Parallel Distributed Compensation Scheme Research Articles

Static Output Feedback Control for Electrohydraulic Active Suspensions via T–S Fuzzy Model Approach

The paper presents a fuzzy static output feedback controller design approach for vehicle electrohydraulic active suspensions based on Takagi–Sugeno (T–S) fuzzy modeling technique. The T–S fuzzy model is first applied to represent the nonlinear dynamics of an electrohydraulic suspension. Then, the fuzzy static output feedback controller is designed for the obtained T–S fuzzy model to optimize the H∞ performance of ride comfort through the parallel distributed compensation scheme. The sufficient conditions for the existence of such a controller are derived in terms of linear matrix inequalities (LMIs) with an equality constraint. A computational algorithm is presented to convert the equality constraint into a LMI so that the controller gains can be obtained by solving a minimization problem with LMI constraints. To validate the effectiveness of the proposed approach, two kinds of static output feedback controllers, which use suspension deflection and sprung mass velocity, and suspension deflection only, respectively, as feedback signals, are designed. It is confirmed by the simulations that the designed controllers can achieve good suspension performance similar to that of the active suspension with optimal skyhook damper.

Stability and Stabilization of Delayed T--S Fuzzy Systems: A Delay Partitioning Approach

This paper proposes a new approach, namely, the delay partitioning approach, to solving the problems of stability analysis and stabilization for continuous time-delay Takagi-Sugeno fuzzy systems. Based on the idea of delay fractioning, a new method is proposed for the delay-dependent stability analysis of fuzzy time-delay systems. Due to the instrumental idea of delay partitioning, the proposed stability condition is much less conservative than most of the existing results. The conservatism reduction becomes more obvious with the partitioning getting thinner. Based on this, the problem of stabilization via the so-called parallel distributed compensation scheme is also solved. Both the stability and stabilization results are further extended to time-delay fuzzy systems with time-varying parameter uncertainties. All the results are formulated in the form of linear matrix inequalities (LMIs), which can be readily solved via standard numerical software. The advantage of the results proposed in this paper lies in their reduced conservatism, as shown via detailed illustrative examples. The idea of delay partitioning is well demonstrated to be efficient for conservatism reduction and could be extended to solving other problems related to fuzzy delay systems.

H ∞ control of non-linear dynamic systems: a new fuzzy delay partitioning approach

The problem of robust H infin control for Takagi-Sugeno (T-S) fuzzy systems with norm-bounded parameter uncertainties and a time delay in the state is investigated. Attention is focused on the design of robust H infin controllers via the parallel distributed compensation scheme such that the closed-loop fuzzy time-delay system is asymptotically stable and the H infin disturbance attenuation is below a prescribed level. By utilising the instrumental idea of delay partitioning, a new Lyapunov-Krasovskii functional is introduced, and some novel ideas for achieving delay dependence and basis dependence have been employed, which guarantee the obtained conditions to be much less conservative than most existing results in the literature. These conditions are formulated in the form of linear matrix inequalities (LMIs), based on which, the controller design is cast into a convex optimisation problem subject to LMI constraints. Finally, two examples are illustrated to show the feasibility and effectiveness of the obtained results.

$H_{\infty}$ Controller Synthesis via Switched PDC Scheme for Discrete-Time T--S Fuzzy Systems

This paper is concerned with the problem of designing switched state feedback <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> controllers for discrete-time Takagi-Sugeno (T-S) fuzzy systems. New types of state feedback controllers, namely, switched parallel distributed compensation (PDC) controllers, are proposed, which are switched based on the values of membership functions. Switched quadratic Lyapunov functions are exploited to derive a new method for designing switched PDC controllers to guarantee the stability and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> performances of closed-loop nonlinear systems. The design conditions are given in terms of solvability of a set of linear matrix inequalities. It is shown that the new method provides better or at least the same results of the existing design methods via the pure PDC scheme with a quadratic Lyapunov function or switched constant controller gain scheme. Numerical examples are given to illustrate the effectiveness of the proposed method.

