Controller Design For Linear Parameter-varying Systems Research Articles

A reconfigurable PID fault tolerant tracking controller design for LPV systems

This paper considers the design of a reconfigurable PID Fault Tolerant Tracking Controller (PID-FTTC) for Linear Parameter Varying (LPV) systems affected by actuator faults with the presence of disturbance. The LPV systems are represented through a polytopic LPV description with measurable gain scheduling functions. A new PID-FTTC scheme with a model reference, an adaptive PID controller and an Adaptive Polytopic Observer (APO), is developed. The main idea is to improve and to compare performances with this developed PID-FTTC versus previous similar FTC techniques especially about the settling time, the overshoot and integral error indices. By the way, this paper can reduce the conservatism of previous methods with more parameters design so as to avoid their disadvantages and to give better control loop performances especially in terms of accuracy and speed of trajectory tracking even when a fault occurs. So, in order to establish the stability of the reconfigured PID-FTTC, a new theoretical study is developed through the use of Linear Matrix Inequality (LMI). This new method is illustrated through a two-tank process where the results compared to previous ones, underline the improvements.

A quadratic matrix inequality based PID controller design for LPV systems

This paper develops a robust gain-scheduled proportional–integral–derivative (PID) controller design method for a linear-parameter-varying (LPV) system with parametric uncertainty. It is recognized in the literature that the robust fixed-order controller design can be formulated as a feasibility problem of a bilinear matrix inequality (BMI) constraint. Unfortunately, the search for a feasible solution of a BMI constraint is an NP hard problem in general. Previous researchers have applied a linearization method, such as a variable change technique or a congruence transformation, to transform the BMI into a LMI. The applicability of the linearization method depends on the specific structure of the problem at hand and cannot be generalized. This paper instead formulates the gain-scheduled PID controller design as a feasibility problem of a quadratic matrix inequality (QMI) constraint, which covers the BMI constraint as a special case. An augmented sequential LMI optimization method is proposed to search for a feasible solution of the QMI constraint iteratively. As an illustrative application, a vehicle lateral control problem is presented to demonstrate the applicability of the proposed algorithm to a real-world output feedback control design system.

A new extended LMI-based robust gain scheduled state feedback H 2 controller design

This paper proposes an improved robust H 2 state feedback control synthesis for the Linear Parameter Varying (LPV) systems by attaining the affine quadratic stability. In place of standard H 2 computation in the literature, a new H 2 computation based on extended Linear Matrix Inequality (LMI) is improved by means of the slack variable, where it is obtained by separation Lyapunov matrix from system matrix. State feedback H 2 synthesis is improved for the systems, and is more effective and less conservative than the common ones in the literature. Therefore, the less conservative results are obtained for gain scheduling controller design for LPV systems. The numerical examples are presented to show the superiority of the proposed controller design.

Smooth switching LPV controller design for LPV systems

This paper presents a method to design a smooth switching gain-scheduled linear parameter varying (LPV) controller for LPV systems. The moving region of the gain-scheduling variables is divided into a specified number of local subregions as well as subregions for the smooth controller switching, and one gain-scheduled LPV controller is assigned to each of the local subregions. For each switching subregion, a function interpolating two local LPV controllers associated with its neighborhood subregions is designed to satisfy the constraint of smooth transition of controller system matrices. The smooth switching controller design problem amounts to solving a feasibility problem which involves nonlinear matrix inequalities. To find a solution to the feasibility problem, an iterative descent algorithm which solves a series of convex optimization problems is proposed. The usefulness of the proposed controller design method is demonstrated with a control example of a flexible ball-screw drive system.

Fixed-order LPV Controller Design for LPV Systems by Convex Optimization

In this paper a new method for fixed-order output-feedback Linear Parameter Varying (LPV) controller design is presented. First, a set of stabilizing LPV controllers is given as an inner convex approximation of the non-convex set of all stabilizing LPV controllers with the same order. This characterization is based on the decoupling of the state and Lyapunov matrices appearing together in the derivative of the Lyapunov function. As a measure of performance the decay-rate related to exponential stability is considered. The efficiency of the proposed method is illustrated on an appropriate simulation example.

Ellipsoid based L_2 controller design for LPV systems with saturating actuators

This paper addresses the L_2 gain control problem for disturbance attenuation in Linear Parameter Varying (LPV) Systems having saturating actuators when the system is subjected to L_2 disturbances. In the presented method, saturating actuator is expressed analytically with a convex hull of some linear feedback which let us construct L_2 control problem via Linear Matrix Inequalities (LMIs) which are obtained by some ellipsoids. It is shown that the stability and disturbance rejection capabilities of the control system are all measured by means of these nested ellipsoids where the inner ellipsoid covers the initial conditions for states whereas the outer ellipsoid designates the L_2 gain of the system. It is shown that the performance of the controller is highly related by the topology of these ellipsoids. Finally, the efficiency of the proposed method is successfully demonstrated through simulation studies on a single-track vehicle dynamics having some linear time-varying parameters.