Disturbance model design for linear model predictive control

Model predictive control (MPC) algorithms typically use a constant output bias for feedback, which can be interpreted by assuming that a constant disturbance perturbs the process output. This assumption leads to sluggish rejection of most real unmeasured disturbances since these disturbances generally enter the loop through state or input channels. An improved performance is often possible by designing an unmeasured disturbance model that explicitly incorporates input and state disturbance effects. A Kalman filter can then be employed to estimate the disturbances, allowing the control algorithm to reject them more quickly. This paper presents design guidelines for a disturbance model that accommodates unmeasured disturbances entering through the process input, state, or output. Conditions that guarantee detectability of the augmented system model are provided. A simulation example illustrates the performance benefits possible through this approach.