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L1 Adaptive Control for Single-Input Multiple-Output (SIMO) Non-Homogeneous System with MR Damper Semi-Active Suspension
Abstract
This paper proposes a control method of the magnetorheological (MR) damper semi-active suspension controlling system with an L1 adaptive controller. The suspension system can be represented as a non-homogeneous system. Therefore, the proposed controller design method is introduced for avoiding the solving process of the convolution of a transfer matrix in the non-homogeneous system and guaranteeing the performance of the system within an acceptable level. The result, which is simulated by MATLAB/SIMULINK, proves that the proposed control architecture can work well for reducing calculation process. Moreover, this method is compared with the auto-tuned PID function in SIMULINK; as a result, the method shows a better overall performance by adjusting a few parameters.
Semi-active control devices have received significant attention in recent years because they offer the adaptability of active control devices without requiring the associated large power sourc- es. Magnetorheological (MR) dampers are semi-active control devices that use MR fluids to pro- duce controllable dampers. They potentially offer highly reliable operation and can be viewed as fail-safe in that they become passive dampers should the control hardware malfunction. To devel- op control algorithms that take maximum advantage of the unique features of the MR damper, models must be developed that can adequately characterize the damper's intrinsic nonlinear be- havior. Following a review of several idealized mechanical models for controllable fluid dampers, a new model is proposed that can effectively portray the behavior of a typical magnetorheological damper. Comparison with experimental results for a prototype damper indicates that the model is accurate over a wide range of operating conditions and is adequate for control design and analy- sis.
In this work, we study the implementation of magnetorheological fluid (MRF) to the semi-active suspension. Owing to the nonlinear hysteretic phenomenon, the analysis and synthesis of a controller is not trivial. The kinematic energy and spring potential function of the suspension system plus an integral term of the hysteretic component of an MR damper is chosen as the Lyaupnov function to verify the stability and dissipativity of the system. Then a multi-level controller, which is constructed in virtue of stability analysis, turns out to be effective in vibration suppression. In addition, the controller algorithm is simple and easy to implement, requires only the measurements of relative displacement and velocity between sprung and unsprung masses, and the damping force of the MR damper.
This article presents the development of L<sub>1</sub> adaptive-control theory and its application to safety critical flight control system (FCS) development. Several architectures of the theory and benchmark examples are analyzed. The key feature of L<sub>1</sub> adaptive-control architectures is the decoupling of estimation and control, which enables the use of arbitrarily fast estimation rates without sacrificing robustness. Rohrs's example and the two-cart system are used as benchmark problems for illustration. NASA's flight tests on subscale commercial jet verify the theoretical claims in a set of safety-critical test flights.
In this research, we study on improving the ride comfort of vehicle for semi-active suspension model with MR damper including its hysteresis behavior which causes complexity for calculating process. There are two main objectives that are concerned in this research. One is that the controller must be able to have fast response and guarantee robustness. The latter is that the control scheme must be able to reduce the process time while the performance is not greatly dropped. Therefore, the suitable approach for these objectives is L 1 adaptive control with Linear Time Invariant (LTI) Controller which will be applied in the control system. MATLAB is used for simulating the control system, and the performance is compared with the PID control system. The result shows that the L 1 control method meets all this research purposes.
This book gives a comprehensive overview of the recently developed ℒ1 adaptive control theory with detailed proofs of the fundamental results. The key feature of ℒ1 adaptive control architectures is the guaranteed robustness in the presence of fast adaptation. This is possible to achieve by appropriate formulation of the control objective with the understanding that the uncertainties in any feedback loop can be compensated for only within the bandwidth of the control channel. By explicitly building the robustness specification into the problem formulation, it is possible to decouple adaptation from robustness via continuous feedback and to increase the speed of adaptation, subject only to hardware limitations. With ℒ1 adaptive control architectures, fast adaptation appears to be beneficial both for performance and robustness, while the trade-off between the two is resolved via the selection of the underlying filtering structure. The latter can be addressed via conventional methods from classical and robust control. Moreover, the performance bounds of ℒ1 adaptive control architectures can be analyzed to determine the extent of the modeling of the system that is required for the given set of hardware.
The book is organized into six chapters and has an appendix that summarizes the main mathematical results, used to develop the proofs.
Chapter 1 starts with a brief historical overview of adaptive control theory. It proceeds with an introduction to the main ideas of the ℒ1 adaptive controller. Two equivalent architectures of model reference adaptive controllers (MRAC) are considered next, and the challenges of tuning these schemes are discussed. The chapter proceeds with analysis of a stable scalar system with constant disturbance and introduces the main idea of the ℒ1 adaptive controller. Two key features are analyzed in detail: the closed-loop system's guaranteed phase margin and the uniform bound for its control signal.
