Approximated modeling and sliding mode control for systems with multiple time delays

This paper shows a new approximated model-based sliding mode controller (SMC) design for continuous-time systems with multiple time delays in states, inputs and outputs. The synthesis design procedure is composed of two steps. At the first step, based on the unit-step response data of the afore-mentioned system, an approximated continuous-time state-space model and its transfer function are determined using the balanced realization and model reduction methods. At the second step, a SMC is designed using the internal model principle to achieve the desired reference model tracking performance. A novel smooth function which substitutes for the exact sign function is presented to reduce the chattering effects. Illustrative example on a general form of distillation column model is given to demonstrate the effectiveness of the proposed method.