| Fractional order calculus based on the integer order calculus is the extension ofinteger order calculus. It makes calculus no longer have the limitation of finitedimensional space. In recent years, fractional controller is more and more pop ular incontrol area because of its good control performance and robustness. This paper ismainly about the application of fractional order controller in servo system withfrictional characteristic.This paper first analyses the complicated friction characteristic of ultra-lowspeed tracking servo system. Servo system is the most common control system, butwhen it comes to the condition of ultra-low speed, the friction of servo systembecomes very complicated. Thus, the traditional friction model can not meet therequirement of servo system with ultra-low speed. Then, a refined friction modelwhich is easy to build and has a clear mathematical meaning that can reflect thecomplication of friction effect of servo system with ultra-low speed has beenproposed.Secondly, this paper is focus on the design of fractional order controller inservo system control issues. Two kinds of fractional order controllers have beendesigned: one is FOPD controller, the other one is PDμcontroller satisfying theH∞-norm. Several integer order controllers have been designed based on theITAE-norm. A conclusion has been achieved that fractional order controllers haveadvantages over integer order controllers for servo system control issues.Thirdly, this paper uses describing function method to explain the reason ofwhy the fractional order controllers outperform the integer order controllers.Furthermore, a new way of uncoupling the linear and nonlinear sections has beenput forward for the study of ultra-low speed servo system.At last, many simulations with different input signals have been compared totestify that servo system with fractional order controllers have a better performancethan that with integer order controllers in tracking performance and systemrobustness. |
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