A minimum variance performance map is introduced for constrained linear model predictive control (MPC). The minimum variance performance map provides a demonstration of the effect of constraints in an MPC on the best achievable controller performance. The constrained minimum variance controller is formulated for the MPC system to be monitored. Using multi-parametric quadratic programming (mp-QP), the linear, piecewise control law is obtained for the constrained minimum variance controller. The linear, piecewise control law is used with a Kalman filter to obtain the minimum output variance in each region of the state space partition. The minimum variance performance map is demonstrated on a second order process with a constraint on the input amplitude. © 2009 Elsevier Ltd. All rights reserved.
Bibliographical noteThis research was supported by a National Science Foundation Graduate Fellowship, a National Science Defense and Engineering Graduate Fellowship, a National Science Foundation grant under DMI-0432433, and the members of the Texas-Wisconsin-California Control Consortium.
- MPC performance map
- Minimum variance
- Performance monitoring