Interpolation for gain-scheduled control with guarantees

Here, a methodology is presented which considers the interpolation of linear time-invariant (LTI) controllers designed for different operating points of a nonlinear system in order to produce a gain-scheduled controller. Guarantees of closed-loop quadratic stability and performance at intermediate interpolation points are presented in terms of a set of linear matrix inequalities (LMIs). The proposed interpolation scheme can be applied in cases where the system must remain at the operating points most of the time and the transitions from one point to another rarely occur, e.g., chemical processes, satellites.Fil: Bianchi, Fernando Daniel. Instituto Tecnológico de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Sánchez Peña, Ricardo S.. Instituto Tecnológico de Buenos Aires; Argentin

Gain Scheduled Control Using the Dual Youla Parameterization

Stability is a critical issue in gain-scheduled control problems in that the closed loop system may not be stable during the transitions between operating conditions despite guarantees that the gain-scheduled controller stabilizes the plant model at fixed values of the scheduling variable. For Linear Parameter Varying (LPV) model representations, a controller interpolation method using Youla parameterization that guarantees stability despite fast transitions in scheduling variables is proposed. By interconnecting an LPV plant model with a Local Controller Network (LCN), the proposed Youla parameterization based controller interpolation method allows the interpolation of controllers of different size and structure, and guarantees stability at fixed points over the entire operating region. Moreover, quadratic stability despite fast scheduling is also guaranteed by construction of a common Lyapunov function, while the characteristics of individual controllers designed a priori at fixed operating condition are recovered at the design points. The efficacy of the proposed approach is verified with both an illustrative simulation case study on variation of a classical MIMO control problem and an experimental implementation on a multi-evaporator vapor compression cycle system. The dynamics of vapor compression systems are highly nonlinear, thus the gain-scheduled control is the potential to achieve the desired stability and performance of the system. The proposed controller interpolation/switching method guarantees the nonlinear stability of the closed loop system during the arbitrarily fast transition and achieves the desired performance to subsequently improve thermal efficiency of the vapor compression system

Robust stabilization of LPV systems with structured uncertainty using minimax controllers

This paper addresses a robust control scheduling scheme for uncertain linear parameter-varying systems with structured uncertainty. A gain-scheduled controller is proposed which employs a set of minimax optimal robust controllers and incorporates an interpolation rule to achieve continuity of the controller gain over a range of operating conditions. Novel weighted time-domain integral quadratic constraints are introduced to assist in the derivation of the controller. The key idea of the interpolation for the structured uncertainty case is to transform the parameterized algebraic Riccati inequalities into equivalent linear matrix inequalities. For every fixed value of the system parameter, the proposed controller guarantees robust stability and a certain bound on the worst-case performance of the corresponding uncertain closed loop system. Furthermore, a bound on the rate of parameter variations is obtained under which the closed loop LPV system is robustly stable. To obtain the proposed controller, a set of semi-definite programming problems are introduced; this enables an efficient numerical solution to the problem under consideration. © 2007 IEEE

Gain scheduled flight control law for a flexible aircraft : A practical approach

Abstract: This paper presents a gain-scheduling method applied to flight control law design. The method is a stabilitypreservinginterpolation technique ofexisting controllers under observer-state feedback form. Application is made on a flexible civil aircraft example considering multiple scheduling parameters. Although the interpolation technique gives powerful a priori stability guarantees, the sufficient condition to satisfy leads to conservative results in practice. We thus use a fixed observer model and check stability andperformance thanks to μ-analysis. Provided results are really satisfactory for a final controller of little complexity

Gain-scheduling through continuation of observer-based realizations-applications to H∞ and μ controllers

The dynamic behavior of gain scheduled controllers is highly depending on the state-space representations adopted for the family of lienar controllers designed on a set of operating conditions. In this paper, a technique for determining a set of consistent and physically motivated linear state-space transformations to be applied to the original set of linear controllers is proposed. After transformation, these controllers exhibits an-observer-based structure are therefore easily interpolted and implemented

A Comparison of LPV Gain Scheduling and Control Contraction Metrics for Nonlinear Control

Gain-scheduled control based on linear parameter-varying (LPV) models derived from local linearizations is a widespread nonlinear technique for tracking time-varying setpoints. Recently, a nonlinear control scheme based on Control Contraction Metrics (CCMs) has been developed to track arbitrary admissible trajectories. This paper presents a comparison study of these two approaches. We show that the CCM based approach is an extended gain-scheduled control scheme which achieves global reference-independent stability and performance through an exact control realization which integrates a series of local LPV controllers on a particular path between the current and reference states.Comment: IFAC LPVS 201