No full-text available
To read the full-text of this research,
you can request a copy directly from the author.
Sliding Modes in Control and Optimization
Abstract
One of the major obstacles in the use of efficient tools for designing control systems is the high order of equations that describe their behaviour. In many cases they may be reduced to a lower order model by neglecting small time constants or rejecting fast components of the system overall motion. Fast motions may, for instance, be caused by small impedances in equations of electromechanical energy converters [155], time constants of electric motors in systems controlling slow processes [68], nonrigidity of flying vehicles construction [74] and many other reasons. The design of control systems resting upon the use of low-order models may be carried out both by analytical and by various computational techniques. (Application of computational techniques to the design of control systems may be seriously hindered not only by their high dimension, but also by the fact that the computational problems in such systems are generally ill-posed and require ad-hoc methods to be developed).
... If we can respect the dynamics of the system to lie on a well behaved surface, then the control problem is greatly simplified. Sliding mode control SMC [56] is based on the design of an adequate "sliding surface" (or "sliding manifold") defined as, ...
... Therefore,σ(t)σ(t) < 0 for t > 0 and σ(t) → 0 as t → +∞. Moreover, according to Utkin [56] the sliding mode on the surface σ = 0 arises in a finite time, i.e. there exists t * > 0 such that σ(t) = s(t) − s * = 0 for t > t * (see Figure 5). ...
... are selected such that the identity σ(t) = 0 for t > t * implies s(t) → s * as t → +∞. Indeed, sinceσ(t) = −αs(t) + βb(t) then the control input b in the latter equation is not delayed with respect to the sliding variable σ, so the conventional sliding mode design scheme can be utilized [56]: (12) Similarly to the previous example we conclude that there exists t * > 0 such that σ(t) = 0 for t > t ⋆ and using equivalent control method we deriveσ(t) = −αs(t) + βb eq (t) = 0 with b eq (t) ∈ (0, 1) and ...
We consider the first closed-loop separation control experiment on an Ahmed body using a robust, model-based strategy called “sliding mode control” (SMC). The main objective of the control is to reduce and further maintain the aerodynamic drag of the square-back Ahmed body flow to an arbitrary value. The Reynolds number considered, based on the body height and free-stream velocity, is Reh=9×104. The wake flow is manipulated by a slotted jet placed on the top trailing edge, combined with a predefined angle direction. The flow modifications are sensed by a drag balance. Base pressure and lift measurements are also performed in real-time. The interactions between the air jet actuator and the mean near-wake flow are depicted by means of Particle Image Velocimetry. In order to evaluate the efficiency of the closed-loop strategy, periodic forcing is first investigated. Continuous blowing is initially used to directly influence the recirculation area and hence achieve a reduction in the drag. A maximum drag reduction of approximately 8% is accomplished with steady blowing. Because steady blowing leads to the highest energy consumption scheme, this strategy is only considered as a reference result. The second type of control involves periodic forcing at different frequencies. The influence of these frequencies on the near-wake and the overall drag is examined in details. Based on the open-loop results, a simplified single-input/single-output (SISO) model of the flow response is proposed and sliding mode control is applied to maintain the drag level at an arbitrarily fixed value. Finally, an experiment is conducted to show the ability of the controller to reject a disturbance, corroborating the robustness and efficiency of this control approach; the limitations of this control approach are also discussed. This kind of controller is found to be able to reduce and maintain remarkably the drag to a desired set-point regardless significant external flow perturbations, suggesting that it may be applicable in multiple experimental and industrial contexts.
... During the last three decades, variable structure systems (VSS) and sliding mode control (SMC) have received significant interest and have become well-established research areas with great potential for practical applications. The theoretical development aspects of SMC are well documented in many books and articles [7,16,20,25,27,29,31]. ...
... According to [20], x will be always kept on S. If we guarantee that the surface S is always zero then x will converge to zero in a finite time. ...
... the sliding condition[20], 2 e and 2 e & converge to zero in a finite time. After 2 e has converged to 0, the dynamical errors 1 e and 3 e can be written as: ...
In this paper, an integral finite-time sliding mode control scheme is presented for controlling a chaotic permanent magnet synchronous motor (PMSM). The controller can stabilize the system output tracking error to zero in a finite time. Using Lyapunov’s stability theory, the stability of the proposed scheme is verified. Numerical simulation results are presented to present the effectiveness of the proposed approach.
