Higher Order Sliding Mode Based Dead-Beat Control with Disturbance Compensation for Multi-Input LTI Systems

This paper presents a new dead-beat control design for a class of multi-input linear time-invariant continuous-time controllable systems. The system is controlled using multi-rate sampled data. First step in design is to obtain the controllability index vector. Using elements of this vector known as controllability indices, the state feedback matrix is computed applying higher order sliding mode control approach. The number of sliding variables is equal to the number of control inputs. Obtained control annihilates system state in a minimal number of sampling periods which is equal to the maximal value of controllability indices. Since, the dead-beat control has poor robustness, a disturbance compensation is designed. In this paper, the compensation control is equal to the negative value of the disturbance estimate. The estimate is obtained using the equivalent control approach, while the compensation sampling period is not the same as the deadbeat control sampling period. The control is formed as the dead-beat control term and the compensation control which suppressed disturbance effects. The sampling period of compensation control is generally smaller than the control sampling period. Properties of the proposed control system are demonstrated on a simulation example.