Design of Optimal MIMO DIVSC Systems and Its Application to Idle Speed Control of Spark Ignition Engine

An optimal multi-input multi-output (MIMO) discrete integral variable structure control (DIVSC) rule is proposed in this paper. This approach can achieve accurate and robust dynamic responses. The modified existence conditions are introduced to assure the existence of the discrete non-ideal sliding motion. The design procedures are clearly developed in this paper. Use optimal LQ method to decide the coefficients of the sliding surfaces and integral gains. On the basis of the nonideal sliding motions, the control functions can be found out to satisfy the modified existence conditions. The idea of boundary layer is used to smoothing the control functions. Furthermore, take the engine idle speed control as an example. Simulation results will demonstrate the potential of the proposed approach.