Discretization of Existing Continuous Control Systems

1997 ◽  
Vol 119 (2) ◽  
pp. 315-318 ◽  
Author(s):  
Somnath Pan ◽  
Jayanta Pal
Keyword(s):  
Frequency Response ◽  
Control Systems ◽  
Closed Loop ◽  
Digital System ◽  
New Method ◽  
Continuous Control ◽  
Algebraic Equations ◽  
Analog System ◽  
Linear Algebraic Equations ◽  
Frequency Response Matching

A new method is presented for discretizing an existing analog controller. The method is based on frequency response matching of the closed-loop digital system with that of the original analog system. The method requires solution of linear algebraic equations and is computationally simple. Efficacy of the method is illustrated through examples taken from the literature.

scholarly journals Hybrid algorithm Newton method for solving systems of nonlinear equations with block Jacobi matrix

2020 ◽  
pp. 208-217
Author(s):  
O.M. Khimich ◽  
◽  
V.A. Sydoruk ◽  
A.N. Nesterenko ◽  
◽  
...  
Keyword(s):  
Nonlinear Equations ◽  
Newton Method ◽  
Jacobi Matrix ◽  
Sparse Matrices ◽  
High Order ◽  
New Method ◽  
Systems Of Nonlinear Equations ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
High Convergence Rate

Systems of nonlinear equations often arise when modeling processes of different nature. These can be both independent problems describing physical processes and also problems arising at the intermediate stage of solving more complex mathematical problems. Usually, these are high-order tasks with the big count of un-knows, that better take into account the local features of the process or the things that are modeled. In addition, more accurate discrete models allow for more accurate solutions. Usually, the matrices of such problems have a sparse structure. Often the structure of sparse matrices is one of next: band, profile, block-diagonal with bordering, etc. In many cases, the matrices of the discrete problems are symmetric and positively defined or half-defined. The solution of systems of nonlinear equations is performed mainly by iterative methods based on the Newton method, which has a high convergence rate (quadratic) near the solution, provided that the initial approximation lies in the area of gravity of the solution. In this case, the method requires, at each iteration, to calculates the Jacobi matrix and to further solving systems of linear algebraic equations. As a consequence, the complexity of one iteration is. Using the parallel computations in the step of the solving of systems of linear algebraic equations greatly accelerates the process of finding the solution of systems of nonlinear equations. In the paper, a new method for solving systems of nonlinear high-order equations with the Jacobi block matrix is proposed. The basis of the new method is to combine the classical algorithm of the Newton method with an efficient small-tile algorithm for solving systems of linear equations with sparse matrices. The times of solving the systems of nonlinear equations of different orders on the nodes of the SKIT supercomputer are given.

scholarly journals Example of polynomial controller synthesis for a non-square object with one input and two outputs

2020 ◽  
pp. 7-20
Author(s):  
Aleksander Voevoda ◽  
◽  
Victor Shipagin ◽  
Keyword(s):  
Control Systems ◽  
Matrix Polynomial ◽  
Controller Synthesis ◽  
Polynomial Method ◽  
Algebraic Equations ◽  
Automatic Control Systems ◽  
Linear Algebraic Equations ◽  
Polynomial Controller ◽  
Polynomial Calculus ◽  
Polynomial Methods

Polynomial methods for synthesizing controllers for automatic control systems with linear objects are becoming increasingly common. The synthesis of multichannel controllers is particularly difficult, which is caused by the need to use matrix polynomial calculus. However, this approach mainly considers objects with the number of inputs equal to the number of outputs. This is due to the convenience of solving a system of linear algebraic equations in matrix polynomial calculus. In this paper, we consider a polynomial method for synthesizing regulators for a non-square object, that is, one whose number of inputs is not equal to the number of outputs. The selected system contains not only a non-square object, but also a non-square controller.

Application of A Spreadsheet Program to Control System Design

1992 ◽  
Vol 29 (1) ◽  
pp. 16-23 ◽  
Author(s):  
Yiu-Kwong Wong
Keyword(s):  
Control System ◽  
Feedback Control ◽  
Frequency Response ◽  
System Design ◽  
Control Systems ◽  
Closed Loop ◽  
Control System Design ◽  
Closed Loop System ◽  
Spreadsheet Program ◽  
Feedback Control Systems

Application of a spreadsheet program to control system design The Symphony spreadsheet program is applied to calculate the frequency response of feedback control systems. A design template which contains the necessary formulae was constructed so that very little knowledge of the program is required to obtain impressive results. The template becomes a powerful tool by providing a fast and efficient means of designing a stable closed-loop system as well as predicting its performance.

scholarly journals A PID and PIDA Controller Design for an AVR System using Frequency Response Matching

2019 ◽  
Vol 8 (10) ◽  
pp. 1675-1681
Keyword(s):  
Transfer Function ◽  
Frequency Response ◽  
Closed Loop ◽  
Reference Model ◽  
Voltage Regulation ◽  
System Model ◽  
Proportional Integral Derivative ◽  
Proportional Integral ◽  
Avr System ◽  
Frequency Response Matching

A proportional integral derivative (PID) and proportional integral derivative acceleration (PIDA) controller have been designed for voltage regulation in power system. The controller (i.e. PID and PIDA) has been proposed via frequency response matching of desired reference model with that of system model transfer function. The proposed PID controller has been designed using one point frequency response matching as well as pole placement technique, while PIDA controller has been designed using two point frequency response matching by equating desired set-point closed loop reference model with that of closed loop transfer function of system model. The response of the proposed PIDA controller shows improved performance for automatic voltage regulator (AVR) system in comparison with recently available literature. The proposed PID and PIDA controllers provide fast and smooth response for an AVR system. The advantages associated with the PIDA controller for an AVR system is to reduce rise time, percentage overshoot and improved robustness, stability margin.

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