... Fixed-time stability is a stronger notion of finite-time stability [13][14][15][16], because in the latter the settling time is an unbounded function of the initial condition of the system. However, the application based on the upper estimate of the settling time provided in [1,3] poses a challenging design problem for real-time constrained scenarios. ...
... Proposition 48 Let (z, t) be given by (14) with h(z) a K 1 Tc function and (z) chosen as in Proposition 46 with a = T c . Therefore, ⌧ (t) = h(t t 0 ). ...
A methodology, based on timescale transformations and Lyapunov analysis, for designing autonomous and non-autonomous dynamical systems exhibiting the predefined-time stability property is provided in this paper. Thus, the current proposal allows characterizing a broad class of predefined-time stable systems, placing them under a common framework with existing methods which use time-varying gains based on time-base generators. What follows from this construction is that the bound of the convergence time for this class of systems is the lowest possible. Moreover, it is independent of the initial conditions and is set a priori through a tuning parameter. This design procedure is a relevant contribution when compared to traditional fixed-time convergent algorithms since the current convergence time bounds are conservative. Finally, we analyze several existing and novel algorithms for autonomous and non-autonomous systems showing the effectiveness of the method.
... By applying a nonlinear control, SMC alters the dynamics of a linear or nonlinear system and forces it to reach a prescribed sliding manifold in finitetime. Then the trajectory of the system will approach its equilibrium point along the sliding manifold asymptotically or in finite-time thereafter [1] . ...
... Motivated by the aforementioned facts, the main contributions of this paper can be described as (1) In the existing results, the unmatched uncertainties are required to be slowly time varying and have constant steady-state values, e.g. [25,26] , even vanishing over time, e.g. ...
To control MIMO systems with unmatched uncertainties, two sliding-mode controllers are presented in this paper. Firstly, a terminal sliding-mode controller is presented to force the output of an MIMO system to a region near zero in finite-time. With the analysis on the effect of the unmatched uncertainties, a full-order terminal sliding-mode control is further proposed to force the output of the MIMO system to converge to zero rather than a region. The virtual control is utilized to establish the reference for the part of the system states, which can reject unmatched uncertainties completely. To generate continuous virtual control signals, the proposed full-order terminal sliding-mode controller makes the ideal sliding motion as the full-order dynamics rather than the reduced-order dynamics in traditional sliding-mode control systems. Finally, the simulations on the control of an L-1011 fixed wing aircraft at cruise flight conditions validate the effectiveness of the proposed method.
... Pl'oper choice of sliding surface: (a) Choosing static sliding surfaces s = sex) which are determined by a set of geometric equations (DeCarlo et al. l 1988;Utkin, 1992); (b) Choosing sliding surfaces wbich are a set of differential equations (Slotine and Coetsee, 1986;Sira-Ramirez, 1993;Lu and Spurgeon, 1995), which are dynamic sliding surfaces. This is a bundle of geometric manifolds. ...
... The sliding reachability condition may produce a discontinuous control signal which is undesirable in pra.ctice. Further work has considered methods to reduce this chattering (Slotine and Coetsee, 1986;Utkin, 1992;Levant, 1993;Sira-Ramirez, 1993;Lu and Spurgeon, 1995). ...
A dynamic sliding mode controller design method is proposed for multiple input systems. The method uses a novel choice of sliding surface to effect asymptotic linearization of nonlinear differential input output systems. The stability of the overall system, i.e. a canonical state space form with a dynamic feedback, is analyzed. This method is shown to be able to control a fairly general class of systems which is not linearizable by dynamic feedback using chatter free control. The theoretical results are applied to Gas Jet Actuators with both one and two inputs. It is known to be not feedback linearizable when only one input is utilised.
... In the recent years, the technique of sliding mode control has been used successfully in the active protection of civil engineering structures in the presence of seismic excitation (LUG) et al., 1998aLUG) et al., , 1998b). In this paper, the principle ofslicling mode (Utkin, 1992) is extended to the centralized and decentralized model reference control in order to attenuate the transversal deflections of a cablestayed bridge caused by the vertical component of an unkno~"n earthquake. ...
