Reduced Order Observer Design with DMPC and LQR for System with Backlash Nonlinearity

In this paper, the robust optimal control strategies discrete model predictive control (DMPC) and linear quadratic regulator (LQR) are proposed to solve the problem of backlash nonlinearity present in the two mass system. The DMPC and LQR need information of all the states within the system, so the role of observers become significant, also by doing so the cost on sensors can also be reduced. Here, we have used the full-order observer (FOO) and reduced order observer (ROO) for the state estimation. The FOO estimates all the states within the system, including the measured state, while ROO estimates only those states, those are not measured by the sensors, hence reducing the computations in the closed-loop system. In simulations, the comparisons have been presented between the two control schemes and also between ROO and FOO. From simulations, it is quite clear that the DMPC performance is much better than LQR, while suppressing oscillations due to the presence of backlash in the system. The advantage of using ROO over FOO is that the settling time is reduced, while achieving tracking.

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