Robust piecewise adaptive control for an uncertain semilinear parabolic distributed parameter systems

2022 ◽  
Vol 27 ◽  
pp. 1-20
Author(s):  
Yanfang Lei ◽  
Junmin Li ◽  
Ailiang Zhao
Keyword(s):  
Adaptive Control ◽  
Closed Loop ◽  
Design Method ◽  
External Disturbance ◽  
Adaptive Controller ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
Closed Loop System ◽  
Semilinear Parabolic ◽  
Parabolic Distributed Parameter Systems

In this study, we focus on designing a robust piecewise adaptive controller to globally asymptotically stabilize a semilinear parabolic distributed parameter systems (DPSs) with external disturbance, whose nonlinearities are bounded by unknown functions. Firstly, a robust piecewise adaptive control is designed against the unknown nonlinearity and the external disturbance. Then, by constructing an appropriate Lyapunov–Krasovskii functional candidate (LKFC) and using the Wiritinger’s inequality and a variant of the Agmon’s inequality, it is shown that the proposed robust piecewise adaptive controller not only ensures the globally asymptotic stability of the closed-loop system, but also guarantees a given performance. Finally, two simulation examples are given to verify the validity of the design method.

Repetitive Control for Rejection of Periodic Multiplicative Disturbances and Adaptive Identification of the Unknown Period

2004 ◽  
Author(s):  
Sandipan Mishra ◽  
Manabu Yamada ◽  
Masayoshi Tomizuka
Keyword(s):  
Control Algorithm ◽  
Closed Loop ◽  
Design Method ◽  
Repetitive Control ◽  
Adaptive Controller ◽  
Least Mean Square ◽  
Closed Loop System ◽  
Internal Model Principle ◽  
Periodic Disturbances ◽  
The Stability

Repetitive control has been used extensively for rejection of periodic disturbances, in systems that have to follow periodic trajectories. To date, most repetitive controllers have focused on rejection of additive periodic disturbances. This paper suggests the use of a repetitive control algorithm for rejection of periodic multiplicative disturbances. The first result is a simple design method of a new controller to reject the multiplicative disturbance effectively, provided that the period of the disturbance is known. This controller is based on the internal model principle and the design method consists of a simple norm condition. It is shown that this repetitive-type controller can reject the disturbance. The second result is an extension of the first one to the case that the period of the disturbance is unknown. A period estimator is added to the control system to identify the period of the multiplicative disturbance. The algorithm, consisting of an adaptive recursive least mean square method, is simple. It is shown that this adaptive controller can reject the disturbance with an uncertain period and guarantee the stability of the adaptive closed-loop system including the period estimator.

scholarly journals Robust H ∞ Feedback Compensator Design for Linear Parabolic DPSs with Pointwise/Piecewise Control and Pointwise/Piecewise Measurement

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Liu Yaqiang ◽  
Ren Zhigang ◽  
Jin Zengwang
Keyword(s):  
Closed Loop ◽  
Design Method ◽  
Coupled System ◽  
Integration Theory ◽  
Distributed Parameter ◽  
Luenberger Observer ◽  
Compensator Design ◽  
New Type ◽  
Parabolic Distributed Parameter Systems ◽  
Performance Constraint

In this paper, a robust H ∞ control problem of a class of linear parabolic distributed parameter systems (DPSs) with pointwise/piecewise control and pointwise/piecewise measurement has been investigated via the robust H ∞ feedback compensator design approach. A unified Lyapunov direct approach is proposed in consideration of the pointwise/piecewise control and point/piecewise measurement based on the distributions of the actuators and sensors. A new type of Luenberger observer is developed on the continuous interval of space domain to track the state of the system, and an H ∞ performance constraint with prescribed H ∞ attenuation levels is proposed in this paper. By utilizing Lyapunov technique, mathematical inequalities, and integration theory, a sufficient condition based on LMI for the exponential stability of the corresponding closed-loop coupled system under an H ∞ performance constraint is presented. Finally, the effectiveness of the proposed design method is verified by numerical simulation results.

Feedback Control of Parabolic Distributed Parameter Systems

2013 ◽  
Vol 455 ◽  
pp. 337-343
Author(s):  
Hai Long Xing ◽  
Wen Shan Cui
Keyword(s):  
Feedback Control ◽  
Closed Loop ◽  
Distributed Parameter Systems ◽  
Linear Matrix ◽  
Distributed Parameter ◽  
Closed Loop Systems ◽  
Uniformly Convergent ◽  
System States ◽  
The Stability ◽  
Parabolic Distributed Parameter Systems

In this paper, the feedback control problem is considered for a class of parabolic distributed parameter systems (DPS). By employing a new Lyapunov-Krasovskii functional as well as the linear matrix inequality (LMI), a novel feedback controller is developed, which can guarantee the closed-loop system states uniformly convergent to zero. The stability conditions for closed-loop systems can be easily checked by utilizing the numerically efficient Matlab LMI toolbox. At last, a numerical example shows the effectiveness of the presented LMI-based methods.

Robustness of Natural Controls of Distributed-Parameter Systems

1996 ◽  
Vol 118 (1) ◽  
pp. 56-63 ◽  
Author(s):  
Jai Hyuk Hwang ◽  
Doo Man Kim ◽  
Kyoung Ho Lim
Keyword(s):  
Closed Loop ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
Control Force ◽  
Spatial Discretization ◽  
Actual System ◽  
Discretization Errors

In this paper, the effect of parameter and spatial discretization errors on the closed-loop behavior of distributed-parameter systems is analyzed for natural controls. If the control force designed on the basis of the postulated system with the parameter and discretization errors is applied to control the actual system, the closed-loop performance of the actual system will be degraded depending on the degree of the errors. The extent of deviation of the closed-loop performance from the expected one is derived and evaluated using operator techniques. It has been found that the extent of the deviation is proportional to the magnitude of the parameter and discretization errors, and that the proportional coeffecient depends on the structures of the natural controls.

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