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.

Robustness of Natural Controls of Distributed-Parameter Systems

1995 ◽  
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

Abstract 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 coefficient depends on the structures of the natural controls.

Frequency Domain Stability Criteria for Distributed Parameter Systems

1970 ◽  
Vol 92 (2) ◽  
pp. 377-384 ◽  
Author(s):  
H. C. Khatri
Keyword(s):  
Frequency Domain ◽  
Stability Criterion ◽  
Closed Loop ◽  
Linear Time ◽  
Distributed Parameter Systems ◽  
Open Loop ◽  
Distributed Parameter ◽  
Stability Criteria ◽  
Domain Stability ◽  
Loop Stability

For distributed parameter systems, open-loop stability in the sense of bounded outputs for bounded inputs, and closed-loop asymptotic stability are considered. Frequency domain stability criteria for open and closed-loop distributed parameter systems are given. The closed-loop stability criterion is similar to V. M. Popov’s stability criterion for lumped systems. The criteria are limited to those linear, time-invariant systems whose dynamics can be described by a transfer function which is the ratio of the multiple transform of the output to the multiple transform of the input. The input may or may not be distributed. An example is given to illustrate the applications of the stability criteria.

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.

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.

scholarly journals Actuator Fault Detection and Accommodation in Distributed Parameter Systems

2015 ◽  
Vol 9 (1) ◽  
pp. 459-466
Author(s):  
Wenying Mu ◽  
Baotong Cui
Keyword(s):  
Fault Detection ◽  
Closed Loop ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
Time Varying ◽  
Actuator Fault ◽  
Actuator Faults ◽  
Automated Control ◽  
Fault Parameter ◽  
Control Reconfiguration

This paper presents a general framework for model-based fault detection and accommodation for a class of distributed parameter systems with control actuator faults. A set of dedicated observers, each with its own time-varying threshold is constructed to detect the occurrence of fault in the corresponding actuator and reduce fault detection time. Additionally, an adaptive diagnostic observer is then designed and analyzed to estimate each individual actuator fault. Based on the online approximation of fault parameter, automated control reconfiguration architecture has been developed to accommodate actuator fault and to preserve closed-loop stability. An example has been discussed using the proposed scheme to demonstrate effectiveness of the method.

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