scholarly journals Robust stabilization withH∞performance for a class of linear parameter-dependent systems

2006 ◽  
Vol 2006 ◽  
pp. 1-15 ◽  
Author(s):  
Hamid Reza Karimi
Keyword(s):  
Linear Time ◽  
Robust Stabilization ◽  
State Feedback Control ◽  
Disturbance Attenuation ◽  
Linear Time Invariant ◽  
Quadratic Lyapunov Functions ◽  
Nonlinear Uncertainties ◽  
Invariant Parameter ◽  
Parameter Dependent ◽  
Time Invariant

We focus on the issue of robust stabilization withH∞performance for a class of linear time-invariant parameter-dependent systems under norm-bounded nonlinear uncertainties. By combining the idea of polynomially parameter-dependent quadratic Lyapunov functions and linear matrix inequalities formulations, some parameter-independent conditions with high precision are given to guarantee robust asymptotic stability and robust disturbance attenuation of the linear time-invariant parameter-dependent system in the presence of norm-bounded nonlinear uncertainties. The parameter-dependent state-feedback control is designed based on the Hamilton-Jacobi-Isaac (HJI) method. The applicability of the proposed design method is illustrated in a simple example.

Design and implementation of decoupled periodic control scheme for a laboratory-based quadruple-tank process

2021 ◽  
pp. 095965182110228
Author(s):  
Jatin K Pradhan ◽  
Arun Ghosh
Keyword(s):  
Real Time ◽  
High Frequency ◽  
Linear Time ◽  
Disturbance Attenuation ◽  
Minimum Phase ◽  
Periodic Control ◽  
Linear Time Invariant ◽  
Control Scheme ◽  
Gain Margin ◽  
Time Invariant

It is well known that linear time-invariant controllers fail to provide desired robustness margins (e.g. gain margin, phase margin) for plants with non-minimum phase zeros. Attempts have been made in literature to alleviate this problem using high-frequency periodic controllers. But because of high frequency in nature, real-time implementation of these controllers is very challenging. In fact, no practical applications of such controllers for multivariable plants have been reported in literature till date. This article considers a laboratory-based, two-input–two-output, quadruple-tank process with a non-minimum phase zero for real-time implementation of the above periodic controller. To design the controller, first, a minimal pre-compensator is used to decouple the plant in open loop. Then the resulting single-input–single-output units are compensated using periodic controllers. It is shown through simulations and real-time experiments that owing to arbitrary loop-zero placement capability of periodic controllers, the above decoupled periodic control scheme provides much improved robustness against multi-channel output gain variations as compared to its linear time-invariant counterpart. It is also shown that in spite of this improved robustness, the nominal performances such as tracking and disturbance attenuation remain almost the same. A comparison with [Formula: see text]-linear time-invariant controllers is also carried out to show superiority of the proposed scheme.

Nonfragile H∞ Output Feedback Controller Design for Linear Systems*

2003 ◽  
Vol 125 (1) ◽  
pp. 117-123 ◽  
Author(s):  
Guang-Hong Yang ◽  
Jian Liang Wang
Keyword(s):  
Output Feedback ◽  
Controller Design ◽  
Linear Time ◽  
Output Feedback Control ◽  
Disturbance Attenuation ◽  
Output Measurement ◽  
Linear Time Invariant ◽  
Measurement Feedback ◽  
Linear Time Invariant Systems ◽  
Time Invariant

This paper is concerned with the nonfragile H∞ controller design problem for linear time-invariant systems. The controller to be designed is assumed to have norm-bounded uncertainties. Design methods are presented for dynamic output (measurement) feedback. The designed controllers with uncertainty (i.e. nonfragile controllers) are such that the closed-loop system is quadratically stable and has an H∞ disturbance attenuation bound. Furthermore, these robust controllers degenerate to the standard H∞ output feedback control designs, when the controller uncertainties are set to zero.

Reduction in the Number of Gain-Scheduling Parameters Using Dimensional Transformation

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Haftay Hailu ◽  
Sean Brennan
Keyword(s):  
Linear Time ◽  
Gain Scheduling ◽  
Linear Parameter Varying ◽  
Linear Time Invariant ◽  
Lti System ◽  
Gain Scheduled Controller ◽  
Parameter Dependent ◽  
Time Invariant ◽  
Linear Parameter Varying System ◽  
Gain Scheduled

A method is presented that can often reduce the number of scheduling parameters for gain-scheduled controller implementation by transformation of the system representation using parameter-dependent dimensional transformations. In some cases, the reduction in parameter dependence is so significant that a linear parameter-varying system can be transformed to an equivalent linear time invariant (LTI) system, and a simple example of this is given. A general analysis of the parameter-dependent dimensional transformation using a matrix-based approach is then presented. It is shown that, while some transformations simplify gain scheduling, others may increase the number of scheduling parameters. This work explores the mathematical conditions causing an increase or decrease in varying parameters resulting from a given transformation, thereby allowing one to seek transformations that most reduce the number of gain-scheduled parameters in the controller synthesis step.

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