal control and robust control theories.
This article focuses on the improvement of the real-time operation of the microgrid based on model predictive control (MPC), taking into account the stochastic nature of renewable resources and demand, as well as fault-tolerant mechanisms. Thus, a fault-tolerant strategy (FTS) module is inserted into the control loop, which is devoted to fault diagnosis and isolation, as well as setting reconfiguration actions that may involve modifications through the model parameters, the objective function, and the constraints used in the optimization problem solved by the MPC. Meanwhile, the MPC controller is responsible for managing the power of the microgrid, where two stochastic approaches are compared: tree-based MPC (TB-MPC) and chance-constrained MPC (CC-MPC). Experiments carried out in a simulated full-scale laboratory microgrid under various conditions demonstrate the effectiveness of the proposed algorithms in dealing with power equipment faults.
An event-triggered stochastic model predictive control (MPC) approach is proposed for the scheduling problem of constrained queueing networks with a dynamic topology. A discrete-time Markov chain (DTMC) in combination with a Bernoulli trial is used to model the time-varying routing of queueing networks. The constituency and positiveness constraints on queue lengths together with the dynamic topology and the stochasticity in packet arrival are incorporated into a stochastic MPC optimization problem. An event-triggered scheme with adaptive event checking involving an estimated waiting horizon is designed to trigger the solution of the optimization problem when necessary, leading to reduced computational burden and improved utilization of communication resources. The stability is analyzed by the relation between the inter-execution time and objective function. The proposed approach is applied to two queueing networks to show its effectiveness.
This article describes the study of Multi-input Multi-output (MIMO) distillation column processes applied to several benchmark problems (2-by-2) namely, Wood and Berry (WB), Vinante and Luyben (VL), Wardle and Wood (WW), and Ogunnaike and Ray (OR) using Model Predictive Control (MPC) strategy. The main objective of the chapter deals with the chain of actions involving teaching and practicing MPC controller design to researchers. The control of the top and bottom compositions in the benchmark distillation column using reflux and steam flow rates has shown to be a particularly difficult problem, due to the significant time delays, non-minimum phases, and nonlinear interactions within the process. In this study, the predictive control algorithm uses the Controlled Auto-Regressive Integrated Moving Average (CARIMA) model to address this problem. The performance of the predictive control scheme gives better setpoint tracking when compared with the conventional controllers available in state-of-the-art, and the simulation result shows the effectiveness of the predictive algorithm to the chosen benchmarks.
Predictive control has great potential in the home energy management domain. However, such controls need reliable predictions of the system dynamics as well as energy consumption and generation, and the actual implementation in the real system is associated with many challenges. This paper presents the implementation of predictive controls for a heat pump with thermal storage in a real single-family house with a photovoltaic rooftop system. The predictive controls make use of a novel cloud camera-based short-term solar energy prediction and an intraday prediction system that includes additional data sources. In addition, machine learning methods were used to model the dynamics of the heating system and predict loads using extensive measured data. The results of the real and simulated operation will be presented.
Solar thermal plants have high nonlinearities and non-manipulated energy source which make their control task a very challenging work. Linear controllers cannot cope with undesirable deviations of the outlet temperature over all the operation range of the dynamics of this type of plants. Moreover, nonlinear predictive control relying on online nonlinear optimization have the drawback of time consuming and numerical calculus issues. In this paper, an infinite gain scheduling neural predictive control is designed and applied to control the temperature in a distributed parabolic trough solar collector field. The performance of both tracking and disturbance rejection of the proposed controller is compared to those of four nonlinear predictive control variants: Two unconstrained neural predictive control using the Levenberg–Marquardt and the Broyden–Fletcher–Goldfarb–Shanno algorithms, and two constrained nonlinear predictive control using interior point algorithm, one is based on a neural network model and the other one is based on a first principal model. The superiority of the proposed control strategy is well demonstrated through simulation results.
Harmonic model predictive control (HMPC) is a model predictive control (MPC) formulation that displays several benefits over other MPC formulations, especially when using a small prediction horizon. These benefits, however, come at the expense of an optimization problem that is no longer the typical quadratic programming problem derived from most linear MPC formulations due to the inclusion of a particular class of second-order cone constraints. This article presents a method for efficiently dealing with these constraints in operator splitting methods, leading to a computation time for solving HMPC in line with state-of-the-art solvers for linear MPC. We show how to apply this result to the alternating direction method of the multipliers algorithm, presenting a solver that we compare against other solvers from the literature, including solvers for other linear MPC formulations. The results show that the proposed solver, and by extension the HMPC formulation, is suitable for its implementation in embedded systems.
This paper provides an overview of power electronics and its applications in various fields, emphasizing power conditioning and minimizing losses for high energy efficiency. It discusses the distinction between unidirectional and bidirectional converters and their applications in power systems. The significance of unidirectional and bidirectional power flow in different scenarios is explored. The importance of battery storage systems (BSSs) for grid stabilization, frequency regulation, and renewable energy integration is highlighted. The paper focuses on flexible active-reactive optimal power flow (A-R-OPF) frameworks in battery storage and power electronic systems, reviewing existing research, identifying gaps, and offering new perspectives. It addresses the challenges and potential of grid-scale energy storage for reliable and cost-effective power systems with high renewable energy penetration. The need for energy curtailment, demand response, and smart grid implementation is discussed. The paper emphasizes comprehensive coordination, new power lines, European collaboration, and smart grid implementation to meet the dynamic needs of Europe's power grids.
Model Predictive Control (MPC) is a popular control approach to ensure constraint satisfaction, while minimizing a cost function. Although MPC usually leads to very good results in terms of performance, its computational overhead is typically non-negligible, and its implementation for systems where the computing capacity is limited may be impossible. To address this issue, this technical note proposes a robust to early termination MPC. That is, the proposed scheme runs until available time for execution runs out, and the solution, while sub-optimal, is guaranteed to enforce the constraints and ensure recursive feasibility despite arbitrary early termination. Also, the closed-loop stability is maintained. Simulations are carried out on a F-16 aircraft to assess the effectiveness of the proposed scheme.
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