Output predictive adaptive control of a single-link flexible arm

Tip position control of flexible single‐link manipulators in the frequency domain without model reduction

“…The gravity effects are neglected and the elastic deformations are considered to be small. Then, according to works reported in the literature (e.g., References 4,11,38,and 41), the governing dynamic equations of the manipulator can be described as…”

“…[26][27][28][29][30][31][32][33][34] After deriving a truncated model, different approaches were utilized to control the tip position where most of them consist of two control loops. These control approaches include proportional-integral-derivative (PID) and sliding mode, 5 proportional-derivative (PD) and state feedback, 6 pole placement using optimization, 7 linear quadratic Gaussian (LQG) and sliding mode, 8 sliding mode, 9,17,19,21 predictive adaptive, 11 PID and input-state linearization, 12,20,22 nonlinear H ∞ , 13,16 neural network, 14 indirect nonlinear adaptive, 15 input-output inversion and PD, 18 PD and adaptive, 23 PID and fractional-order, 26,27 PD and integral resonant, 28 resonant control and a high-gain integral control, 29 state feedback, 30 pole and zero placement using two output feedbacks, 31 linear H ∞ , 32 LQG and H ∞ , 33 and LQG. 34 The control methods based on a reduced-order model may result in instability of a practical flexible manipulator due to neglecting the higher order modes of vibrations (spillover phenomenon 35 ).…”

“…Due to the complexity of infinite‐dimensional systems, the published works on the tip position control approximated the model of a flexible single‐link manipulator system with a reduced‐order model using such methods as assumed mode (see References 5–11 for linear models and References 12–18 for nonlinear models), lumped mass, 19–24 and finite element 25 . Besides these methods, because of theoretical and practical simplicity of analyzing and designing output feedback control systems in the frequency domain and also lack of proper tools to analyze the infinite‐dimensional models in the frequency domain, many other works approximated the model by a finite order transfer function 26–34 …”

Experiments in Control of a Flexible-Link Robotic Manipulator With Unknown Payload Dynamics: An Adaptive Approach

“…Although other researchers have explored selftuning regulators for the control of flexible-link robotic manipulators (Rovner and Franklin 1988;Tzes and Yurkovich 1991;Cetinkunt and Wu 1991;Koivo and Lee 1992), their work has focused on identifying a complete robot assembly, assuming that the payload is known to be a rigid body. One group (Carton et al 1989) addressed the issue of payload dynamics but only from the standpoint of low-performance robust control.…”

Control of a very flexible robot in gravity

“…17 shows the 64% mass loaded end point response. The end point has significant overshoot and the response has not settled after 5 seconds.…”