Abstract
In this paper, a new Direct Model Reference Adaptive Control Procedure (DMRAC) for Linear Time-Invariant (LTI) delay systems is presented with the use of the concept of the command generator tracker which expands the class of processes that can now be controlled with zero output error. The stability of the error between the system and the model is guaranteed by the Lyapunov theory. The new algorithm is applied to control a perturbed delay system. Matlab simulation examples are given to demonstrate the usefulness of the algorithm.
Highlights
The stability of time delay systems has been studied with the Lyapunov–Krasovskii and the Lyapunov–Razumikhin approach
In [8], a delay-dependent stabilization condition was proposed for the stability of a class T–S fuzzy time-delay system using homogeneous polynomials scheme and Polya's theorem with application on a truck-trailer model
The adaptive control law based on the extended Command Generator Tracker (CGT) approach is given by: u p (t) = Ke (t)ey (t) + Kx (t)xm (t) + Ku (t)um (t) (7)
Summary
The stability of time delay systems has been studied with the Lyapunov–Krasovskii and the Lyapunov–Razumikhin approach These two concepts have been used in order to avoid the classical Lyapunov method. In [13], the author applied a sliding mode controller to stabilize uncertain time-delay chaotic systems. Authors in [36] developed a saturated command for planar systems where the stabilization is achieved in finite time using just a simple proportional derivative corrector PD whose parameters are optimally adapted. This finite time stability is analyzed with Lyapunov's theory and homogeneity concept. After finding an actuator’s model of electromagnetic valve actuator which replaces the classic mechanical valve actuator, the PD parameters are adjusted adaptively and on line with the variance minimization method
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