Nonlinear PD control for trajectory tracking with consideration of the design for control methodology

Contour tracking control in position domain

“…The stability analysis will be based on Eq. (20), and it will show in next section the convergence of the proposed position domain PD control regardless the sign of the speed of the X-axis motion. From Eq.…”

“…To solve this problem and avoid the noise occurred in the speed, we can modify the control law by using the sampling distance of the master motion as follows: F y ðxÞ ¼ K py ðy d ðtÞ À yðtÞÞ þ K dy Dx ðy d ðtÞ À yðtÞ À ðy d ðt À DtÞ À yðt À DtÞÞÞ 21) can be viewed as a varying sampling rate PD control in the time domain [12]. Also, the position domain PD control law can be viewed as a nonlinear PD control in the time domain [20] when the speed of X-axis is not constant.…”

“…It is clearly shown that the position domain linear PD control[18][19][20] is equivalent to a nonlinear PD control in time domain when the speed of the X-axis is not constant. The dynamic model in position domain Eq.…”

Sequential Co-Design of an Artifact and its Controller Via Control Proxy Functions

“…In robotic applications, typical objectives for the artifact design are minimizing weight or minimizing deflection. Controller objectives may be minimizing tracking errors for a particular trajectory, overshoot, or settling time [Ouyang et al (2002)]. In these problems, speed and accuracy are in conflict; mechanisms with lower inertia are more flexible, resulting in a fast response but lower accuracy, while a higher inertia will produce a stiffer mechanism that is more accurate but results in lower speeds [Zhu et al (2001)].…”

Nonlinear adaptive task space control for a 2-DOF redundantly actuated parallel manipulator

“…In the kinematic control strategies, parallel manipulators are decoupled into a group of single-axis systems, so they can be controlled by a group of individual controllers. Proportional-Derivative (PD) control [1,2], nonlinear PD control [3,4], and artificial-intelligence based control [5,6] belong to this type of control strategies. The nonlinear dynamics is not considered in these controllers, so the complex computation of dynamics can be avoided and the controller design can be simplified considerably.…”