Implicit discrete-time twisting controller without numerical chattering: analysis and experimental results

In this paper, we present an implementation of the sliding mode twisting controller on an electropneumatic plant for a tracking control problem. To this end, implicitly and explicitly discretized twisting controllers are considered. We discuss their structure, properties and implementations, as well as the experimental results. The analysis of the performance sustains the theoretical superiority of the implicitly discretized version, as shown in previous works. The main advantages of the implicit method are better tracking performance and drastic reduction in the input and output chattering. This is achieved without modifying the structure of the controller compared to its continuous-time version. The tracking error cannot be used as the sliding variable: it has a relative degree 3 w.r.t. the control input. The tuning of the sliding surface has well as some other parameters in the control loop was instrumental in achieving good performance. We detail the selection procedure of those parameters and their influence on the closed-loop behaviour. Finally we also present some results with an implicitly discretized EBC-SMC controller.