Discrete-time sliding mode control of systems with matched uncertainty using infrequent output measurements

Abstract

This paper proposes a new algorithm for achieving discrete-time sliding mode for single input single output systems with bounded matched uncertainty using output feedback. The concept of periodic output feedback is used here. It has been shown that, when the output of the uncertain system with matched uncertainty is sampled slower than the input, there exist a discrete-time quasi sliding mode. The method is very general and is applicable to any controllable and observable linear time invariant single input single output system. The proposed technique is illustrated with numerical examples.

Periodic output feedback control for Delta operator systems

“…The gain K can be calculated in the similar manner as in the case of a shift operator system [14], [15]. Consider the τ system of a Delta operator system represented as,…”

“…This technique is known as multirate output feedback technique [10]. If the system output is sampled faster than the input [11], the method is known as Fast Output Sampling (FOS) and if the system output is sampled slower than the input, the method is known as Periodic Output Feedback (POF) [12], [13], [14], [15], [16] technique. But with high sampling rates these techniques also fail due to the numerical ill-conditioning with the use of shift operators.…”

Periodic output feedback based discrete-time sliding mode control for multivariable systems

“…The algorithm for obtaining a sliding surface, S(k) Mx(k) for the system (14) is presented here, in a similar manner as explained in [20], for a general nth order square system with m inputs.…”

“…An attempt has been made to propose a method for discrete sliding mode control based on Periodic Output Feedback in [19]. Recently a method is proposed in [20] for discrete-time sliding mode control using infrequent output observations where periodic output feedback based sliding mode control is presented for a single input single output system.…”

“…In this paper, the method presented in [20] is extended. Here, Periodic Output feedback based sliding mode control for multivariable square systems is presented.…”