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.

Closed-loop system disturbance recovery

2003 ◽  
Vol 217 (6) ◽  
pp. 631-649 ◽  
Author(s):  
R Whalley ◽  
M Ebrahimi
Keyword(s):  
Closed Loop ◽  
Low Frequency ◽  
Closed Loop Control ◽  
Multivariable System ◽  
Closed Loop System ◽  
Outer Loop ◽  
Loop Control ◽  
Passive Network ◽  
Loop Tuning ◽  
Reference Input

The regulation of linearized multivariable system models, following input set point and load disturbance changes, is considered. An inner and outer closed-loop control strategy is outlined, enabling targeted recovery rates, offset attenuation and low steady state interaction to be achieved. Proportional control and passive network compensation alone are employed. Gain ratio selection and outer loop tuning are exercised, ensuring thereby the confinement of output perturbations to low-frequency load disturbances and reference input changes. Application studies are presented for purposes of comparison.

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.

Three-dimensional suboptimal guidance law based on θ – D technique and nonlinear disturbance observer

2019 ◽  
Vol 233 (14) ◽  
pp. 5122-5133
Author(s):  
Chaoyuan Man ◽  
Rongjie Liu ◽  
Shihua Li
Keyword(s):  
Disturbance Observer ◽  
Three Dimensional ◽  
Guidance System ◽  
Nonlinear Disturbance Observer ◽  
Guidance Law ◽  
Quadratic Performance Index ◽  
Unknown Disturbances ◽  
Quadratic Performance ◽  
Nonlinear Disturbance ◽  
Hamilton Jacobi Bellman

In this paper, a nonlinear suboptimal guidance system is presented for the missile targeting an unknown arbitrary target. An integrated quadratic performance index is minimized in this guidance law, and the whole design is based on the exact 3D nonlinear missile-target dynamics without any linearization. Considering that the Hamilton–Jacobi–Bellman equation of a nonlinear system is quite difficult to be solved, the [Formula: see text] method is used to obtain the approximate solution without complicated online computations. Moreover, the target accelerations are regarded as the unknown disturbances, and the robustness against the target maneuvering and the external disturbances is enhanced by introducing the feedforward compensation based on the nonlinear disturbance observer. In addition, no priori knowledge like the time-to-go is needed in this suboptimal guidance law. Simulation studies show that the proposed composite guidance system can guarantee that the missile intercepts the arbitrary maneuvering target with satisfied performance.

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 Indefinite LQ Problem for Irregular Singular Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Qingxiang Fang ◽  
Jigen Peng ◽  
Feilong Cao
Keyword(s):  
Optimal Control ◽  
Riccati Equation ◽  
State Feedback ◽  
Closed Loop ◽  
Singular Systems ◽  
Algebraic Riccati Equation ◽  
Closed Loop System ◽  
State Pair ◽  
Lq Problem ◽  
Control State

The indefinite LQ problem for irregular singular systems is investigated. Under some general conditions, the optimal control-state pair is obtained by solving an algebraic Riccati equation. The optimal control is synthesized as state feedback. All the finite poles of the closed-loop system are located on the left-half complex plane. An example is given to show the validity of the proposed conclusion.

scholarly journals The Design of Frequency Filters of Iterative Feedback Tuning Using Particle Swarm Optimization

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Arman Sharifi
Keyword(s):  
Particle Swarm Optimization ◽  
Closed Loop ◽  
Particle Swarm ◽  
Weighting Coefficient ◽  
Swarm Optimization ◽  
New Approach ◽  
Quadratic Performance Index ◽  
Quadratic Performance ◽  
Iterative Feedback

Iterative feedback tuning (IFT) is a data-based tuning approach that minimizes a quadratic performance index using some closed-loop experimental data. A control weighting coefficient, known as lambda, and two frequency filters are the most important parameters which can significantly improve the performance of the method. One of the major problems in IFT is tuning these parameters. This paper presents a new approach to tune frequency filters using particle swarm optimization (PSO). At the end, the performance of the proposed method is evaluated by two case study simulations.

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].

scholarly journals Active Vibration Control of PID Based on Receptance Method

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Lijuan Peng ◽  
Jian Wang ◽  
Guicheng Yu ◽  
Zuoxue Wang ◽  
Aijun Yin ◽  
...  
Keyword(s):  
Vibration Control ◽  
Closed Loop ◽  
Damping Ratio ◽  
Active Vibration Control ◽  
Loop System ◽  
Closed Loop System ◽  
Integral Control ◽  
Active Vibration ◽  
Receptance Method ◽  
Poles And Zeros

Active vibration control approaches have been widely applied on improving reliability of robotic systems. For linear vibratory systems, the vibration features can be altered by modifying poles and zeros. To realize the arbitrary assignment of the closed-loop system poles and zeros of a linear vibratory system, in this paper, an active PID input feedback vibration control method is proposed based on the receptance method. The establishment and verification of the proposed method are demonstrated. The assignable poles during feedback control are calculated and attached with importance to expand the application of the integral control. Numerical simulations are conducted to verify the validity of the proposed method in terms of the assignment of closed-loop poles, zeros, and both. The results indicate that the proposed method can be used to realize the active vibration control of closed-loop system and obtain the desired damping ratio, modal frequency, and dynamic response.

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