Sensitivity Analysis and Experimental Evaluation of PID‐Like Continuous Sliding Mode Control

ABSTRACT Continuous higher order sliding mode (CHOSM) controllers represent an efficient tool for disturbance rejection. For the systems with relative degree , CHOSM approaches provide theoretically exact compensation of the matched Lipschitz perturbation, ensuring the finite‐time convergence to the ‐th sliding‐mode set, by using only information on the sliding output and its derivatives up to the order . In this paper, we investigate the disturbance rejection properties of a PID‐like CHOSM controller, as the simplest and most intuitively clear example which incorporates nonlinear actions on the output error, its derivative, and integration of its sign. We use the harmonic balance approach and develop an analysis of the propagation of the matched Lipschitz perturbation through the control loop in frequency domain. The resulting solution appears in the form of the Bode‐like loci, which also depend on the amplitude of the harmonic disturbances. Such amplitude‐frequency characteristics allow certain comparability with standard disturbance sensitivity functions of a linear PID‐controlled system in the frequency domain. Also, a simple design procedure for the robust linear PID controller targeting the second‐order system plants under investigation is provided for benchmarking. Additional (parasitic) actuator dynamics, which can lead to self‐induced steady oscillations, that is, chattering, is also respected. A detailed experimental case study, accomplished on an electro‐mechanical actuator in a laboratory setting, highlights and makes the pros and cons of both PID and CHOSM controllers comparable for broadband disturbance rejection.