The Linear Quadratic Optimal Control Theory for Systems with Delays in State and Control Variables 1

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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A New Approach for Solving Optimal Nonlinear Control Problems Using Decriminalization and Rationalized Haar Functions

Advanced Engineering Forum ◽

10.4028/www.scientific.net/aef.1.387 ◽

2011 ◽

Vol 1 ◽

pp. 387-394 ◽

Cited By ~ 1

Author(s):

Zhen Yu Han ◽

Shu Rong Li

Keyword(s):

Optimal Control ◽

Optimal Control Problems ◽

Nonlinear Optimal Control ◽

Control Problems ◽

State Variables ◽

Linear Quadratic ◽

Control Variables ◽

Linear Quadratic Optimal Control ◽

Haar Functions ◽

And Control

This paper presents a numerical method based on quasilinearization and rationalized Haar functions for solving nonlinear optimal control problems including terminal state constraints, state and control inequality constraints. The optimal control problem is converted into a sequence of quadratic programming problems. The rationalized Haar functions with unknown coefficients are used to approximate the control variables and the derivative of the state variables. By adding artificial controls, the number of state and control variables is equal. Then the quasilinearization method is used to change the nonlinear optimal control problems with a sequence of constrained linear-quadratic optimal control problems. To show the effectiveness of the proposed method, the simulation results of two constrained nonlinear optimal control problems are presented.

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Semi-active control of space manipulator soft contacting based on magnetorheological rotational damper

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406215594827 ◽

2015 ◽

Vol 230 (14) ◽

pp. 2390-2398 ◽

Cited By ~ 1

Author(s):

Xiaoping Du ◽

Hang Chen ◽

Zhengjun Liu ◽

Chao Wang

Keyword(s):

Optimal Control ◽

Control Theory ◽

Active Control ◽

Optimal Control Theory ◽

Passive Control ◽

Control Force ◽

Linear Quadratic ◽

Linear Quadratic Optimal Control ◽

Space Manipulator ◽

Dynamic Formulation

A novel soft contacting technology is proposed to reduce the risks of contacts that space manipulator is on-orbit service. The magnetorheological (MR) rotational damper is considered and utilized for cushioning and vibration reduction in the space manipulator. Based on the extended manipulator model, a linear dynamic formulation of free-floating space manipulator is built. Subsequently, the mechanical property of magnetorheological rotational damper is analyzed by using Bingham model. Then, the optimal control force can be obtained by using the linear quadratic optimal control theory. Finally, the optimal control force is served as the parameters to achieve the semi-active control of soft contacting by employing the clipped optimal control theory. The hard contacting and passive control technology are introduced to make comparison with the results of soft contacting. Some numerical simulations are made to demonstrate the validity and capability of the proposed soft contacting technology.

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

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.3426416 ◽

1979 ◽

Vol 101 (2) ◽

pp. 172-178 ◽

Cited By ~ 79

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.

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