scholarly journals Experimental Study ofH∞Control of Flexible Plate with Time Delay

2013 ◽  
Vol 20 (2) ◽  
pp. 227-246
Author(s):  
Tong Zhao ◽  
Long-Xiang Chen ◽  
Guo-Ping Cai
Keyword(s):  
Time Delay ◽  
Controller Design ◽  
Experimental Studies ◽  
Parameters Optimization ◽  
System Stability ◽  
Flexible Plate ◽  
Matrix Inequality ◽  
Weighting Matrix ◽  
Guarantee System ◽  
The Matrix

This paper presents theoretical and experimental studies ofH∞control of a flexible plate with time delay. A matrix inequality used for stability analysis is proposed and proved by using the Lyapunov-Krasovskii functional and free-weighting matrix. AnH∞controller is designed based on the matrix inequality and by using the parameter-adjusting method. Three control scenarios are discussed in detail by transforming the problem into parameters optimization: (i) controller design when maximum time delay of the system is known; (ii) allowable time delay when controller is known; (iii) the biggest allowable time delay to guarantee system stability when controller is unknown. Numerical simulations and experiments are also given to demonstrate the validity and feasibility of the proposed methods in this paper.

Experimental study of H∞ control for a flexible plate

2011 ◽  
Vol 18 (11) ◽  
pp. 1631-1649 ◽  
Author(s):  
Zhao Tong ◽  
Chen Long-Xiang ◽  
Cai Guo-Ping
Keyword(s):  
Time Delay ◽  
Integral Transformation ◽  
External Disturbance ◽  
Experimental Studies ◽  
State Equation ◽  
Small Time ◽  
Linear Matrix ◽  
Structural Parameter ◽  
Flexible Plate ◽  
Standard State

This paper presents theoretical and experimental studies of H∞ control for a flexible plate. Firstly, the dynamic equation of the plate with time delay is established with consideration of external disturbance. Then the standard state equation without explicit time delay is deduced by using a particular integral transformation to the time-delay equation. Finally, a H∞ time-delay controller is designed based on the standard state equation using the method of linear matrix inequality. In the controller designed, it contains not only the current step of state feedback but also the linear combination of some former steps of control. In the experiment, piezoelectric patches are used as actuators and sensors. The experiment system is structured based on the DSP TMS320F2812. Single time delay and double time delay are both considered in the experiment. The robustness of H∞ controller against the structural parameter of the plate and time delay is experimentally investigated. Simulation and experimental results indicate that the control system may suffer from instability if time delay is not treated in control design. The time-delay controller presented in this paper can effectively deal with time delay in the system, and is available for small-time delay and large-time delay as well. Furthermore, this delay controller is robust to the variance of structural parameter of the plate and time delay.

scholarly journals Robust and Passive Constrained Fuzzy Control for Discrete Fuzzy Systems with Multiplicative Noises and Interval Time Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Wen-Jer Chang ◽  
Cheung-Chieh Ku ◽  
Zong-Guo Fu
Keyword(s):  
Time Delay ◽  
Fuzzy Control ◽  
Fuzzy Controller ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Asymptotical Stability ◽  
Linear Matrix ◽  
Weighting Matrix ◽  
Multiplicative Noises ◽  
Feedback Scheme

The passive fuzzy control for discrete-time uncertain Takagi-Sugeno (T-S) fuzzy models with multiplicative noises and time delay is investigated subject to robust asymptotical stability. Applying Jensen’s inequality and free-weighting matrix technique, less conservative sufficient conditions are derived via choosing Lyapunov function to analyze and synthesize the robust asymptotical stability and passivity of closed-loop system. The derived conditions are not strictly linear matrix inequality (LMI) problems, thus the cone complementarity technique is employed to propose a suboptimal technique to solve the proposed nonstrictly LMI problems. An algorithm is developed in this paper to design the fuzzy controller which can be accomplished by state-feedback scheme or output-feedback scheme. Finally, numerical examples are provided to demonstrate the feasibility and applicability of the proposed fuzzy controller design technique.

scholarly journals A Nonlinear Backstepping Controller Design for High-Precision Tracking Applications with Input-Delay Gimbal Systems

2021 ◽  
Vol 9 (5) ◽  
pp. 530
Author(s):  
Hwan-Cheol Park ◽  
Soumayya Chakir ◽  
Young-Bok Kim ◽  
Thinh Huynh
Keyword(s):  
Delay Time ◽  
Controller Design ◽  
Sliding Mode ◽  
Experimental Studies ◽  
Euler Angle ◽  
System Stability ◽  
Control Approach ◽  
Maritime Surveillance ◽  
Control Scheme ◽  
Backstepping Controller

This paper proposes a novel nonlinear control approach for a two-axis gimbal to achieve accurate real-time tracking performance in maritime surveillance applications. For this objective, the control system must overcome system complexities and limitations, including nonlinear dynamics, coupled Euler angle-based measurements, and delay time constraints. The nonlinear backstepping controller was designed, taking into consideration the nonlinearities and system couplings to preserve the system stability. Then, an extra backstep was incorporated to minimize the control errors due to the delay time. The proposed control scheme enhances the tracking performances and expands the system’s bandwidth, which is validated in the simulations and experimental studies in comparison with a super-twisting sliding mode controller introduced in a previous study.

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