Adaptive Output Feedback Control for Nonminimum Phase Systems
A non-minimum phase system in general imposes fundamental limitations on achievable performance and poses challenges to nonlinear control methods due to its unstable zero dynamics. In this research, a linear controller that takes into account of unstable zero dynamics is augmented by a NN to compensate for a matched portion of system uncertainties.
Experiments
An inverted pendulum is regulated by a baseline LQG controller, which is augmented by a NN. The LQG controller that is low-gain fails to stabilize the inverted pendulum. However, the controller augmented by a NN successfully stabilizes the system. The main uncertainties in the system include actuation nonlinearity due to gearing mechanism and friction.
* A LQG controller with a NN augmented, movie (13.7 MB)
Simulations
The approach is also extended to a multi-input multi-output (MIMO) system. In simulations, the cart on which the inverted pendulum mounted is connected by a spring and a damper to another cart. The third cart represents unmodeled dynamics.
Extensions to decentralized control
The control methodology is further extended to a decentralized setting in which each pendulum is independently regulated by its own controller without any communication between subsystems. It is assumed, however, that each subsystem share information regarding the desired behavior of the overall system.