A New Approach to Guaranteed Cost Control of T-S Fuzzy Dynamic Systems With Interval Parameter Uncertainties

This paper investigates the problem of guaranteed cost control for Takagi-Sugeno fuzzy dynamic systems with interval parameter uncertainties. The parameter uncertainty is characterized by the matrix bound, which is quite natural in real applications. Attention is focused on the fuzzy state feedback controller design via the so-called parallel distributed compensation scheme, which guarantees the closed-loop system to be robustly stable with a prescribed upper bound of the cost function. By utilizing the instrumental idea of delay dividing, a new Lyapunov-Krasovskii functional is introduced, which leads the resultant conditions to be much less conservative than most existing results in the literature. Some other new ideas such as basis dependence are also employed, which help to reduce the conservatism. All the results are formulated in the form of linear matrix inequalities (LMIs), which can readily be solved via standard numerical software. Finally, illustrative examples are given to show the less conservatism and applicability of the obtained results.

Fuzzy Control for Nonlinear Uncertain Electrohydraulic Active Suspensions With Input Constraint

This paper presents a Takagi-Sugeno (T-S) model-based fuzzy control design approach for electrohydraulic active vehicle suspensions considering nonlinear dynamics of the actuator, sprung mass variation, and constraints on the control input. The T-S fuzzy model is first applied to represent the nonlinear uncertain electrohydraulic suspension. Then, a fuzzy state feedback controller is designed for the obtained T-S fuzzy model with optimized H infin performance for ride comfort by using the parallel-distributed compensation (PDC) scheme. The sufficient conditions for the existence of such a controller are derived in terms of linear matrix inequalities (LMIs). Numerical simulations on a full-car suspension model are performed to validate the effectiveness of the proposed approach. The obtained results show that the designed controller can achieve good suspension performance despite the existence of nonlinear actuator dynamics, sprung mass variation, and control input constraints.

Descriptor modelling towards control of a two link pneumatic robot manipulator: A T–S multimodel approach

This paper presents the first steps towards a robust model-based controller design for two-link manipulators using a Takagi Sugeno multimodel descriptor form. Due to the circumstances that this form is more similar to a given original nonlinear equation as a Takagi Sugeno multimodel, it allows to reduce the conservatism of the controller design by using common matrix structures. The model-based control law here is equivalent to the well-known parallel distributed compensation scheme. The challenge of the investigated modelling and control problem in this case is the highly nonlinear dynamics of the dual-actuator drive powered by air-pressure that interacts with the dynamics of the robot manipulator.

Stability Analysis and Stabilization for Discrete-Time Fuzzy Systems With Time-Varying Delay

This paper is concerned with the problems of stability analysis and stabilization for discrete-time Takagi-Sugeno fuzzy systems with time-varying state delay. By constructing a new fuzzy Lyapunov function and by making use of novel techniques, an improved delay-dependent stability condition is obtained, which is dependent on the lower and upper delay bounds. The merit of the proposed stability condition lies in its reduced conservatism, which is achieved by avoiding the utilization of some bounding inequalities for the cross products between two vectors. Then, a delay-dependent stabilization approach based on a parallel distributed compensation scheme is developed for both state feedback and observer-based output feedback cases. The proposed stability and stabilization conditions are formulated in terms of linear matrix inequalities, which can be solved efficiently by using existing optimization techniques. Two illustrative examples are provided to demonstrate the effectiveness of the results proposed in this paper.

H ∞ Fuzzy Tracking Control Design for Nonlinear Active Fault Tolerant Control Systems

Abstract This paper studies the problem of H∞ fuzzy tracking control design for nonlinear active fault tolerant control systems based on the Takagi and Sugeno fuzzy model. Two random processes with Markovian transition characteristics are introduced to model the system component fault process and the fault detection and isolation decision process used to reconfigure the control law, respectively. The random behavior of the FDI process is conditioned on the fault process state. The parallel distributed compensation scheme is employed for the control design. As a result, a closed-loop fuzzy system with two Markovian jump parameters is obtained. Based on a stochastic Lyapunov function, a sufficient condition for stochastic stability of the closed-loop fuzzy system with a guaranteed H∞ model reference tracking performance is first derived. A linear matrix inequality approach to the control design is then developed to reduce the effect of the external disturbance and reference input on tracking error as small as possible. Finally, a simulation example is presented to illustrate the effectiveness of the proposed design method.

Delay-dependent robust control of uncertain stochastic fuzzy systems with time-varying delay

The problem of delay-dependent robust fuzzy control for stochastic nonlinear systems with parameter uncertainties and time-varying delay is considered. A generalised Takagi-Sugeno fuzzy model is introduced to represent a stochastic nonlinear system in which the consequent parts are composed of a set of uncertain stochastic time-varying delay systems. Delay-dependent stability criterion is first obtained such that for all admissible uncertainties, the overall fuzzy system is asymptotically stable in the mean square. Then, based on the stability criterion and the parallel distributed compensation scheme, a state feedback fuzzy controller is proposed to guarantee the asymptotical stability in the mean square for the closed-loop system. These conditions are expressed in terms of linear matrix inequalities, and are dependent on the size of the time delay and on the size of the derivative of time delay. Finally, a simulation example is given to illustrate the effectiveness of the developed method.