... T'he equation of motion of the tracking error dynamic subsystem Sei in sliding lllode can be obtairled by using the so-called "technique of equivalent control" (Utkin, 1992) such that ...
In this paper, robust model reference sliding mode controllers are designed to reduce the magnitude of the transversal vibrations of a flexible cable-stayed bridge structure induced by a seismic excitation. The dynamic behaviour of the bridge is described by a mathematical model which takes into account the inherent nonlinearities due to the stay cable's geometry. A numerical simulation example is presented to illustrate the effectiveness of the proposed control schemes.
... The paper presents a new approach to the design of rigid-flexible structure systems, based on a sliding mode technique (Utkin V.I., 1992) and on the method of dynamic compensation 01.A. Utkin and V.1. Utkin, 1983). ...
... Let us constructed the observer as follows: Note that the equivalent u eq = -(CB}-l(AEI+ L 1 DLl.6+ L z G.6.q) control derived from the equation s = 0 (Utkin V.I., 1992) is substituted to the equation (16). By virtue of suitable choices of the matrix C and pair (L1,L z) independently dimension of the obsetver (16) causes to a drlIiculty of the design procedure. ...
The paper presents a new approach to the flexible structure systems synthesis on the base of using a method to dynamic compensation and a division of motion on rate within the framework of systems with large coefficients and discontinuous control, allowing to decompose a problem of large dimensionality to the independently solved a problems of smaller dimensionality (Drakunov at el. 1990).
... According to the SMC theory [15], the sliding surface, S(e,ė), is defined as ...
... Substituting parameter learning rules (Eqs.) (12), (13), (15), (16), andȦ 1i ,Ḃ 2 j mentioned above into Eq. (28), thuṡ ...
... Théorie du mode glissant : principe de la commande Le principe consiste à générer une entrée de commande permettant de restreindre les trajectoires du système pour atteindre, en un temps ni, une surface glissante et y rester comme le montre la Figure 3.25 [Utkin, 1992, Shtessel et al., 2014. La surface de glissement S est dénie avec un degré relatif, par rapport à l'entrée u, égale à un. ...
Les travaux de cette thèse visent à garantir un guidage sûr en présence de certaines situations critiques de conduite telles qu'une perte de stabilité latérale du véhicule ou une défaillance d’actionneurs (système de direction, de freinage, etc.). Pour ce faire, des architectures hiérarchisées de contrôle global du châssis tolérantes aux défauts sont proposées. D’abord, la stabilisation latérale est traitée à travers une architecture de commande permettant de coordonner les correcteurs de manœuvrabilité et de stabilité. La coordination est faite par un superviseur proposé basé sur un pseudo plan de phase combinant des critères de stabilité latérale. Ensuite, le guidage en situation normale/urgence en présence d'une défaillance du système de direction est abordé en proposant une architecture de commande permettant de remplacer l'action du braquage par un freinage différentiel. Les différents niveaux composant cette architecture, allant de la génération des références à l’allocation de commande en passant par la synthèse du correcteur de guidage longitudinal-latéral, sont développés et adaptés afin de prendre en compte la situation d'urgence. Enfin, l'architecture globale est traitée afin de coordonner les objectifs de commande, à savoir la stabilisation et le guidage du véhicule. La coordination se fait au niveau d’une allocation de commande tolérante aux défauts actionneurs (FTCA) basée sur optimisation. Cette dernière permet prioriser les objectifs de commande et de minimiser l’action de commande selon la situation de conduite. La formulation de la FTCA est généralisée afin de tenir compte de plusieurs types de défauts actionneurs et de configurations de véhicules.
... SMC is known for the complete rejection of matched external disturbances entering the system and matched uncertainties that are present in the system [5]- [7]. In SMC, a discontinuous high-frequency switching control is used to neutralize the effect of the uncertainties and disturbances entering the system [6]. ...
