Digital implementation of a continuous-time nonlinear optimal controller: An experimental study with real-time computations

In this paper, the digital implementation of a continuous-time robust nonlinear optimal controller is presented as an experimental study with real-time computations. Complicated computations, solutions, and algorithms of nonlinear optimal policies were always reported as limits to experimental implementations. This work uses a combination of integral sliding mode control (ISMC) and the state-dependent Riccati equation (SDRE) approach for controlling an experimental setup, a rotary inverted pendulum (RIP) with nonlinear dynamics. Designing in the continuous-time domain and performing an experiment using digital computers are common and that leads to extra tuning in practice. Digital components are considered in simulations to provide a more real output and omit extra tuning. Analysis of sampling time effect on instability of a stable controller was done and the obtained bound of sampling time was verified in the experiment. The experimental study showed that the computations of the proposed controller were able to be programmed into the platform interface with time-varying sampling time which was bounded to the generated sampling time in the simulation. Successful swinging up and stabilization of the RIP demonstrated the effectiveness of the ISMC plus SDRE approach. The comparison of the proposed controller with the solo SDRE controller validated the results and showed the performance of the design.