Presented is the derivation and analysis of a viable and practical discrete time sliding mode control system. Sliding mode control attempts to constrain the natural dynamics of a system to pre-specified modes. The developed controller captures the positive aspects of continuous time sliding mode control:​ robustness to bounded unmodelled plant dynamics and exogenous disturbances, while allowing implementation at slow sampling rates.

Sampling period limits are presented for discretized continuous sliding control beyond which the closed loop system may become unstable. A discrete sliding mode controller design is examined in detail. The controller incorporates a sliding region which is characterized and leads to an original tuning rule for second order systems. A novel, alternative controller is derived based on input and output data only. The case of multiple inputs is considered where the controller is shown to decouple the system. Analysis includes sliding surface design where two methods are derived, one based on eigenstructures and the other, an original result, using linear quadratic optimization. The time for a system to reach the sliding mode, from initial conditions, is estimated using two novel techniques. Optimal static and dynamic switching gains for the controller switching component of the controller are found using original analysis of robustness and stochastic methods. Indirect adaptive control is derived as an original result for the state space form presented.

Simulation results demonstrate the utility and properties of the controller. Data from an experimental coupled drives provide a model for experimental discrete sliding control in velocity and position control tasks with encouraging results as compared with a benchmark measure. A challenging gantry crane model with pulsewidth modulation actuation is developed in simulation giving a realistic test of discrete sliding control as compared with a linear quadratic optimal controller. Experimental results on the actual gantry crane demonstrate effective control.