In this paper, a third-order sliding mode control (SMC) with a super-twisting finite time observer is proposed for the position control of a Stewart platform. The Stewart platform is a parallel robotic manipulator with a fixed base platform connected to a movable top platform with the help of six actuator legs. The proposed control makes the movable platform track a reference trajectory in finite time while rejecting matched disturbances. Conventional SMC offers robustness towards matched disturbances, but will induce chattering in the system. The proposed third-order SMC can ease out the chattering problem and achieve finite-time tracking. Furthermore, a robust super-twisting observer is designed, which converges to the actual states in finite time, such that the proposed control can be computed from the system output using the observer. A simulation study of the Stewart platform is done for the proposed robust continuous finite-time control with the finite-time observer. The results using the proposed control are compared with conventional SMC, PID control and twisting control.
... For the first-order sliding modes, it is common to deal with the issues of stability, robustness, and convergence rate of the equilibrium by means of a Lyapunov approach [20]. For higher sliding mode and finite-time observers, the proof of stability is usually done using geometric homogeneity-based methods. ...
... Remark 3. It is well-known from the SMC literature [31] that due to the presence of the multidimensional sign function S a / S a , the practical implementation of the control law (32) (e.g., subject to actuator delays) will show a chattering behavior. There are many standard mechanisms to reduce this chattering; the simpler one is just to replace S a / S a by its sigmoid approximation ...
This paper is concerned with the robust flight control of multirotor aerial vehicles (MAVs) subject to bounded force and torque disturbances. The focus is on the entire class of MAVs containing an arbitrary even number (≥ 4) of fixed (not 4 vectoring) rotors. To deal with this problem, firstly, a ubiquitous hierarchical control architecture in which the attitude control loop is nested inside the position control loop is adopted and augmented with a control allocator which makes the design of the control laws themselves independent of the rotor arrangement. Especially, the control allocation problem is formulated as a quadratic program that minimizes the thrust commands and accounts for the thrust range and rate bounds. Secondly, geometric attitude and position control laws are designed separately using a multi-input fast nonsingular terminal sliding mode control (FNTSMC) strategy, which guarantees singularity-free finite-time stability and robustness. The main contributions are: 1) the augmentation of the hierarchical control scheme for extending its applicability to any fixed-rotor MAV; and 2) detailed geometric design and finite-time stability analysis of the position and attitude control loops using the FNTSMC theory. The system is evaluated on computational simulations as well as on a hardware-in-the-loop experiment, showing that it is effective, simple to implement and adjust, and reliable to operate in nonlinear regimes as well as under bounded disturbances.
... In [16], the control technique was suggested for controlling the nonlinear characteristics of the SVC in the transmission line. In [17][18][19], SMCs were proposed; resulting good performance for controlling the system uncertainties and external disturbances. In [20][21][22], the advantage and supremacy of the SMC method have been examined in terms of the dynamic behavior of the system and the closed-loop response. ...
... Owing to the particular importance in modelbased fault detection and diagnosis [97][98][99], the observer design for state estimation of uncertain nonlinear systems has been a popular field of research over the past few decades. Sliding mode control has been an effective approach in dealing with disturbances and modeling uncertainties through the concepts of sliding surface design and equivalent control [100]. On the basis of the same concept, sliding mode observers (SMO) have been developed to robustly estimate the system states [101,102]. ...
This proposed research is aimed to develop a novel modeling and control algorithm for the PDE described systems. When dealing with time-dependent PDE problems, the partial derivatives of a function over spatial variables are obtained by approximating the function values at interpolation nodes and their corresponding neighbors as a finite summation of polynomial series. A cluster of interpolation nodes guarantees the boundedness of the residual derivatives. Substituting these approximations in the PDE and discretizing the spatial domain of variables while keeping the time domain continuous yields a system of ODEs. By using an eigenvalue-based technique, a reduced-order model is derived, which is incorporated with unmodeled dynamics described as bounded-input, bounded-output (BIBO) stable. To establish the equivalence with original PDE, the reduced-order ODE is augmented with nonlinear time-varying uncertainties and unmodeled dynamics. The final goal is to design an L1 adaptive controller for handling of model mismatch and delivering a good tracking performance.
... Hence, state estimation is used to access state information for feedback control. Common methods include, for example, the ubiqui- tous Kalman Filter (KF) and various extensions [16], [17], [18], particle filters [19], [20], sliding mode observers [21], [22] and neural networks [23]. ...
