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UBC Theses and Dissertations

Experimental sliding mode control of a flexible single link manipulator Qian, Timothy W. T.


Employing flexible robot arms is of great importance to the intended enhancement of the performance of current generation robots to achieve higher efficiency. It is also indispensable to space related applications due to various restraining factors in that field. The reason that there is still very scarce usage of flexible arm lies in the difficulties involved in designing and implementing a good controller to achieve the desired performance. Though a wealth of literature has already appeared on this subject, the number of controller design schemes presented has been small. Still fewer are the experimental verifications which are essential to evaluating the real applicability of these designs. The objective of this thesis is to explore and develop practical controller designs based on the variable structure system (VSS) and sliding mode theory, and experimentally test them on a flexible robot arm. A new control design method (VSSMC) is firstly proposed based on the continuous time variable structure sliding mode theory. It can significantly simplify the VSS system designing process. Moreover, the variables concerned can be assigned separate gains. Direct application of the VSSMC to the flexible arm, however, has limitations due to the inherent properties of the system. Though these limitations are overcome by using a bigger sampling period and lower gain, these measures also constrain the maximum achievable response speed and the robustness margin on parameter uncertainties. To deal with the above mentioned problem and facilitate digital implementation and solve the undesirable "chattering" in conventional VSS control, another novel controller design method is developed, i.e., the Discrete-time Quasi-Sliding Mode Control(DQSMC). This design is proposed based on a re-visit to the necessary and sufficient conditions for the existence of the discrete-time sliding hypersurfaces. Two control algorithms are derived satisfying these two conditions. The analysis on these two algorithms results in the development of DQSMC. It is proven that this design is equivalent to a full state feedback with its steady-state motion constrained to the sliding hypersurfaces. It is also shown that the DQSMC method provides a general structure that unifies the three different kinds of discrete-time sliding mode control, i.e., the VSS, the non-VSS and the VSS with a smoothing boundary layer. Experimental testings for the DQSMC controller showed quite good results, thus verifying the effectiveness of the design method. The robustness under load variations is also tested. The experimental results compared favorably against the Linear Quadratic Gaussian (LQG) controller under the same load variations. To realize the proposed new controller designs, a novel approach is devised for these kinds of plants to obtain all the states. Separate first order observers are used to estimate the states that are not directly accessible. The advantages of the method are the simplified observer design processes and easier pole assignments for the observer according to different mode requirements. The designed observers are quite successful in obtaining the desired state estimates. The new control design methodologies developed in this thesis are easy to understand, design and implement. The smoothness in the control signal of DQSMC is especially desirable for applications where one wants to avoid exciting the high frequency un-modeled dynamics. It can be used in many control applications.

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