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.

Three-Stage Feedback Controller Design With Applications to Three Time-Scale Linear Control Systems

2017 ◽  
Vol 139 (10) ◽  
Author(s):  
Verica Radisavljevic-Gajic ◽  
Milos Milanovic ◽  
Garrett Clayton
Keyword(s):  
Time Scale ◽  
State Feedback ◽  
Controller Design ◽  
Feedback Controller ◽  
New Technique ◽  
Feedback Controllers ◽  
Linear Dynamic ◽  
Subsystem Level ◽  
Full State ◽  
Full State Feedback

This paper presents a new technique for design of full-state feedback controllers for linear dynamic systems in three stages. The new technique is based on appropriate partitioning of the linear dynamic system into linear dynamic subsystems. Every controller design stage is done at the subsystem level using only information about the subsystem (reduced-order) matrices. Due to independent design in each stage, different subsystem controllers can be designed to control different subsystems. Partial subsystem level optimality and partial eigenvalue subsystem assignment can be achieved. Using different feedback controllers to control different subsystems of a system has not been present in any other known linear full-state feedback controller design technique. The new technique requires only solutions of reduced-order subsystem level algebraic equations. No additional assumptions were imposed except what is common in linear feedback control theory (the system is controllable (stabilizable)) and theory of three time-scale linear systems (the fastest subsystem state matrix is invertible)). The local full-state feedback controllers are combined to form a global full-state controller for the system under consideration. The presented results are specialized to the three time-scale linear control systems that have natural decomposition into slow, fast, and very fast subsystems, for which numerical ill conditioning is removed and solutions of the design algebraic equations are easily obtained. The proposed three-stage three time-scale feedback controller technique is demonstrated on the eighth-order model of a fuel cell model.

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

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.

scholarly journals Robust Full State Feedback Controller Design Using H∞ for Inverted Pendulum System

2018 ◽  
pp. 39-48
Keyword(s):  
State Feedback ◽  
Inverted Pendulum ◽  
Controller Design ◽  
Upright Position ◽  
Feedback Controller ◽  
Pendulum System ◽  
Integral Term ◽  
Inverted Pendulum System ◽  
Full State ◽  
Full State Feedback

This paper presents the design of a full state feedback H∞ controller to an inverted pendulum system. The nonlinear and linearized models of the system are obtained. The main goal of the proposed controller is to maintain the pendulum in the upright position and achieve a desirable tracking for the cart position. To achieve desirable tracking properties an integral term is added. The robustness of the proposed controller is examined when a 20% variation in the parameters of system is considered.

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