This paper shows how a standard proportional-integral-plus controller, based on a non-minimal state space (NMSS) design, can be extended to reduce the effects of measurement noise and so yield smoother control inputs for automated drug delivery control applications. Use of a NMSS model for state variable feedback control design, in which all the states are based on the directly measured input and output variables, removes the need for state estimation. Nonetheless, a stochastic NMSS form, with a Kalman filter, can optionally be introduced to reduce the effect of measurement noise and so yield smoother control inputs. In this case, the Kalman filter attenuates measurement noise but does not address state disturbances. In this article, we propose a modification to the stochastic NMSS control system to enable the elimination of such state disturbances. This involves further extending the non--minimal state vector to include additional terms based on the innovations. We compare the deterministic, stochastic and extended stochastic NMSS controllers via a simulation of the control of anaesthesia using propofol.
... Consequently, there exists a time T such that e 1 (t) = e 2 (t) = 0, ∀t ≥ T and equation (18b) may further be processed in order to obtain an estimate for the uncertainty ∆. Following the equivalent control methodology as discussed in Utkin (1992), the estimated uncertainty∆ is gained via a first order low pass filter ...
In this paper a novel approach for observer-based suspension control is presented. The control concept consists of two parts: An unknown-input state observer estimating both unknown forces acting upon the suspension system and a model-based control algorithm. The major advantage of the proposed concept is that it does not require the knowledge of uncertain wheel parameters. The observer relies on ideas of sliding mode control whereas the control algorithm pursues the goal of adjusting a desired suspension damping with the help of disturbance feedforward. The performance of the concept is demonstrated in numerical simulation and experiment.
... The control algorithms, for consensus and the synchronization, need to be robust because, in practice, these systems operate under the action of disturbances. In the existing literature, a number of approaches, based on sliding mode theory [20], are developed for the robustness performance of uncertain nonlinear systems [1,7]. Note that sliding-mode-based techniques were used for the consensus and synchronization control of multi-agent systems [10,12,23]. ...
This paper proposes a consensus tracking control for a class of second-order multi-agent nonlinear systems and generalizes the concept of integral sliding mode for networked systems. This design relies upon an integral manifold which is defined as a function of the consensus error variables. The designed integral manifold helps in the establishment of sliding mode without reaching phase. Consequently, the robustness against uncertainties is guaranteed from the very start. The continuous control components, of the control laws, governs the dynamics of the nonlinear system in sliding mode and the discontinuous terms handle the disturbances. The stability analysis is given to show the sliding mode establishment and an example is considered to demonstrate the benefits of the proposed strategy.
... For hydraulic systems of the excavator, force measurements from load pins are employed in our application to provide estimate of the disturbance force F . The Utkin observer [10] for (6) is described by The schematic diagram of the proposed observer is shown in Figure 2. In order to reduce chattering associated with the sliding motion of the output error, the signum function 6 = p sgn(e y) in (9) is replaced by a sigmoidal one resulted from a fuzzy reasoning technique presented in [11]: Q = p tanh(e y l y,) , (12) where y, is some positive constant. ...
... For a linear system operating under uncertainty conditions, the control enforces sliding motion governed by a linear equation. The control of the system should be independent of perturbations [7]- [8]. ...
... Sliding mode control aims to force the state of t he controlled system to reach a manifold given in its statespace and after, to slide along this manifold towards the desired equilibrium st.te (Utkin, 1977;Utkin, 1992;Slotine and Li, 1991). The sliding manifold is defined by the equation s ~ 0 where s is a function of the state variables. ...
Sliding mode control is applied to the control of point-to-point displacements of servomechanisms with elastic joints. The control law requires only values of positions and velocities of both sides of the elastic joint, and includes a boundary layer in order to avoid chattering. Possible steady state errors are cancelled via a disturbance observer. Simulation analysis shows the robustness of this control system.
... To derive the reduced-order motion equation, control should be substituted by the so-called "equivalent control". Its estimation can be used in the control law, which has to involve the "robust term" for driving system states toward the sliding manifold (Utkin, 1992). ...
A new position control algorithm for a belt-driven servomechanism of a lasercutting machine is described. The high-accuracy motion control procedure for the system with inherent elasticity caused by the low-cost belt-drives was derived using Variable System Structure (VSS) control theory and Lyapunov design. The control design yields the continuos sliding mode control law. It possesses all the good properties of the robust sliding mode and avoids the unnecessary discontinuity of the control input, thus eliminating chattering. The proposed robust control algorithm was used in an industrial application of a motion controller for a CNC laser-cutting machine. Experimental results are reported.
