Active Vibration Control of PID Based on Receptance Method

Abstract

Active vibration control approaches have been widely applied on improving reliability of robotic systems. For linear vibratory systems, the vibration features can be altered by modifying poles and zeros. To realize the arbitrary assignment of the closed-loop system poles and zeros of a linear vibratory system, in this paper, an active PID input feedback vibration control method is proposed based on the receptance method. The establishment and verification of the proposed method are demonstrated. The assignable poles during feedback control are calculated and attached with importance to expand the application of the integral control. Numerical simulations are conducted to verify the validity of the proposed method in terms of the assignment of closed-loop poles, zeros, and both. The results indicate that the proposed method can be used to realize the active vibration control of closed-loop system and obtain the desired damping ratio, modal frequency, and dynamic response.

Active Approaches to Vibration Absorption through Antiresonance Assignment: A Comparative Study

“…An extension of the receptance method in the case of the rank-one control has been proposed in [52] to include the integral control action by adopting a formulation of the integral similar to the one previously proposed in [64] for pole placement in flexible link mechanisms with state feedback and integral action. The use of an integral term is widely adopted in positioning control to improve disturbance rejection and reduce steady-state errors; in contrast, it is infrequently adopted whenever the sole goal is assigning poles or zeros, since proportional and derivative (PD) controllers, i.e., position and speed feedback, suffice to perform the assignment.…”

“…The open-loop and closed-loop receptances h 3,3 (jω) are compared in Figure 8 to confirm the fulfilment of the assignment task. The same control task is performed through the state feedback with integral action by solving the system in Equation ( 26) [52] and comparing the results provided pinv and mldivide. The open-loop and closed-loop zeros of receptance h 3,3 (jω) are reported in Table 6; the 2-norm of the control gains are listed in Table 7.…”

“…Method [52] Solved Through Mldivide -−0.0049 -−0.005 ± 0.720 j −0.005 ± 0.720 j −0.005 ± 0.720 j −0.005 ± 1.176 j 0 ± 1.000 j 0 ± 1.000 j −0.005 ± 1.520 j −0.005 ± 1.520 j −0.005 ± 1.520 j −0.005 ± 1.902 j −0.005 ± 1.897 j −0.004 ± The goal of this section is to assign two antiresonances, i.e., two complex conjugate pairs of zeros (0 ± 0.5j and −0.01 ± 1j), in the cross-receptance h 3,4 (jω). For example, let us consider b C = [1, 0, 0, 0, 1, 0] T , which ensures the complete assignability of the receptance zeros.…”

“…This issue is tackled in Section 4.4.3 through the method proposed in [51] to cluster the closed-loop poles to ensure the stability of the closed-loop system. If the integral action is included too, as in [52], both the solutions of Equation ( 26) obtained through mldivide and pinv lead to RHCP poles, as shown in Figure 10. The test case of Section 4.4.2 is solved in this section through the two-stage approach proposed in [51] to ensure that the closed-loop poles must belong to the left half of the complex plane for asymptotic stability, i.e., introducing a LMI with R = 0 and Z = 1 in Equation (25).…”

Workpiece Surface Quality Improvement through Vibration Active Control in Precision Milling Process

“…Reference source not found.- [11]. Among them, PID control [13] is simple, reliable and robust, which is the most extensively applied controller in the industrial processes. However, the parameter adjustment takes tremendous time and experience.…”