On the Optimal Digital State Vector Feedback Controller With Integral and Preview Actions

1979 ◽  
Vol 101 (2) ◽  
pp. 172-178 ◽  
Author(s):  
Masayoshi Tomizuka ◽  
Dan E. Rosenthal
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Optimal Control Theory ◽  
State Vector ◽  
Feedback Controller ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Future System ◽  
Control Situations ◽  
Quadratic Optimal Control

A digital state vector feedback controller with integral and preview actions, which can be called a proportional plus integral plus derivative plus preview (PIDP) controller, is derived based on linear quadratic optimal control theory. The preview action is a generalization of the feedforward concept which has been exercised in many process control situations. Preview of future system disturbance inputs is shown to be effective to improve the performance of the control system.

The Design of High-Speed Dwell-Rise-Dwell Cams Using Linear Quadratic Optimal Control Theory

1994 ◽  
Vol 116 (3) ◽  
pp. 867-874 ◽  
Author(s):  
B. C. Fabien ◽  
R. W. Longman ◽  
F. Freudenstein
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Optimal Control Theory ◽  
High Speed ◽  
Numerical Procedure ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Trajectory Sensitivity ◽  
Cam Design ◽  
Quadratic Optimal Control

This paper uses linear quadratic optimal control theory to design high-speed Dwell-Rise-Dwell (D-R-D) cams. Three approaches to D-R-D cam design are compared. In the first approach the cam is designed to be optimal at a fixed operating speed, i.e., a tuned cam design is obtained. In the second approach the cam profile is determined by minimizing a sum of quadratic cost functions over a range of discrete speeds, thus producing a cam-follower system which is optimal over a range of speeds. The third technique uses trajectory sensitivity minimization to design a cam which is insensitive to speed variations. All design methods are formulated as linear quadratic optimal control problems and solved using an efficient numerical procedure. It is shown that the design techniques developed can lead to cams that have significantly lower peak contact stress, contact force and energy loss when compared to a polydyne cam design. Furthermore, the trajectory sensitivity minimization approach is shown to yield cams that have lower residual vibration, over a range of speeds, when compared to a polydyne cam design.

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