scholarly journals A novel order reduction procedure for linear time invarient interval systems using SGO algorithm

2018 ◽  
Vol 7 (1.8) ◽  
pp. 118
Author(s):  
Vijaya Anand N ◽  
Siva Kumar M ◽  
Srinivasa Rao R
Keyword(s):  
Linear Time ◽  
Optimal Solution ◽  
Order Reduction ◽  
Order System ◽  
Time Interval ◽  
Motor Speed ◽  
Interval Model ◽  
Seventh Order ◽  
Social Group Optimization ◽  
Interval Systems

In this paper, the authors presented a new algorithm for the reduction of high order linear time interval systems. In the proposed method, the Reduced Order Interval Model (ROIM) denominator and numerator polynomials are determined based on minimization ofobjective function comprising of Integral Squared Error r using Social Group Optimization (SGO). The SGO technique is found to be simple, easy in implementation and provides the optimal solution. Applicability and effectiveness of the proposed method are illustrated through a DC motor speed control system and a typical Seventh order system taken from the literature.

A novel reduced order modeling of interval system using soft computing optimization approach

2018 ◽  
Vol 232 (7) ◽  
pp. 879-894 ◽  
Author(s):  
N Vijaya Anand ◽  
M Siva Kumar ◽  
R Srinivasa Rao
Keyword(s):  
Soft Computing ◽  
Linear Time ◽  
Optimization Technique ◽  
Order Reduction ◽  
Recursive Formula ◽  
Time Interval ◽  
Optimization Approach ◽  
Order Interval ◽  
Interval Model ◽  
Reduced Order

This research article presents a novel algorithm for the model order reduction of higher order linear time interval systems using soft computing optimization approach. In the proposed method, a new recursive formula for alpha parameters is developed for determining reduced order interval model without formulating alpha and beta tables. The denominator and numerator polynomials of reduced order interval model are determined based on minimization of a multi-objective function comprising integral squared error and impulse response energy error using particle swarm optimization technique. The proposed algorithm has several advantageous features such as reduced computational complexity and stability preservation property. The efficacy of the proposed algorithm is illustrated through typical numerical examples available in the literature, and the results are successfully compared with the other familiar methods.

Order Reduction and Control of Large-Scale Linear Time Periodic Dynamical Systems

1999 ◽  
Author(s):  
Venkatesh Deshmukh ◽  
S. C. Sinha
Keyword(s):  
Large Scale ◽  
Linear Time ◽  
Parametric Instability ◽  
Order Reduction ◽  
System Stability ◽  
Order System ◽  
Control Laws ◽  
Reduced Order ◽  
Time Invariant ◽  
Time Periodic

Abstract This paper provides methodology for designing reduced order controllers for large-scale, linear systems represented by differential equations having time periodic coefficients. The linear time periodic system is first converted into a form in which the system stability matrix is time invariant. This is achieved by the application of Liapunov-Floquet transformation. Then a system called an auxiliary system is constructed which is a completely time invariant. Order reduction algorithms are applied to this system to obtain a reduced order system. The control laws are calculated for the reduced order system by minimizing the least square error between the auxiliary and the transformed system. These control laws when transformed back to time varying domain provide the desired control action. The schemes formulated are illustrated by designing full state feedback and output feedback controllers for a five mass inverted pendulum exhibiting parametric instability.

Complementary Sensitivity Design of PID Controllers for Arbitrary-Order Transfer Functions With Time Delay

2008 ◽  
Author(s):  
Tooran Emami ◽  
John M. Watkins
Keyword(s):  
Time Delay ◽  
Transfer Functions ◽  
Linear Time ◽  
Order System ◽  
Pid Controllers ◽  
Single Input Single Output ◽  
Linear Time Invariant ◽  
Single Output ◽  
Plant Transfer ◽  
Time Invariant

A graphical technique for finding all proportional integral derivative (PID) controllers that stabilize a given single-input-single-output (SISO) linear time-invariant (LTI) system of any order system with time delay has been solved. In this paper a method is introduced that finds all PID controllers that also satisfy an H∞ complementary sensitivity constraint. This problem can be solved by finding all PID controllers that simultaneously stabilize the closed-loop characteristic polynomial and satisfy constraints defined by a set of related complex polynomials. A key advantage of this procedure is the fact that it does not require the plant transfer function, only its frequency response.

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