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Research And Implementation Of Fractional Order Sliding Mode Variable Structure Control Based On Rotary Double Inverted Pendulum

Posted on:2013-06-24Degree:MasterType:Thesis
Country:ChinaCandidate:Y GaoFull Text:PDF
GTID:2298330467478448Subject:Pattern Recognition and Intelligent Systems
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Rotary double inverted pendulum system is a typical nonlinear, more variable, high order and unstable underactuated system. As a plant of control system, it can be controlled stably with many theories and methods, like PID control, state feedback control, nonlinear control and so on. However, most of these methods are integer order control, if fractional theory is applied to current these control strategies, the result would be more beautiful. Fractional calculus, that is to say, differential and integral’s order can be arbitrary or fractional. The mathematical model built on fractional differential equation comes into being fractional system. This dissertation designed sliding variable structure controller for the rotary double inverted pendulum and developed it to fractional order system. Because of more adjustable parameters than original and their continuously variable parameter attribution, fractional sliding variable structure control is superior to integer control. This dissertation’s main research contents and innovation can be summarized as follows.(1) Rotary double inverted pendulum system’s structure is introduced, and then on the basis of homogeneous transformation matrix theory among coordinate systems, total potential energy and kinetic energy are obtained. Finally, the mathematical model is derived from Euler-Lagrange’s equation, and is linearized around the balance point. At the same time, system performance is analyzed like stability, controllability and observability.(2) Based on sliding variable structure control basic theory, switch function’s solution is studied and analyzed. Constant switch controller is designed and simulated, but the result displayed serious vibration. So after analyzing the vibration’s cause, the exponential approach law can weaken the vibration and its effectiveness is confirmed by simulation.(3) With the fractional calculus theory as a background, combining fractional order with sliding variable structure control, exponential approach law is improved and fractional exponential approach law controller is designed. Simulation displayed that it is more effective than integral exponential approach law controller, overshoot decreasing, adjusting time shortening, and vibration weakening obviously and importantly.(4) A hardware-in-loop simulation platform is developed and the experiment’s basic operation is studied. In this platform, fractional exponential approach law is experimented and it confirms that it is available, effective and perfect performance.
Keywords/Search Tags:rotary double inverted pendulum, fractional order, sliding variable structure, fractional order exponential approach law, the hardware-in-loop simulation
PDF Full Text Request
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