Sliding Mode Observers for Rotational Robotics Structures

摘要

This work presents some aspects regarding modelling and control of some robotics rotational experiments: flexible beam and inverted pendulum experiments. The experiments were realised using WinConTM application that allows running code generated from a Simulink diagram in real-time. For the model describing the flexible beam experiment the control goal was to achieve the flexible beam position control and to damp the arm vibrations. The inverted pendulum experiment objective was to design a feedback control system that positions the arm as well as maintains the inverted pendulum vertical. Both experiments are highly nonlinear and consequently, the real mathematical models of the systems are very complicated, so for control purpose simplified models were used. Using the formulas of the kinetic and potential energies, from the generalized dynamic equations one obtained approximated linear models expressed by ordinary differential equations. Nonlinear systems model imprecision compensation and perturbations rejection were achieved using the robust controllers design. The LQG/LTR method was used in order to obtain feedback controllers for the benchmark robotic experiments. The aim of these controllers is to achieve robust stability margins and good performance in step response of the system. LQG/LTR method is a systematic design approach based on shaping and recovering open-loop singular values. The control strategies required the use of all state variables. Many of the proposed control strategies suppose that the state variables are available; this fact is not always true in practice so, it was necessary to design a state observer. The LQG/LTR control method and the modified Utkin SMO were designed and implemented. Sliding mode observers differ from more traditional observers e.g. Luenberger observers, in that there is a non-linear discontinuous term injected into the observer depending on the output estimation error. These observers are much more robust than Luenberger observers, as the discontinuous term enables the observer to reject disturbances. The Lyapunov based SMO (the so-called Walcott-Zak observer) provides exact estimation for certain class of nonlinear systems under existence of certain class of uncertainties. The difficulty in finding the design and gain matrices is the main drawback of this observer. A negative output feedback term was added to each equation of the Utkin observer and this result in a new error system. The addition of a Luenberger type gain matrix, feeding back the output error, yields the potential to provide robustness against certain classes of uncertainty. The problem considered was that of reconstructing the state variables using only measured output information. For the flexible beam experiment a LQG/LTR controller was developed in order to achieve the flexible link position control and to damp the arm vibrations. The LQG/LTR controller uses the state estimations from a sliding-mode observer. A lot of experiments using the Quanser rotational experiments show that the modified Utkin sliding-mode observer provides better results than the classical Utkin sliding-mode observer. The results show also good angle reference tracking and vibration suppression. For the inverted pendulum experiment a LQG/LTR controller was developed also in order to maintain it upright. The non-measurable state variables are obtained using the modified Utkin SMO. The robustness of the controller is tested to some perturbations. The efficiency of the control-observer