Representations for the optimal feedback control law for stable hereditary systems

2006 ◽  
pp. 253-271
Author(s):  
Mark H. Milman
Keyword(s):  
Feedback Control ◽  
Optimal Feedback Control ◽  
Control Law ◽  
Optimal Feedback

scholarly journals Design of Optimal Hybrid Position/Force Controller for a Robot Manipulator Using Neural Networks

2007 ◽  
Vol 2007 ◽  
pp. 1-23 ◽  
Author(s):  
Vikas Panwar ◽  
N. Sukavanam
Keyword(s):  
Neural Network ◽  
Feedback Control ◽  
Dynamic Model ◽  
Sliding Mode ◽  
Robot Manipulator ◽  
Optimal Feedback Control ◽  
Control Law ◽  
State Variables ◽  
Bounded Control ◽  
Optimal Feedback

The application of quadratic optimization and sliding-mode approach is considered for hybrid position and force control of a robot manipulator. The dynamic model of the manipulator is transformed into a state-space model to contain two sets of state variables, where one describes the constrained motion and the other describes the unconstrained motion. The optimal feedback control law is derived solving matrix differential Riccati equation, which is obtained using Hamilton Jacobi Bellman optimization. The optimal feedback control law is shown to be globally exponentially stable using Lyapunov function approach. The dynamic model uncertainties are compensated with a feedforward neural network. The neural network requires no preliminary offline training and is trained with online weight tuning algorithms that guarantee small errors and bounded control signals. The application of the derived control law is demonstrated through simulation with a 4-DOF robot manipulator to track an elliptical planar constrained surface while applying the desired force on the surface.

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