Guaranteed Performance State-Feedback Gain-Scheduling Control With Uncertain Scheduling Parameters

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Ali Khudhair Al-Jiboory ◽  
Guoming G. Zhu ◽  
Jongeun Choi
Keyword(s):  
State Feedback ◽  
Gain Scheduling ◽  
Measurement Noise ◽  
Control Synthesis ◽  
Linear Matrix ◽  
Feedback Gain ◽  
Uncertainty Model ◽  
Gain Scheduling Control ◽  
Uncertain Scheduling

State-feedback gain-scheduling controller synthesis with guaranteed performance is considered in this brief. Practical assumption has been considered in the sense that scheduling parameters are assumed to be uncertain. The contribution of this paper is the characterization of the control synthesis that parameterized linear matrix inequalities (PLMIs) to synthesize robust gain-scheduling controllers. Additive uncertainty model has been used to model measurement noise of the scheduling parameters. The resulting controllers not only ensure robustness against scheduling parameters uncertainties but also guarantee closed-loop performance in terms of H2 and H∞ performances as well. Numerical examples and simulations are presented to illustrate the effectiveness of the synthesized controller. Compared to other control design methods from literature, the synthesized controllers achieve less conservative results as measurement noise increases.

LPV Modeling of Buck Converter and Gain Scheduling Control

2011 ◽  
Vol 317-319 ◽  
pp. 1390-1393
Author(s):  
Guo Xian Lin ◽  
Wei Xie
Keyword(s):  
State Feedback ◽  
Specific Area ◽  
Gain Scheduling ◽  
Buck Converter ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Signal Model ◽  
Line Voltage ◽  
Gain Scheduling Control ◽  
Gain Scheduled

A kind of gain scheduling control is designed for Buck converter. The small signal model of the Buck converter is translated into the Linear Parameter-Varying (LPV) dynamic equation with the load and the line voltage as the scheduled parameters. Based on it, the closed-loop system poles assignment is taken to the specific area with gain scheduled state feedback via linear matrix inequalities (LMIs) technique, the gain scheduled state feedback is designed to regulate the duty cycle of the switch conduction. Compared with robust state feedback control, it has better disturbance rejection performance.

A Nonlinear Gain-Scheduling Compensation Approach Using Parameter-Dependent Lyapunov Functions

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Fen Wu ◽  
Xun Song ◽  
Zhang Ren
Keyword(s):  
Lyapunov Functions ◽  
Gain Scheduling ◽  
Control Synthesis ◽  
Linear Matrix ◽  
Nonlinear Gain ◽  
Control Approach ◽  
Lpv Control ◽  
Gain Scheduling Control ◽  
Output Information ◽  
Parameter Dependent

This paper addresses the gain-scheduling control design for nonlinear systems to achieve output regulation. For gain-scheduling control, the linear parameter-varying (LPV) model is obtained by linearizing the plant about zero-error trajectories upon which an LPV controller is based. A key in this process is to find a nonlinear output feedback compensator such that its linearization matches with the designed LPV controller. Then, the stability and performance properties of LPV control about the zero-error trajectories can be inherited when the nonlinear compensator is implemented. By incorporating the exosystem, nominal input, and measured output information into the LPV model, the LPV control synthesis problem is formulated as linear matrix inequalities (LMIs) using parameter-dependent Lyapunov functions (PDLFs). Moreover, explicit formulae for the construction of the nonlinear gain-scheduled compensator have been derived to meet the linearization requirement. Finally, the validity of the proposed nonlinear gain-scheduling control approach is demonstrated through a ball and beam example.

scholarly journals Gain Scheduling Controller Design for Two-Rotor Hovering System and its Experimental Verification

2006 ◽  
Vol 18 (5) ◽  
pp. 589-597
Author(s):  
Makoto Yamashita ◽  
◽  
Masami Saeki ◽  
Nobutaka Wada ◽  
Izumi Masubuchi ◽  
...  
Keyword(s):  
Flight Control ◽  
State Feedback ◽  
Optimization Problem ◽  
Controller Design ◽  
Gain Scheduling ◽  
Linear Matrix ◽  
Feedback Gain ◽  
Convex Optimization Problem ◽  
Linear Parameter Varying ◽  
Lpv System

We propose two design methods of a gain scheduling controller for flight control of two-rotor hovering system. We first propose a method of converting whole dynamics of the hovering system to a linear parameter-varying (LPV) system at once. Secondly, we propose a method of linearizing longitudinal dynamics of the system exactly and converting remaining dynamics to an LPV system. In both cases, the state feedback gain scheduling controller is designed for the obtained LPV system by solving a convex optimization problem with linear matrix inequality (LMI) constraints. Experimental results show the effectiveness of the proposed methods.

Robust H∞ Control and Stabilization of Uncertain Switched Linear Systems: A Multiple Lyapunov Functions Approach

2005 ◽  
Vol 128 (3) ◽  
pp. 696-700 ◽  
Author(s):  
Zhijian Ji ◽  
Xiaoxia Guo ◽  
Long Wang ◽  
Guangming Xie
Keyword(s):  
Linear Systems ◽  
Lyapunov Functions ◽  
State Feedback ◽  
Robust Stabilization ◽  
Disturbance Attenuation ◽  
Control Synthesis ◽  
Linear Matrix ◽  
Multiple Lyapunov Functions ◽  
Switched Linear Systems ◽  
Switched State Feedback

This paper addresses robust H∞ control and stabilization of switched linear systems with norm-bounded time-varying uncertainties. First, based on multiple Lyapunov functions methodology, a sufficient condition is derived for robust stabilization with a prescribed disturbance attenuation level γ only by employing state-dependent switching rules. Then the robust H∞ control synthesis via switched state feedback is studied. It is shown that a switched state-feedback controller can be designed to stabilize the switched systems with an H∞-norm bound if a matrix inequality based condition is feasible. This condition can be dealt with as linear matrix inequalities (LMIs) provided that the associated parameters are selected in advance. All the results presented can be regarded as an extension of some existing results for both switched and nonswitched systems.

A Linear Matrix Inequality Solution to the Input Covariance Constraint Control Problem

2013 ◽  
Author(s):  
Andrew White ◽  
Guoming Zhu ◽  
Jongeun Choi
Keyword(s):  
Linear Matrix Inequality ◽  
Control Problem ◽  
Continuous Time ◽  
Covariance Matrices ◽  
Control Synthesis ◽  
Linear Matrix ◽  
Multiple Constraints ◽  
Matrix Inequality ◽  
Output Performance

In this paper, the input covariance constraint (ICC) control problem is solved by a convex optimization with linear matrix inequality (LMI) constraints. The ICC control problem is an optimal control problem that is concerned with finding the best output performance possible subject to multiple constraints on the input covariance matrices. The contribution of this paper is the characterization of the control synthesis LMIs used to solve the ICC control problem. To demonstrate the effectiveness of the proposed approach a numerical example is solved with the control synthesis LMIs. Both discrete and continuous-time problems are considered.

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