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.

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.

scholarly journals Minimizing Energy Cost in Electric Arc Furnace Steel Making by Optimal Control Designs

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Er-wei Bai
Keyword(s):  
Optimal Control ◽  
Production Cost ◽  
Control Design ◽  
Electric Arc Furnace ◽  
Electric Arc ◽  
Arc Furnace ◽  
Feedback Form ◽  
Steel Making ◽  
Furnace Steel ◽  
Control Designs

Production cost in steel industry is a challenge issue and energy optimization is an important part. This paper proposes an optimal control design aiming at minimizing the production cost of the electric arc furnace steel making. In particular, it is shown that with the structure of an electric arc furnace, the production cost which is a linear programming problem can be solved by the tools of linear quadratic regulation control design that not only provides an optimal solution but also is in a feedback form. Modeling and control designs are validated by the actual production data sets.

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].

Optimal Control Design for Nonlinear Systems with Disturbances

2011 ◽  
Vol 130-134 ◽  
pp. 3672-3676
Author(s):  
De Zhi Zhan
Keyword(s):  
Optimal Control ◽  
Nonlinear Systems ◽  
Controller Design ◽  
Infinite Horizon ◽  
Control Design ◽  
Original System ◽  
Optimal Controller ◽  
Augmented System ◽  
Performance Indexes ◽  
Quadratic Performance

This paper considers the optimal control design problem for nonlinear systems with composite disturbances. First, the original system is transformed into an augmented system without disturbances. Then with respect to the quadratic performance indexes of infinite horizon, we design an optimal controller for the augmented plant without disturbances. Thus the disturbances can unfold of the signal through the Taylor series for the form of polynomial function of time, and obtain optimal controller design approach to eliminate the general disturbance. Finally, a practical example is given to illustrate the effectiveness of the theory.

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