Analysis And Suppression Of Limit Cycle Oscillation For Servo System With Backlash Nonlinearity

In servo system, the driving part and the driven part are usually connected by a reducing mechnism, which will induce the non-linear backlash inevitably. Once the backlash exists in transmission mechanism, it will lead to stable limit cycle oscillation easily. It will also result in noise, increase wear of mechanical components and reduce the position control accuracy. Accordingly, a comprehensive knowledge of limit cycle characteristics, and appropriate measures to reduce the negative impact of the system with limit cycle bring a very important engineering value and significance. This article takes the two-mass system with backlash as the research object, mainly studying on the limit cycle oscillation caused by nonlinear backlash when the system is operating in the position control loop. Linear state feedback control approach is applied to eliminate limit cycle oscillation, thereby realizing high-precision position tracking performance.Firstly, this paper discusses the modeling methods of nonlinear backlash and selects the typically used dead-zone as the backlash model. From the dynamical process of servo system, two-mass system with backlash is abstracted and then resonant characteristics are obtained. Moreover, this paper discusses the advantage and disadvantage of different position control methods. It is found that the existence of backlash will reduce the control precision of semi-closed loop servo system. And it will also lead to limit cycle oscillation in full-closed loop servo system.Then, the describing function method is used for in-depth analysis. Based on the principles of describing function, the block diagram of the closed loop system can be separated into linear and nonlinear parts. Nyquist criterion is taken as the main theoretical basis to discuss the existence, the number, the stability and other issues of limit cycle within the target system. Then, limit cycle frequency is derived though the mathematical relationship and the influence of different system parameters on the limit cycle is researched.Next, this paper presents the traditional notch filter and the linear state feedback control schemes. And ultimately, the latter one is selected as the core scheme to verify the effectiveness of limit cycle suppression. The core idea of state feedback control is to design the state feedback coefficients based on pole placement method, in order to make the two-mass system equivalnet to one-mass system. Thus, the effect of limit cycle on the system is eliminated and the high-precision position tracking performance is achived. Meanwhile, a third-order Butterworth filter is designed to reduce the noise of the feedback signal, further improving control accruacy.Finally, the limit cycle characteristics analyses and the control method above are verified by the experiments on the backlash platform. In the mechanism analysis part, the theoretical derivation and stability analysis of limit cycle, together with the impact of system parameters on limit cycle are totally verified respectively. While in the limit cycle suppression part, the comparison of the traditional notch filter and state feedback control is given. And on the basis of the latter one, the validity of the method is concluded from different stiffness, backlash values and load torque.