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 r, CHOSM approaches provide theoretically exact compensation of the matched Lipschitz perturbation, ensuring the finite-time convergence to the (r+1)-th sliding-mode set, by using only information on the sliding output and its derivatives up to the order (r-1). In this paper, we investigate the disturbance rejection properties of a PID-like CHOSM controller, as the simplest and 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 propagation of the matched Lipschitz perturbation through the control loop in frequency domain. The resulted solution appears in form of the Bode-like loci which depend also on the amplitude of harmonic disturbances. Such amplitude-frequency characteristics allow certain comparability with standard disturbance sensitivity functions of a linear PID-controlled system in frequency domain. Also a simple and straightforward 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, i.e. chattering, is ditto respected. A detailed experimental case study, accomplished on an electro-mechanical actuator in the laboratory setting, highlight and make the pros and cons of both PID and CHOSM controllers well comparable for a broadband disturbance rejection.

Figures (11)

• Figure 1: Standard single-input-single-output (SISO) feedback control loop with the objective of disturbance rejection.
• Figure 2: Computed, based on \ref{['eq:absPart']}, amplitude $A$ of the output steady-state oscillations over the angular frequency $\omega$ of the periodic disturbance, with $E=1$ (dash-dotted red line) and $E=10$ (solid blue line).
• Figure 3: Experimental setup of the motion system.
• Figure 4: Bode plot of the experimental data and estimated transfer function.
• Figure 5: Exemplary evaluation of the 2nd order RED with $r=8$: the measured output value in (a) and RED estimate $x_1$ over the low-pass (LP) filtered discrete time derivative of $y$ in (b).