Time-Optimal Control of Flexible Robots Made Robust Through Wave-Based Feedback

2010 ◽  
Vol 133 (1) ◽  
Author(s):  
William J. O’Connor ◽  
David J. McKeown
Keyword(s):  
Optimal Control ◽  
Control Strategy ◽  
Robustness Analysis ◽  
Optimal Solution ◽  
Open Loop ◽  
Time Optimal Control ◽  
System Model ◽  
Optimal Control Strategy ◽  
Modeling Errors ◽  
Time Optimal

This paper presents a new, robust, time-optimal control strategy for flexible manipulators controlled by acceleration-limited actuators. The strategy is designed by combining the well-known, open-loop, time-optimal solution with wave-based feedback control. The time-optimal solution is used to design a new launch wave input to the wave-based controller, allowing it to recreate the time-optimal solution when the system model is exactly known. If modeling errors are present or a real actuator is used, the residual vibrations, which would otherwise arise when using the time-optimal solution alone, are quickly suppressed due to the additional robustness provided by the wave-based controller. A proximal time-optimal response is still achieved. A robustness analysis shows that significant improvements can be achieved using wave-based control in conjunction with the time-optimal solution. The implications and limits are also discussed.

scholarly journals An iterative method for time optimal control of dynamic systems

2011 ◽  
Vol 21 (1) ◽  
pp. 5-23 ◽  
Author(s):  
Navvab Kashiri ◽  
Mohammad Ghasemi ◽  
Morteza Dardel
Keyword(s):  
Optimal Control ◽  
Iterative Method ◽  
Dynamic Systems ◽  
Minimum Principle ◽  
Minimum Energy ◽  
Optimal Solution ◽  
Initial Guess ◽  
Open Loop ◽  
Time Optimal Control ◽  
Time Optimal

An iterative method for time optimal control of dynamic systemsAn iterative method for time optimal control of a general type of dynamic systems is proposed, subject to limited control inputs. This method uses the indirect solution of open-loop optimal control problem. The necessary conditions for optimality are derived from Pontryagin's minimum principle and the obtained equations lead to a nonlinear two point boundary value problem (TPBVP). Since there are many difficulties in finding the switching points and in solving the resulted TPBVP, a simple iterative method based on solving the minimum energy solution is proposed. The method does not need finding the switching point so that the resulted TPBVP can be solved by usual algorithms such as shooting and collocation. Also, since the solution of TPBVPs is sensitive to initial guess, a short procedure for making the proper initial guess is introduced. To this end, the accuracy and efficiency of the proposed method is demonstrated using time optimal solution of some systems: harmonic oscillator, robotic arm, double spring-mass problem with coulomb friction and F-8 aircraft.

Observer-based time-optimal control of an aerobic SBR for chemical and petrochemical wastewater treatment

2000 ◽  
Vol 42 (5-6) ◽  
pp. 163-170 ◽  
Author(s):  
A. Vargas ◽  
G. Soto ◽  
J. Moreno ◽  
G. Buitrón
Keyword(s):  
Optimal Control ◽  
Reaction Time ◽  
Control Strategy ◽  
Optimal Operation ◽  
Time Optimal Control ◽  
Nonlinear Observer ◽  
Synthetic Wastewater ◽  
Optimal Control Strategy ◽  
Time Optimal ◽  
High Concentrations

The present study implements a time-optimal control strategy for a discontinuous aerobic bioreactor, used to treat highly concentrated toxic wastewater present in some effluents of the chemical and petrochemical industries, using respirometric techniques. The control strategy regulates the feed rate to maintain a constant optimal substrate concentration in the reactor, which in turn minimizes the reaction time. Since this control requires on-line knowledge of unmeasurable variables, an Extended Kalman Filter is used as a nonlinear observer. The experimental setup was a 7 litre laboratory bioreactor used to treat synthetic wastewater with high concentrations of 4-chlorophenol. The controller consisted of a personal computer with data acquisition hardware and real-time software tools, peristaltic pumps and an electronic oxygen meter. Three experiments were performed: one to obtain parameters and calibrate the observer, another one to validate the time-optimal strategy and a final one to evaluate theperformance of a fully automated time-optimal operation. When well calibrated, the observer provided good enough estimates and the controller worked as expected, reducing reaction time and increasing the overall efficiency of the bioreactor, when compared with the usual SBR-type operation.

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