Pointwise-Optimal Control of Robotic Manipulators

1988 ◽  
Vol 110 (2) ◽  
pp. 210-213 ◽  
Author(s):  
S. Tadikonda ◽  
H. Baruh
Keyword(s):  
Optimal Control ◽  
Adverse Effects ◽  
Sampling Period ◽  
Approximate Expression ◽  
Robotic Manipulators ◽  
Joint Angles ◽  
Time Step ◽  
Quadratic Performance Index ◽  
Linear Regulator ◽  
Quadratic Performance

A method is presented for the pointwise-optimal control of robotic manipulators along a desired trajectory. An approximate expression for the manipulator response is used to minimize a quadratic performance index with a linear regulator and tracking criterion, during each sampling period. The delay associated with implementation of the control action is analyzed, and its adverse effects are eliminated by estimation of the joint angles and torques one time step ahead.

Optimization of Weighting Parameters for an Active Suspension System of a Vehicle

2008 ◽  
Author(s):  
Ahmad A. Fayed ◽  
Mohamed B. Trabia ◽  
Mohamed M. ElMadany
Keyword(s):  
Optimal Control ◽  
Performance Index ◽  
Ride Comfort ◽  
Active Suspension ◽  
Suspension System ◽  
Performance Criteria ◽  
Penalty Function Method ◽  
Quadratic Performance Index ◽  
Quadratic Performance ◽  
Optimization Loop

Optimal control schemes are usually employed to minimize different performance criteria of active suspension system of a vehicle such as, ride comfort and road safety. These factors are usually combined into a single quantity using proper weighting parameters that depend on the designer’s preferences. Generally, the selection of these weighting parameters is based on trial and error, which can be a time-consuming and computationally-intensive process. This paper proposes the use of an approach based on nested optimization loops to automate the selection process of these weighting parameters. The objective of the inner optimization loop is to minimize of the quadratic performance index associated with the original active suspension problem while the objective of the outer optimization loop is to minimize driver’s acceleration, for ride comfort, while maintaining both tire deflection and suspension deflection within acceptable limits. The design variables are the weighting parameters associated with the quadratic performance index used in the optimal control of active suspension. A modified form of Hooke-Jeeves algorithm is used to handle this problem while the penalty function method is used to handle the constraints. Simulation results show that this approach can improve the design process for active suspension of vehicles.

Perturbation Analysis of Optimal Integral Controls

1984 ◽  
Vol 106 (1) ◽  
pp. 114-116 ◽  
Author(s):  
G. L. Slater
Keyword(s):  
Optimal Control ◽  
Closed Loop ◽  
Guidance System ◽  
Primary System ◽  
Eigenvalues And Eigenvectors ◽  
Closed Loop System ◽  
Outer Loop ◽  
Integral Control ◽  
Quadratic Performance Index ◽  
Quadratic Performance

The application of linear optimal control to the design of systems with integral control action on specified outputs is considered. Using integral terms in a quadratic performance index, an asymptotic analysis is used to determine the effect of variable quadratic weights on the eigenvalues and eigenvectors of the closed loop system. It is shown that for small integral terms the placement of integrator poles and gain calculation can be effectively decoupled from placement of the primary system eigenvalues. This technique is applied to the design of integral controls for a STOL aircraft outer loop guidance system.

On a Problem of Letov in Optimal Control

1965 ◽  
Vol 87 (1) ◽  
pp. 81-89 ◽  
Author(s):  
C. D. Johnson ◽  
W. M. Wonham
Keyword(s):  
Optimal Control ◽  
Present Note ◽  
Control Variable ◽  
Control Law ◽  
Initial Value ◽  
Bounded Control ◽  
Quadratic Performance Index ◽  
Linear Plant ◽  
Quadratic Performance ◽  
Optimal Regulator

In a series of papers [1, 2], A. M. Letov discussed an optimal regulator problem for a linear plant with bounded control variable and quadratic performance index. This problem was also discussed by Chang [3]. Krasovskii and Letov observed later [4] that the solution proposed in [1, 2, and 3] may be correct only for special choices of the initial value of the state vector. In the present note, further aspects of the solution in the general case are described and three examples are given. The possible existence of a regime of unsaturated-nonlinear optimal control is demonstrated. The presence of this regime in the optimal control law was apparently overlooked in [1–4].

Using Constrained Bilinear Quadratic Regulator for the Optimal Semi-Active Control Problem

2017 ◽  
Vol 139 (11) ◽  
Author(s):  
I. Halperin ◽  
G. Agranovich ◽  
Y. Ribakov
Keyword(s):  
Optimal Control ◽  
Active Control ◽  
Control Design ◽  
Control Signal ◽  
Structural Vibration ◽  
Feedback Form ◽  
Quadratic Performance Index ◽  
Active Feedback ◽  
Quadratic Performance ◽  
Bilinear Quadratic Regulator

Semi-active systems provide an attractive solution for the structural vibration problem. A useful approach, aimed to simplify the control design, is to divide the control system into two parts: an actuator and a controller. The actuator generates a force that tracks a command which is generated by the controller. Such approach reduces the complexity of the control law design as it allows for complex properties of the actuator to be considered separately. In this study, the semi-active control design problem is treated in the framework of optimal control theory by using bilinear representation, a quadratic performance index, and a constraint on the sign of the control signal. The optimal control signal is derived in a feedback form by using Krotov's method. To this end, a novel sequence of Krotov functions which suits the multi-input constrained bilinear-quadratic regulator problem is formulated by means of quadratic form and differential Lyapunov equations. An algorithm is proposed for the optimal control computation. A proof outline for the algorithm convergence is provided. The effectiveness of the suggested method is demonstrated by numerical example. The proposed method is recommended for optimal semi-active feedback design of vibrating plants with multiple semi-active actuators.

Research on Unmanned Aerial Vehicles Autonomous Soft Landing Based on Optimal Control

2012 ◽  
Vol 562-564 ◽  
pp. 1442-1446
Author(s):  
Ze Yin Xu ◽  
Xiao Hu Xia ◽  
Yun Jian Ge
Keyword(s):  
Optimal Control ◽  
Time Varying ◽  
Unmanned Helicopter ◽  
Linear Quadratic ◽  
Soft Landing ◽  
Quadratic Performance Index ◽  
Input Signals ◽  
Model Helicopter ◽  
Output System ◽  
Quadratic Performance

This paper deals with the autonomous soft landing of unmanned helicopter aiming to enhance its application. Soft landing means to reduce the shock force upon ground during the helicopters land. Helicopter is a multi-input multi-output system and for which optimal control provides graceful and coordinated controls. Firstly, the experimental platform configuration for autonomous soft-landing system is introduced, which is based on the model helicopter. The time-varying gains and time-varying quadratic performance index Linear Quadratic control for autonomous soft landing of miniature helicopter is applied to unmanned helicopter. Simulation shows that the outputs of the system can respond the input signals accurately.

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