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The design of robust computer control systems for balancing and attitude control of double and triple inverted pendulums is considered in this paper. For the double inverted pendulum, a DC motor mounted at the upper hinge is used to balance and control attitude of the upper link. For the triple inverted pendulum a DC motor mounted at the middle hinge is used to control the middle link, whereas proportional position control applied to a motor at the upper hinge is utilised to maintain the upper link in alignment with the middle link. In both cases the lower hinge is left free to rotate. The controller designs are based on linearised discrete-time models of the inverted pendulums. Each controller utilises state feedback implemented via reduced-order state observers. The relative stability properties of the control systems are evaluated using Nyquist plots of suitably defined functions. The controllers are designed using Matlab and implemented in a PC using C language. Experimental results showed satisfactory performance.

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In this paper, a discretization-based sliding mode observer (DBSMO) is proposed for the state and parameter estimation of nonlinear systems. In the DBSMO structure, an accurate discretized dynamics are derived for the state and parameter update of the sliding mode observer (SMO) instead of integration-based state update. In this way, faster converging observer dynamics are obtained. The stability properties of the conventional SMO remain the same for DBSMO. In the application presented here, first a real-time DC/DC power converter is designed with a computer interface. Then, to show the enhancement of convergence properties, conventional SMO and DBSMO-based model predictive controllers are designed and applied to control of the DC/DC power converter. Through simulation and experimental results, it is shown that the estimation performance of SMO is greatly improved so that the tracking performance is also increased, which are the main contributions of the paper.

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