Chapter 2 presents the ℒ1 adaptive controller for systems in the presence of matched uncertainties. It starts from linear systems with constant unknown parameters and develops the proofs of stability and the performance bounds. The results in this section prove that the ℒ1 adaptive controller leads to guaranteed, uniform, and decoupled performance bounds for both the system's input and output signals. First, it is proved that with fast adaptation the state and the control signal of the closed-loop nonlinearℒ1 adaptive system follow the same signals of a reference linear time-invariant (LTI) system for all t ≥ 0. As compared to the original reference system of MRAC, which assumes perfect cancelation of uncertainties, the reference LTI system in ℒ1 adaptive control theory assumes only partial cancelation of uncertainties, namely, those that are within the bandwidth of the control channel. Despite this, and because it is an LTI system, its response scales uniformly with changes in the initial conditions, reference inputs, and uncertain parameters.
This paper presents the L1 adaptive controller for a class of uncertain nonlinear systems in the presence of time and state dependent unknown nonlinearities with unmodeled nonlinear dynamics. The L1 controller achieves performance specifications, defined via a time-varying reference system. We prove that subject to standard regularity assumptions, the L1 adaptive controller ensures uniformly bounded transient and steady-state tracking for system's input and output signals simultaneously. The performance bounds can be systematically improved by increasing the rate of adaptation. Simulations of a nonlinear system, coupled to a Lorenz attractor, verify the theoretical findings.
Semi-active H∞ control of vehicle suspension with magneto-rheological (MR) damper is studied in this paper. First, an experiment is conducted on an MR damper prototype subjected to cyclic excitation. Then, a polynomial model is adopted to characterize the dynamic response of the MR damper. Such a model has an advantage that it can represent the inverse dynamics of the MR damper analytically, so that the desired output in the open-loop control scheme can be realized easily. Finally, a static output feedback H∞ controller which utilizes the measurable suspension deflection and sprung mass velocity as feedback signals for active vehicle suspension is designed. The active control force is realized with the MR damper using the obtained polynomial model. A quarter-car suspension model is considered in this paper for analysis and simulation. The proposed scheme is further validated by numerical simulation under random excitation. Simulation results showed that the designed static output feedback H∞ controller realized by the MR damper can achieve good active suspension performance.
This book attempts to find a middle ground by balancing engineering principles and equations of use to every automotive engineer with practical explanations of the mechanics involved, so that those without a formal engineering degree can still comprehend and use most of the principles discussed. Either as an introductory text or a practical professional overview, this book is an ideal reference.
This paper is aimed to develop semi-active control for automotive suspension systems with magneto-rheological (MR) fluid dampers. A two degree-of-freedom quarter car model is considered. A mathematical model of MR fluid damper is adopted. In this study, there are two nested controllers including system controller and damper controller. For the system controller, a model-reference sliding mode controller is developed for considering loading uncertainty to result in a robust control system. In order to choose a good reference model, the single-degree-of-freedom skyhook system is analysed. For the damper controller, the continuous-state control is used to track the actual damping force to the desired damping force. The transmissibilities of the MR suspension system are investigated. The performances of the MR suspension systems are evaluated by computer simulation with bump and random excitations. The effectiveness of the MR suspension system is also demonstrated via hardware-in-the-loop simulation (HILS) with sinusoidal excitation.
This book explores three areas: development of the mathematical skills of matrices, linear algebra, eigenvalue theory, and Cayley-Hamilton theory; definitions of state, how to describe dynamic systems in state variable format, the intrinsic properties of these systems - i.e., controllability, observability, and stability; and applications of state-variable methods, and introductions to some related advance topics including minimal realizations, control using state or output feedback, pole placement, observers, decoupling, system identification, and optimization.
Suspension systems are one of the most critical components of transportation vehicles. They are designed to provide comfort to the passengers, to protect the chassis and the freight. Suspension systems are normally provided with dampers that mitigate these harmful and uncomfortable vibrations. In this paper, we explore two control methodologies (in time and frequency domain) used to design semiactive controllers for suspension systems that make use of magnetorheological dampers. These dampers are known because of their nonlinear dynamics which requires the use of nonlinear control methodologies for an appropriate performance. The first methodology is based on the backstepping technique which is applied with adaptation terms and H-inf constraints. The other methodology to be studied is the Quantitative Feedback Theory (QFT). Despite QFT is intended for linear systems, it can still be applied to nonlinear systems. This can be achieved by representing the nonlinear dynamics as a linear system with uncertainties that approximately represents the true behavior of the plant to be controlled. The semiactive controllers are simulated in MATLAB/Simulink for performance evaluation.
From April 1991 he was the Assistant Professor of the same department. From April 1996 he was the Associate Professor of Department of System Design Engineering, Keio University. Currently he is working as Professor at the same department
- Ieice Iee
Hiromitsu OHMORI (Member)
He received Bachelor of Electrical Engineering, Master of Electrical Engineering and Ph.D from Keio University, Japan in 1983, 1985 and 1988, respectively. From
April 1988 he was the instructor of Department of Electrical Engineering, Keio University, Japan. From April
1991 he was the Assistant Professor of the same department. From April 1996 he was the Associate Professor of
Department of System Design Engineering, Keio University. Currently he
is working as Professor at the same department. His research interests are
in the field of adaptive control, robust control, nonlinear control and their
applications. He is member of IEEE, ISCIE, IEE, IEICE, and EICA etc.