... denotes t.he so-called Lipschitz constant of O'.(x.). The equivalent control method (Utkin , 1992) is used to det.ermine the slow reduced syst.em motion restricted to the slow switching surface 0' .. (%,) = 0 , ohtaining the so-called slow equivalent control ...
A control-observer structure for a class of nonlinear singularly perturbed systems is presented. The structure is based on a two-time scale sliding-mode control and an output injection observer. Also, an stability analysis is carried out to study the stability properties of the resultant closed-loop system using the stability characteristics of the observer and the closed-loopsystem without observer.
... The interpretation of hybrid systems as variable structure systems (Utkin, 1992) comes straightforwardly (Drakunov, 1994;Dogruel et al., 1996;Puri and Varaiya, 1995), due to the fact that a widely accepted model for hybrid systems is based on multiple models switching (Branicky et al., 1994). In this view, a universal framework is that of differential inclusions. ...
The term hybrid systems designates those physical processes that exhibit both continuous and discrete aspects. On the other hand, some fully continuous systems can benefit from the introduction of an inherently event-based system such as an intelligent supervisor thus becoming hybrid themselves. In the present paper, the focus is on this last class of system. More precisely, a new control approach for continuous time systems with unknown high frequency gain sign is presented relying on a logic-driven sliding mode control. Such an approach is compared with a consolidated one based on the so-called Nussbaum function.
... VSC features a non-linear feedback with a discontinuity on one or more switching surfaces in order to drive the plant's state trajectory to this surface and maintain it there. VSC can force the system to act as a reduced ordered system while on the sliding (or switching ) surface and achieve stability and regulation over a wide range of transmission conditions (DeCarlo, 1988, 1994, Dorling and Zinober, 1990, Utkin, 1992. ...
This paper presents a case study of a static VAR system (SVS) installed for voltage control and power oscillation damping. The SVS provides voltage support of a long transmission line and is equipped with power oscillation damping equipment. The power system is modelled as a single-machine infinite-bus system with an automatic voltage regulator in the generator representation. The current control scheme of the SVS is modelled in EMTP and compared with a variable structure control (VSC) system.
... The continuous-time variable structure (VS) controller is known robust to parameter uncertainty and external disturbance because of the sliding motion on a predefined hyperplane (Utkin, 1964)(DeCarlo et al., 1988) (Zinober, 1990) (Utkin~ 1992) (Hung et al., 1993). The control law has employed a nonlinear feedback varying the system structure by switcbing~ This switching frequency is theoretically infinite. ...
For any control systems, it is shown that in the state space there exists a subset around a hyperplane, inside which a norm of the state decreases without any control action. Therefore it is possible to use this natural feature of control systems to design a VS controller. In this paper, such subset is named the sliding sector. An algorithm to design the sliding sector using Riccati equation is given for controllable systems. A variable structure (VS) controller with the sliding sector for continuous-time system is proposed. With the VS control law designed in the paper, the state will move to the inside of the sliding sector and the norm of the state, i.e. some Lyapunov function decreases in all of the state space. Therefore the VS controller with the sliding sector quadratically stabilizes the system. A rotational pendulum system is used as a simulation model. The simulation results show that the proposed VS controller is chattering-free and with good control performance.
In this chapter, a new approach to achieve output synchronization for uncertain complex networks with non-identical nodes using neural sliding-mode pinning control is introduced. The control scheme is composed by an on-line identifier based on a recurrent high-order neural network, and a sliding-mode controller, where the former is used to build an on-line model for the unknown dynamics, and the latter to force the unknown node dynamics to achieve output synchronization.
In this chapter, a new approach for trajectory tracking of uncertain complex networks with identical and non-identical nodes is introduced. To achieve this goal, a neural controller is applied to a small fraction of nodes (pinned ones). Such a controller is composed of an on-line identifier based on a recurrent high-order neural network, and an inverse optimal controller to track the desired trajectory. A complete stability analysis is also presented. In order to verify the applicability and good performance of the control scheme, representative examples are simulated, which consist of a complex network with each node described by a chaotic Lorenz oscillator, and a network with different chaotic nodes.
