Long-Range Predictive Control and Identification with Steady-State Error Weighting

The Overall objective of an adaptive controller is to ensure that the process output tracks the set point at all future time or at least asymptotically. Minimization of a discrete quadratic cost function for large finite prediction horizon is computationally "heavy". On the other hand, a small prediction horizon reduces the computational load considerably, but results in less robustness. Therefore, an alternative control objective is used to approximate the overall objective function by minimizing the error between a trajectory of finite-horizon output predictions in combination with weighted prediction of the steady state output and the set points. The resulting control law is Generalized Predictive Control [1] with weighting on the square of steady state error. The addition of this weighting term allows a smaller range of future predictions and yet retains robustness. The dual of this control objective in identification is a combination of Long-range Predictive Identification criterion with steady-state output error minimization. The control-relevant identification is, therefore, implemented by combining the adaptive filtering approach [7] with a gain estimation scheme included in this paper. The performance of this new control objective is demonstrated by simulations.