Evaluation of tracking performance of NPID double hyperbolic controller design for XY table ball-screw drive system

摘要

This paper presents design and evaluation of a Nonlinear PID (NPID) Double Hyperbolic controller to improve tracking performance under the influence of disturbance forces in machine tools application. Popov stability criterion was applied in order to obtain the nonlinear proportional and the nonlinear integral gains for the controller. The nonlinear proportional component was designed by applying smaller gains when error magnitude produced is small. In contrast, the nonlinear integral was designed such that higher gain was applied when larger error is produced. Meanwhile, the derivative gain acts as a linear control. The performance of this controller was evaluated based on maximum tracking error and root mean square of the errors (RMSE). In order to verify the robustness of this controller, cutting forces measured at 1500 rpm spindle speed was inserted as input disturbance signal. Reference signal of magnitude 15 mm and at frequencies of 0.2 Hz and 0.4 Hz were applied. Results showed that NPID Double Hyperbolic controller has superior performance than conventional PID controller. The error reductions in term of RMSE values between both controllers during experimental work were 94.79% and 96.50% at 0.2 Hz and 0.4 Hz, respectively.