scholarly journals LCToolbox: Facilitating Optimal Linear Feedback Controller Design

2020 ◽  
Vol 9 (2) ◽  
pp. 109-116
Author(s):  
Jan Swevers ◽  
Laurens Jacobs ◽  
Taranjitsingh Singh ◽  
Dora Turk ◽  
Maarten Verbandt ◽  
...  
Keyword(s):  
Controller Design ◽  
Feedback Controller ◽  
Linear Feedback ◽  
Linear Feedback Controller ◽  
Optimal Linear

Three-Stage Feedback Controller Design With Applications to a Three Time-Scale System

2016 ◽  
Author(s):  
Verica Radisavljevic-Gajic ◽  
Milos Milanovic
Keyword(s):  
Time Scale ◽  
Controller Design ◽  
Feedback Controller ◽  
Linear Feedback ◽  
Feedback Controllers ◽  
Linear Feedback Controller ◽  
Full State ◽  
Full State Feedback ◽  
A New Technique ◽  
Natural Decomposition

A new technique was presented that facilitates design of independent full-state feedback controllers at the subsystem levels. Different types of local controllers, for example, eigenvalue assignment, robust, optimal (in some sense L1, H2, H∞, ...) may be used to control different subsystems. This feature has not been available for any known linear feedback controller design. In the second part of the paper, we specialize the results obtained to the three time-scale linear systems (singularly perturbed control systems) that have natural decomposition into slow, fast, and very fast subsystems. The proposed technique eliminates numerical ill-condition of the original three-time scale problems.

Optimal Linear Feedback Control for a Class of Nonlinear Nonquadratic Non-Gaussian Problems

1991 ◽  
Vol 113 (4) ◽  
pp. 568-574 ◽  
Author(s):  
R. J. Chang
Keyword(s):  
Control System ◽  
Stochastic Systems ◽  
Feedback Controller ◽  
Performance Criteria ◽  
Linear Feedback ◽  
Feedback Gain ◽  
Linear Feedback Controller ◽  
Gaussian Method ◽  
Optimal Linear ◽  
Non Gaussian

An optimal linear feedback controller designed for a class of nonlinear stochastic systems with nonquadratic performance criteria by a non-Gaussian approach is presented. The non-Gaussian method is developed through expressing the unknown stationary output density function as a weighted sum of the Gaussian densities with undetermined parameters. With the aid of a Gaussian-sum density, the optimal feedback gain for a control system with complete state information is derived. By assuming that the separation principle is valid for the class of stochastic systems, a nonlinear precomputed-gain filter is then implemented. The method is illustrated by a Duffing-type control system and the performance of a linear feedback controller designed through both quadratic and nonquadratic performance indices is compared.

Linear feedback controller design method for time-delay chaotic systems

2012 ◽  
Vol 70 (1) ◽  
pp. 355-362 ◽  
Author(s):  
Hua Wang ◽  
Xin Wang ◽  
Xiao-Jin Zhu ◽  
Xiao-Hua Wang
Keyword(s):  
Time Delay ◽  
Chaotic Systems ◽  
Controller Design ◽  
Design Method ◽  
Feedback Controller ◽  
Linear Feedback ◽  
Linear Feedback Controller

Stability Analysis and Controller Design for Linear Time Periodic Systems Using Normal Forms

2020 ◽  
Author(s):  
Susheelkumar C. Subramanian ◽  
Sangram Redkar
Keyword(s):  
Stability Analysis ◽  
Normal Forms ◽  
Controller Design ◽  
Linear Time ◽  
Identity Transformation ◽  
Feedback Controller ◽  
Linear Feedback ◽  
Periodic Systems ◽  
Linear Feedback Controller ◽  
Time Periodic

Abstract The investigation of stability bounds for linear time periodic systems have been performed using various methods in the past. The Normal Forms technique has been predominantly used for analysis of nonlinear equations. In this work, the authors draw comparisons between the Floquet theory and Normal Forms technique for a linear system with time periodic coefficients. Moreover, the authors utilize the Normal Forms technique to transform a linear time periodic system to a time-invariant system by using near identity transformation, similar to the Lyapunov Floquet (L-F) transformation. The authors employ an intuitive state augmentation technique, modal transformation and near identity transformations to enable the application of time independent Normal Forms directly without the use of detuning or book-keeping parameter. This method provides a closed form analytical expression for the state transition matrix with the elements as a function of time. Additionally, stability analysis is performed on the transformed system and the resulting transitions curves are compared with that of numerical simulation results. Furthermore, a linear feedback controller design is discussed based on the stability bounds and the implementation of an effective feedback controller for an unstable case is discussed. The theory is validated and verified using numerical simulations of temporal variation of a simple linear Mathieu equation.

