Abstract

This paper presents a strategy for designing a robust discrete‐time adaptive controller for stabilizing linear time‐invariant (LTI) continuous‐time dynamic systems. Such systems may be unstable and noninversely stable in the worst case. A reduced‐order model is considered to design the adaptive controller. The control design is based on the discretization of the system with the use of a multirate sampling device with fast‐sampled control signal. A suitable on‐line adaptation of the multirate gains guarantees the stability of the inverse of the discretized estimated model, which is used to parameterize the adaptive controller. A dead zone is included in the parameters estimation algorithm for robustness purposes under the presence of unmodeled dynamics in the controlled dynamic system. The adaptive controller guarantees the boundedness of the system measured signal for all time. Some examples illustrate the efficacy of this control strategy.

Highlights

  • Adaptive control theory has been widely applied for stabilizing increasingly complex engineering systems with large uncertainties 1, including the incorporation of parallel multiestimation and time-delayed and hybrid models 2–6

  • This paper presents a strategy for designing a robust discrete-time adaptive controller for stabilizing linear time-invariant LTI continuous-time dynamic systems

  • The discretized dynamic system model parameters are on-line updated; the controller gains vector is time varying and converges asymptotically to a constant one. Another method, which does not relax the MRAC objective, to overcome the drawback of the unstable zeros of a continuous-time dynamic system is the design of a discrete-time controller with the use of a hold device combined with a multirate sampling with fast input rate in the discretization of the continuous-time system 7, 8

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Summary

Introduction

Adaptive control theory has been widely applied for stabilizing increasingly complex engineering systems with large uncertainties 1 , including the incorporation of parallel multiestimation and time-delayed and hybrid models 2–6. The discretized dynamic system model parameters are on-line updated; the controller gains vector is time varying and converges asymptotically to a constant one Another method, which does not relax the MRAC objective, to overcome the drawback of the unstable zeros of a continuous-time dynamic system is the design of a discrete-time controller with the use of a hold device combined with a multirate sampling with fast input rate in the discretization of the continuous-time system 7, 8. The control scheme is based on the discretization process by combining the use of a fractionalorder hold FROH and a multirate with fast sampling control signal In this way, the estimated discretized model can be guaranteed to be inversely stable by means of a suitable on-line updating of the multirate gains without requirements neither on the stability of the continuous-time zeros nor the size of the sampling period.

Problem Statement
Input-Output Relation for the Discretized Plant
Adaptive Control Design
Known Plant The proposed control law is obtained from
Unknown Plant
Estimation Algorithm
Stability Analysis
Simulations
Conclusions
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