A sliding-mode controller for an automotive selective catalytic reduction system is designed to drive its ammonia surface coverage ratio to the target level. The proposed controller only requires NOx, temperature and air flow sensor measurement installed on most mass production vehicles. Selective catalytic reduction systems have been widely equipped on diesel-powered ground vehicles to remove excessive NOx emissions. The tradeoff between NOx removal efficiency and ammonia slip poses a control challenge on regulating the ammonia surface coverage ratio to a proper level in the presence of disturbance. In this study, a sliding-mode controller is designed with explicit consideration of measurement noise and actuator saturation. The finite time convergence of tracking error is proved by a Lyapunov approach. For implementation purpose, an observer of ammonia surface coverage ratio and ammonia slip is also designed to provide states feedback and fault diagnostic information. The closed-loop controller performance is evaluated under an urban driving scenario based on an experimentally validated model. Results demonstrate the robust tracking performance and estimation accuracy against bounded uncertainties. The overall NOx efficiency is maintained with an acceptable ammonia slip level during the transient test cycle FTP75.
The aim of this paper is to design a robust control for stabilization of a class of nonlinear perturbed system subject to matched and unmatched disturbances. Here, the concept of dynamic sliding mode control and the attractive ellipsoid method advantages are used to design a robust nonlinear control algorithm, which reduces considerably the perturbation effects. Hence, in finite time, the dynamic sliding mode control brings the system trajectory to a specific configuration. After this time, the controller reduces the perturbation effects by using the high‐gain control obtained in the attractive ellipsoid method. Thus, based on the solution of a specific matrix inequality, the feedback control of the system guarantees that the trajectory will be stabilized in the ultimate uniform bounded sense. To illustrate the theoretical results, a numerical example with a comparative study is introduced. Finally, the performance of the controller designed in this paper is tested on an electromechanical real‐time system.
This paper investigates the event-triggered sliding mode control problem for discrete-time Markov jump systems under the unavailable states and partially unknown transition probabilities. To save the limited computational source, an event-triggered scheme is implemented to determine whether the current data should be sent or not, and an observer is constructed to estimate the unmeasurable states of the system. Then, on the basis of the Lyapunov functional technique, the sufficient conditions of stochastic stability for the closed-loop system are derived. Moreover, the sliding mode controller based on event-triggered mechanism is designed to ensure that the state trajectories of the closed-loop system can be driven onto the predefined sliding manifold and maintain there for all subsequent time. Finally, a numerical example is utilized to demonstrate the effectiveness of the proposed method.
A novel speed-flux tracking controller for induction motors has been developed and experimentally verified. Direct rotor flux field oriented controller is designed for current-fed induction motor model on the base of full-order hybrid continuous time-sliding mode flux observer. Controller guarantees local asymptotic speed-flux tracking and asymptotic direct field-orientation under condition of unknown constant load torque. The flux subsystem is invariant with respect to limited rotor resistance variations due to special structure of the flux observer. The efficiency of the proposed solution is confirmed by the results of experimental studies, which demonstrate the improved robustness properties in all motor operating conditions including nearby zero speeds.
This paper develops a novel adaptive neural integral sliding‐mode control to enhance the tracking performance of fully actuated uncertain surface vessels. The proposed method is built based on an integrating between the benefits of the approximation capability of neural network (NN) and the high robustness and precision of the integral sliding‐mode control (ISMC). In this paper, the design of NN, which is used to approximate the unknown dynamics, is simplified such that just only one simple adaptive rule is needed. The ISMC, which can eliminate the reaching phase and offer higher tracking performance compared to the conventional sliding‐mode control, is designed such that the system robust against the approximation error and stabilize the whole system. The design procedure of the proposed controller is constructed according to the backstepping control technique so that the stability of the closed‐loop system is guaranteed based on Lyapunov criteria. The proposed method is then tested on a simulated vessel system using computer simulation and compared with other state‐of‐the‐art methods. The comparison results demonstrate the superior performance of the proposed approach.
