Robust Nonminimal State Feedback Control for a Furuta Pendulum With Parametric Modeling Errors

Nonminimal state feedback control, also known as proportional-integral-plus control, together with antiwindup integrator, is applied, for the first time, to stabilize a Furuta pendulum (FP). The key elements in the nonminimal state space (NMSS) state transition matrix is obtained directly from the original minimal state space model. The NMSS model is proved to be controllable if the controllability conditions are met. In order to demonstrate the potential robustness of NMSF control, the controller is designed based on the model with two deliberate plant parameter mismatches. The feedback gains are optimized in an eigenvalue assignment way by minimizing a robust cost function, which is related to the closed-loop state matrix's eigenvalues' sensitivities to the two mismatched plant parameters. The sum of the normalized eigenvalue sensitivities (NES) is defined as cost function. In this article, multiple simulations with different plant parameters are implemented to evaluate the robustness. The optimized FP control system shows smaller envelope of multiple time responses compared to the one before optimization. Experimental results also confirm the optimized controller's improved robustness under parametric mismatches.