Formal analysis of state estimation for nonlinear model predictive control - Moeti, Sekhonyana (Department of Electrical Engineering, 2016)
The main goal of this study is to carry out a closed-loop performance analysis of state estimation methods when implemented in the formulation of nonlinear model predictive control. The analysis is facilitated by two nonlinear optimal state estimation methods: augmented state EKF (ASEKF) and augmented state UKF (ASUKF) for comparison purposes. Each state estimation method is coupled to the same NMPC controller to form state estimation-based NMPC controllers, that is, to form the ASEKF-NMPC and ASUKFNMPC controllers. The resulting NMPC controllers are applied for position control of the magnetic levitation system to validate their closed-loop performances. The ASEKFNMPC and ASUKF-NMPC controllers are further applied for the angular position control of the inverted pendulum mounted on a cart system for comparative analysis. The controlled system is perturbed with different error sources: output step disturbance and 5%parametric plant-model mismatch. Output step disturbance is introduced to the system to disturb the pendulum from its upright position while the 5% mismatch is applied to the parameters of the model of the controlled system throughout the simulation. To facilitate fair analysis, Pareto front ranking method is chosen as an evaluation method whereby the cost functions are defined according to the author's preferences. The cost functions served as performance markers for analyzing performance of ASEKF and ASUKF in NMPC formulation in multidimensional space. The tunable parameters of the ASEKFNMPC and ASUKF-NMPC controllers are chosen to be the decision variables of the evaluation problem. The state estimation methods are evaluated in terms of estimation accuracy, system's response time, peak overshoot and control performance. The Level Diagrams tool is used for good visualization of the Pareto fronts to evaluate which estimator performs better in the closed-loop. Finally, the points on the Level Diagrams which provide a performance closest to the desired are selected and tested through simulation runs on the inverted pendulum on a moving cart system.