Model-free sliding mode control with estimated equivalent control signal

Abstract

Sliding mode control (SMC) is a robust, precise and quite popular nonlinear control technique using a control signal having two parts: switching and equivalent control signals. In order to calculate the equivalent control signal, a model of the system to be controlled is necessary. However, modeling a system can be so challenging due to limited project time, complexity of the system, lack of highly qualified person, inability to disassemble the system, modeling errors, variable parameters or uncertainties in the model and drawing the equivalent control signal from a nonlinear system model, etc. In this study, with an innovative model-free approach, the equivalent control signal is estimated recursive online system identification and used to comprise the total control signal. Thus it has been possible to make generally mathematically complex SMC technique more practical and easily applicable. For this purpose, the ARX (AutoRegressive with eXogenous) model of the system was obtained by using the least squares method iteratively. With the ARX model, the equivalent control signal for discrete-time SMC was calculated and model-free sliding mode control of the system was realized. The proposed controller was tested on a real simple inverted pendulum system having nonlinear behavior and was found to be quite effective both theoretically and experimentally. Results were compared to classical PID control and classical continuous-time SMC results and were found to be so satisfactory. Hence, the proposed model-free SMC method is easily recommended as an innovative superior model-free control technique for precise and robust industrial controls, encourages practical control engineers to use SMC, with a minimum simple mathematics.