This paper develops the sliding mode control (SMC) design for N‐coupled reaction‐diffusion parabolic PDEs with boundary input disturbances. In order to reject the disturbances, the backstepping‐based boundary SMC law is constructed to steer the system trajectory to a suitable sliding surface and then maintain sliding motion on the surface thereafter, resulting in the exponential convergence to the zero equilibrium state. The well‐posedness of the closed‐loop system is established based on a detailed spectral analysis and Riesz basis generation. Finally, a simulation example is provided to illustrate the effectiveness of the SMC design.
This paper presents sufficient conditions to ensure the exponential stability of uncertain switched time‐delay systems with time‐delayed state‐dependent switching conditions, which can model high speed supercavitation vehicles (HSSVs). Based on the intrinsic properties of HSSVs, cavity can be represented by a relation between the states and time‐delayed states of the system. Moreover, a sliding behavior can be occurred at the cavity boundary in HSSVs. Therefore, the main contribution of this paper is to develop a set of LMI stability conditions in the presence of time‐delayed states in the linear state‐dependent switching signal and absorbing sliding modes in the state space, simultaneously. In addition, because of the possible existing uncertainties in HSSVs, another set of LMI‐based sufficient conditions is derived in order to analyze the stability of switched time‐delay systems with additive norm bounded uncertainties. The application of the proposed theorems are also validated through numerical examples. Finally, the stability of a two‐degrees‐of‐freedom longitudinal description of an HSSV is shown using the proposed stability theorems.
Unmanned Aerial Vehicles (UAVs) offer a wide range of interesting military and commercial applications at reduced costs. A couple of their more interesting characteristics include: They are capable of hovering and flying at high and low speeds, and they can move in any direction and take off and land vertically. A very promising class of these vehicles comprises small vehicles that can be flown either indoor or outdoor and offer the possibility for near-area surveillance, crop dusting, precision farming [1], microwave autonomous copter systems for geological remote sensing as shown in [2], geographic studies, fire monitoring, security applications, search- and-rescue, and attack and rendezvous [3], [4]. However, challenging requirements in terms of size, weight, and maneuverability for these systems are presented in [5]. A type of aircraft with an important and significant potential is the so-called Quadrotor that is considered by most research studies as a promising UAV [6].
In this paper, the adaptive fault compensation problem is investigated for high-speed trains in the presence of time-varying system parameters, disturbances and actuator failures. To deal with the time-varying system parameters, a new time-varying indicator function instead of commonly used 0-1 function, is proposed to model the train dynamics as a piecewise model with unparameterizable time-varying disturbances, which can cover more time variations and help parametrization for adaptation. A backstepping adaptive controller is designed for the healthy system with unknown piecewise model parameters and known piecewise bounds on disturbances. For both the parameterizable and unparameterizable failures, the backstepping adaptive failure compensation with the adaptive laws are derived to achieve the position tracking under the known bound disturbances. The adaptive failure compensation for unknown bounds on disturbances is also discussed under the parameterizable failure. Through introducing the nonlinear damping in the proposed controller, the failure compensation controller is proposed for the model with unparameterizable system parameters to achieve an arbitrary degree of position tracking accuracy. The stability of the corresponding closed-loop system and asymptotic state tracking are proved via Lyapunov direct method, and validated using a high-speed train model.
Numerous types of hybridizations between type 2 fuzzy logic system (T2FLS) and sliding mode control (SMC) have been proposed to construct an intelligent and robust controller that departs from the drawbacks of SMC and T2FLS. Recently, these hybridizations have been extended to the hybrid structures that are composed of type 2 fuzzy neural network (T2FNN) and SMC in order to produce adaptive, intelligent and robust controllers. Moreover, optimization algorithms are integrated with these controllers in order to tune/optimize their parameters for a superior control performance. In this paper, a survey of the advances on the hybridization of T2FLS, T2FNN, SMC and computational intelligence algorithms is presented. It has been observed that all the works involving T2FLS employed interval type 2 fuzzy logic systems. Despite the advantages of general type 2 fuzzy logic systems (GT2FLS), no record of applying GT2FLSs has been encountered in this domain. The trend of publications, the limitations associated with previous works and future research directions are outlined in the paper. Expert researchers can use this survey as a benchmark for proposing novel approaches while novice researchers (especially graduate students) can use this survey as a starting point.
ResearchGate has not been able to resolve any references for this publication.