Comparative Study of Linear Control Strategies for Regulation, Tracking of Unstable Systems and the Scope for LQR Infusion in Optimisation Problems

The control of real world systems with inherent instability is an extremely challenging task. This work addresses the control challenges associated with such systems, by exploring various methodologies applied to stabilise an unstable, nonminimum phase, underactuated system within the framework of linear control. The control strategies have been tested on a two Degrees of Freedom (DoF) underactuated system. All the control strategies have been tested in real time and the performance of the strategies have been tabulated. The results highlight the efficacy of Linear Quadratic Regulator (LQR) in stabilising an underactuated unstable system. LQR computes gains that provide robust control for small deviations from the nominal operating point. These gains can be attempted to initialise predictive control based optimisation problems and can help in improving system performance.