A New Fuzzy Lyapunov Approach to Non-Quadratic Stabilization of Takagi-Sugeno Fuzzy Models

A New Fuzzy Lyapunov Approach to Non-Quadratic Stabilization of Takagi-Sugeno Fuzzy ModelsIn this paper, new non-quadratic stability conditions are derived based on the parallel distributed compensation scheme to stabilize Takagi-Sugeno (T-S) fuzzy systems. We use a non-quadratic Lyapunov function as a fuzzy mixture of multiple quadratic Lyapunov functions. The quadratic Lyapunov functions share the same membership functions with the T-S fuzzy model. The stability conditions we propose are less conservative and stabilize also fuzzy systems which do not admit a quadratic stabilization. The proposed approach is based on two assumptions. The first one relates to a proportional relation between multiple Lyapunov functions and the second one considers an upper bound to the time derivative of the premise membership functions. To illustrate the advantages of our proposal, four examples are given.

CONTROL-ORIENTED MODELING OF HYDROSTATIC TRANSMISSIONS CONSIDERING LEAKAGE LOSSES

Hydrostatic Transmissions, also called hydrostatic gears, have been widely used in mobile machines and off-road vehicles such as wheel loaders, graders or tractors. The hydrostatic transmissions are gears with high power density which offer important advantages like continuously variable transmission, maximum tractive force at low speeds and reversing without changing gear. In the industrial practice the transmission output torque, transmission ratio or output speed are usually controlled by model-free PID control methods. This approach results in limited closed-loop bandwidth, limited working efficiency and accuracy due to the high nonlinear characteristic of the plant.This paper presents a control-oriented model of a general hydrostatic transmission as a first step towards a multivariable model-based fuzzy state feedback gain scheduling controller based on parallel distributed compensation scheme (PDC) using Takagi-Sugeno (TS) fuzzy systems. First principles are used to determine the structure of the TS fuzzy system. The relevance of the approach is shown by simulation studies.

Stability conditions of fuzzy systems and its application to structural and mechanical systems

This paper provided the stability conditions and controller design for a class of structural and mechanical systems represented by Takagi–Sugeno (T–S) fuzzy models. In the design procedure of controller, parallel-distributed compensation (PDC) scheme was utilized to construct a global fuzzy logic controller by blending all local state feedback controllers. A stability analysis was carried out not only for the fuzzy model but also for a real mechanical system. Furthermore, this control problem can be reduced to linear matrix inequalities (LMI) problems by the Schur complements and efficient interior-point algorithms are now available in Matlab toolbox to solve this problem. A simulation example was given to show the feasibility of the proposed fuzzy controller design method.

Robust H∞ Control for Uncertain Fuzzy Neutral Delay Systems

This paper deals with the problems of robust stabilization and robust H ∞ control for a class of Takagi–Sugeno fuzzy neutral delay systems with norm-bounded timevarying parameter uncertainties. Attention is focused on the design of a fuzzy state feedback controller, which is implemented by utilizing the so-called parallel distributed compensation scheme. Sufficient conditions for the solvability of these problems are obtained in terms of linear matrixin equalities (LMIs). When these LMIs are feasible, an explicit expression of the desired fuzzy state feedback gains is also given. Finally, a simulation example is provided to illustrate the effectiveness and applicability of the proposed design approach.

A multiple lyapunov function approach to stabilization of fuzzy control systems

This paper addresses stability analysis and stabilization for Takagi-Sugeno fuzzy systems via a so-called fuzzy Lyapunov function which is a multiple Lyapunov function. The fuzzy Lyapunov function is defined by fuzzily blending quadratic Lyapunov functions. Based on the fuzzy Lyapunov function approach, we give stability conditions for open-loop fuzzy systems and stabilization conditions for closed-loop fuzzy systems. To take full advantage of a fuzzy Lyapunov function, we propose a new parallel distributed compensation (PDC) scheme that feedbacks the time derivatives of premise membership functions. The new PDC contains the ordinary PDC as a special case. A design example illustrates the utility of the fuzzy Lyapunov function approach and the new PDC stabilization method.