Comparison between ultra-local model and auto-tuning PID controls strategies applied to the redundant manipulator robot for several inputs

Smooth motion profile for trajectory planning of a flexible manipulator

“…Take for example the case of the fifth-polynomial motion profile detailed in [19], by comparing this motion profile with that of our case (seventh-polynomial motion profile), we note that the first profile whose acceleration curve contains fluctuations requires more time to reach the desired endpoint while the second profile whose acceleration curve does not contain any fluctuation allows reaching the desired endpoint in a minimum time. Hence, it can be said that the seventhpolynomial motion profile is optimal in time with respect to the fifth-polynomial motion profile for example.…”

“…In the third step, the estimation of F is performed using an on-line estimation approach called an algebraic derivation method ( [18], [19]) which is given by…”

Improvement of Ultra-local Model Control Using the Auto-tuning PID Control Applied to Redundant Manipulator Robot

“…where: - is the opposite of one of the poles. As described in [18], by comparing the Auto-tuning PID and the ultra-local model control strategies, it is clear that, in presence of flexible structure, the second strategy of control is more robust than the first one.…”

“…Based on [18] and after imposing  , the estimation of the function M can be obtained using the knowledge of the estimation of the derivative   Ot , the control input…”

“…On the basis of the previous process of calculation and using the approach proposed by Fliess and Join [18], the desired closed-loop performances for 1   can be obtained thanks to a simple PID controller calculated in [3]. The expression of the control signal can be deduced as follows:…”