Reducing Engine Idle Speed Deviations Using the Internal Model Principle

2006 ◽  
Vol 128 (4) ◽  
pp. 869-877 ◽  
Author(s):  
Andrew W. Osburn ◽  
Matthew A. Franchek
Keyword(s):  
Internal Model ◽  
Controller Design ◽  
Low Frequency ◽  
Feedback Controller ◽  
Linear Feedback ◽  
Ignition Timing ◽  
Idle Speed ◽  
Internal Model Principle ◽  
Single Output ◽  
Linear Feedback Controller

Presented in this paper is a multivariable linear feedback controller design methodology for idle speed control of spark-ignition engines. The engine is modeled as a multi-input, single-output system. The proposed feedback control system employs both throttle and ignition timing to control engine speed and engine roughness. Throttle is used to attenuate low frequency components of the speed error and reject mean speed errors. Spark advance is used to reduce cylinder-to-cylinder differences in torque production by limiting high frequency speed deviations. The algorithm is executed in the crank-angle domain, and the internal model principle serves as the basis for cylinder torque balancing. The nonlinear relationship between ignition timing and torque production is explicitly incorporated into the design process using a sector bound. A loop shaping approach is proposed to design the feedback controller, and absolute stability of the nonlinear closed-loop system is guaranteed through the Tsypkin Criterion. Experimental results from implementation on a Ford 4.6L V-8 engine are provided.

Observer-Based Feedback Linearizing Control of an Electromagnetic Suspension

1996 ◽  
Vol 118 (3) ◽  
pp. 615-619 ◽  
Author(s):  
B. C. Fabien
Keyword(s):  
Feedback Controller ◽  
Superior Performance ◽  
Linear Feedback ◽  
Nonlinear Controller ◽  
Electromagnetic Suspension ◽  
Weakly Coupled ◽  
Coupled Riccati Equations ◽  
Linear Feedback Controller ◽  
Lyapunov’S Second Method ◽  
Feedback Linearizable Systems

This paper develops a stabilizing observer-based feedback linearizing controller for a single-axis electromagnetic suspension. The controller uses only the measured output of the system, and is shown to be robust with respect to parameter uncertainty. The controller differs from other robust feedback linearizing controllers that have appeared in recent literature, because it is continuous, and non-adaptive. Lyapunov’s second method is used to prove stability and robustness of the controller. The controller has a simple structure and its gains are determined by solving two weakly coupled Riccati equations. Numerical simulations are performed to compare a linear feedback controller and the observer-based feedback linearizing controller. Results obtained demonstrate that the nonlinear controller yields superior performance when compared with the linear feedback controller. The controller synthesis technique developed in this paper is applicable to other fully feedback linearizable systems, not just electromagnetic suspensions.

Robust Controllers for Pulse-Width-Modulated D.C./D.C. Converters Using Internal-Model-Control Design

1993 ◽  
Vol 207 (3) ◽  
pp. 127-134 ◽  
Author(s):  
D Garabandić ◽  
T Petrović
Keyword(s):  
Model Uncertainty ◽  
Pulse Width ◽  
Internal Model ◽  
Controller Design ◽  
Optimization Method ◽  
Internal Model Control ◽  
Linear Feedback ◽  
Pulse Width Modulated ◽  
Linear Feedback Controller ◽  
Model Control

A linear feedback controller for pulse-width-modulated d.c./d.c. regulator is designed using a frequency domain optimization method based on internal-model-control theory. This method aims to produce suboptimal low-order controllers which are ‘robust’, in the sense that the closed-loop system is guaranteed to meet stability objectives in the presence of model uncertainty. The small-signal model of a d.c./d.c. converter is used for the controller design. The model uncertainty description derived here is based on experiments and non-linear modelling. The result of the synthesis is a family of controllers, and each member of this family satisfies the robust control objectives. All controllers have a multi-loop structure including two feedback loops and one feedforward loop. A detailed design of the controller, including experimental results, is presented.

Chaotic Control in a Fractional-Order Modified Van Der Pol Oscillator

2011 ◽  
Vol 474-476 ◽  
pp. 83-88
Author(s):  
Xin Gao
Keyword(s):  
Fractional Order ◽  
Feedback Controller ◽  
Van Der Pol Oscillator ◽  
Linear Feedback ◽  
Fractional Order Systems ◽  
Van Der Pol ◽  
Chaotic Control ◽  
Linear Feedback Controller

The dynamics of fractional-order systems have attracted increasing attention in recent years. In this paper, we study the chaotic behaviors in a fractional-order modified van der Pol oscillator. We find that chaos exists in the fractional-order modified van der Pol oscillator with order less than 3. In addition, the lowest order we find for chaos to exist in such system is 2.4. Finally, a simple, but effective, linear feedback controller is also designed to stabilize the fractional order chaotic van der Pol oscillator.

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