Model free sliding mode control with estimated equivalent control signal

Sliding mode control is an advanced nonlinear control technique and consists of two parts: switching and equivalent control signals. To obtain the equivalent control signal, a model of the controlled system is needed. However, in the modeling process of a system, many difficulties may be encountered such as insufficient time for modeling, inability to disassemble the system, modeling errors, modeling difficulties of complex systems, uncertainties in the model, and the inability to analytically obtain the equivalent control signal from the nonlinear system model. In such cases, the system can be considered as a black box and system identification methods and model determination methods can be applied by using the system's input and output signals. In this study, estimation of the equivalent control signal by system identification was used to eliminate the difficulties of modeling and to use the sliding mode control widely and practically. The satisfactory performance of the proposed controller has been proven both theoretically and experimentally on the simple inverted pendulum system having nonlinear behaviour. To obtain the equivalent control signal, the ARX (AutoRegressive with eXogenous) model of the simple inverted pendulum system was obtained by using the least squares method handling the input and output data of the system. The ARX model of the system was obtained using the iterative least squares (RLS) method for both online and offline cases. With the created ARX model, the equivalent control signal for the discrete-time sliding mode control is obtained and the model free sliding mode control of the system is realized. The simulation and experimental results obtained using the proposed method are compared in detail with the results obtained using classical PID control and classical continuous time sliding mode control methods. It was clearly seen that the developed method outperformed the expectations and it was recommended as an innovative controller for industrial applications.