Control performance monitoring via model residual assessment

Model quality is a key factor that affects the control performance of model predictive control. In this paper, a new closed-loop model assessment approach is proposed to assess model deficiency from routine closed-loop data. The proposed model quality index is a minimum variance benchmark for the model residuals obtainable from closed-loop data. From the feedback invariant principle the disturbance innovations at current instance are shown to be unaffected by the controller even if it is a nonlinear time-varying controller. Then it is shown that the disturbance innovations sequence can be estimated from closed loop data by an orthogonal projection of the current output onto the space spanned by past outputs, inputs or setpoints. With the disturbance innovations as the benchmark, a model quality index is developed by using the ratio of a quadratic form of model residuals and that of the estimated disturbance innovations. The effectiveness of the proposed methods is shown by simulation results.