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.

Online Switching Control of LFT Parameter-Dependent Systems

2009 ◽  
Vol 131 (2) ◽  
Author(s):  
Ke Dong ◽  
Fen Wu
Keyword(s):  
Switching Control ◽  
Control Synthesis ◽  
Linear Matrix ◽  
Multiple Lyapunov Functions ◽  
Control Approach ◽  
Control Scheme ◽  
Gain Scheduling Control ◽  
Gain Scheduled Controller ◽  
Parameter Dependent ◽  
Gain Scheduled

To improve controlled performance and expand gain-scheduling control capability, we propose a switching control approach of linear fractional transformation parameter-dependent systems using multiple Lyapunov functions combined with online control techniques. At each switching instant, a gain-scheduled controller working for the next switching interval will be designed online. The switching control synthesis condition is formulated as linear matrix inequalities and can be solved efficiently, upon which the controller will be constructed. The online switching control scheme is demonstrated using an uninhabited combat aerospace vehicle problem.

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.

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.

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.

scholarly journals Less Conservative Control Design for Linear Systems with Polytopic Uncertainties via State-Derivative Feedback

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Emerson R. P. da Silva ◽  
Edvaldo Assunção ◽  
Marcelo C. M. Teixeira ◽  
Luiz Francisco S. Buzachero
Keyword(s):  
Linear Systems ◽  
Lyapunov Functions ◽  
State Feedback ◽  
Controller Design ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Polytopic Uncertainties ◽  
Parameter Dependent ◽  
Finsler’S Lemma ◽  
Time Linear

The motivation for the use of state-derivative feedback instead of conventional state feedback is due to its easy implementation in some mechanical applications, for example, in vibration control of mechanical systems, where accelerometers have been used to measure the system state. Using linear matrix inequalities (LMIs) and a parameter-dependent Lyapunov functions (PDLF) allowed by Finsler’s lemma, a less conservative approach to the controller design via state-derivative feedback, is proposed in this work, with and without decay rate restriction, for continuous-time linear systems subject to polytopic uncertainties. Finally, numerical examples illustrate the efficiency of the proposed method.

scholarly journals A Parameter-Dependent Approach to Observer-BasedH∞Control for Networked Control LPV Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Yanhui Li ◽  
Xiujie Zhou ◽  
Chang Zhang ◽  
Hamid Reza Karimi
Keyword(s):  
Collaborative Design ◽  
Controller Design ◽  
Lyapunov Stability Theory ◽  
Networked Control ◽  
Control Synthesis ◽  
Linear Matrix ◽  
Time Varying ◽  
Infinite Dimensional ◽  
Lpv Systems ◽  
Parameter Dependent

We address the observer-basedH∞controller design problem for networked control LPV (NC LPV) systems, which are network-based systems that depend on unknown but measurable time-varying parameters. According to the analysis of the special issues brought by introducing network into LPV systems and the state reconstruction based on the observer, a new augmented model is established with two independent time-varying delays, which can carry out the controller and observer collaborative design effectively. Based on the parameter-dependent Lyapunov stability theory, a sufficient condition is proposed to ensure that the closed-loop system is asymptotically stable with a guaranteedH∞performance levelγ, in which the coupling between Lyapunov function matrices and the system matrices existed. By using the Projection Lemma and introducing a slack matrix, the decoupling is achieved successfully, which refers to reducing conservatism. In the present study, the condition for stability analysis and control synthesis is formulated in terms of the parameterized linear matrix inequality (PLMI), which is infinite-dimensional and can be transformed into finite by using the basis function method and gridding technique. A numerical example is given to demonstrate the high validity and merit of the proposed approach.

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