scholarly journals Corrigendum to “Stabilizing Parametric Region of Multiloop PID Controllers for Multivariable Systems Based on Equivalent Transfer Function”

2017 ◽  
Vol 2017 ◽  
pp. 1-1
Author(s):  
Xiaoli Luan ◽  
Qiang Chen ◽  
Pedro Albertos ◽  
Fei Liu
Keyword(s):  
Transfer Function ◽  
Pid Controllers ◽  
Multivariable Systems ◽  
Parametric Region

scholarly journals Stabilizing Parametric Region of Multiloop PID Controllers for Multivariable Systems Based on Equivalent Transfer Function

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Xiaoli Luan ◽  
Qiang Chen ◽  
Pedro Albertos ◽  
Fei Liu
Keyword(s):  
Transfer Function ◽  
Design Procedure ◽  
Pid Controllers ◽  
Multivariable Systems ◽  
Parameterization Method ◽  
Model Based ◽  
Complete Set ◽  
Practical Model ◽  
Parametric Region

The aim of this paper is to determine the stabilizing PID parametric region for multivariable systems. Firstly, a general equivalent transfer function parameterization method is proposed to construct the multiloop equivalent process for multivariable systems. Then, based on the equivalent single loops, a model-based method is presented to derive the stabilizing PID parametric region by using the generalized Hermite-Biehler theorem. By sweeping over the entire ranges of feasible proportional gains and determining the stabilizing regions in the space of integral and derivative gains, the complete set of stabilizing PID controllers can be determined. The robustness of the design procedure against the approximation in getting the SISO plants is analyzed. Finally, simulation of a practical model is carried out to illustrate the effectiveness of the proposed technique.

scholarly journals Analytical Multiloop Control for Multivariable Systems with Time Delays

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Zhiguo Wang ◽  
Peng Wei
Keyword(s):  
Transfer Function ◽  
Process Model ◽  
Controller Design ◽  
Design Method ◽  
Open Loop ◽  
Multivariable Systems ◽  
Performance Improvements ◽  
Loop Transfer Function ◽  
Multiloop Control ◽  
Multiloop Control System

In this paper, a new design method with performance improvements of multiloop controllers for multivariable systems is proposed. Precise expression is developed to show the relationship between the dynamic- and steady-state characteristics of the multiloop control system and its parameters. First, an equivalent transfer function (ETF) is introduced to decompose the multivariable system, based on which the multiloop controller parameters are calculated. According to the ETF matrix property, an analytical expression for the PI controller for multivariable systems is derived in terms of substituting the ETF matrix for the inverse open-loop transfer function. In the proposed controller design method, no approximation of the inverse of the process model is needed, implying that this method can be applied to some multivariable systems with high dimensions. The simulation results obtained from several examples demonstrate the effectiveness of the proposed method.

DC Motor Speed Control Using Hybrid PID-Fuzzy with ITAE Polynomial Initiation

2019 ◽  
Vol 3 (1) ◽  
pp. 7
Author(s):  
Hari Wibawa ◽  
Oyas Wahyunggoro ◽  
Adha Imam Cahyadi
Keyword(s):  
Transfer Function ◽  
Fuzzy Logic Controller ◽  
Dc Motor ◽  
Industrial Sector ◽  
Pid Controllers ◽  
Motor Speed ◽  
Dc Motors ◽  
Working Parameters ◽  
Motor Operation ◽  
Load Simulation

DC motors are widely applied in industrial sector, especiallyprocesses of automation and robotics. Given its role in the sector, DC motor operation needs to be optimized. One of optimization steps is controlling speed using several control methods, for example conventional PID methods, PID Ziegler Nichols, PID based on ITAE polynomials, and Hybrid PID-Fuzzy. From these methods, Hybrid PID-Fuzzy was chosen as a method to be proposed in this paper because it can anticipate shortcomings of PID controllers and fuzzy controllers so as to produce system responses that are fast and adaptive to errors. This paper aimed to design a Hybrid PID-Fuzzy system based on ITAE polynomials (Hybrid-ITAE), to analyze its performance parameters values, and tp compare Hybrid-ITAE performance with conventional PID method. Working parameters being reviewed include overshoot, rise time, settling time, and ITAE. First of all, JGA25-370 DC motor was modeled in a form of a third order transfer function equation. Based on the transfer function, PID parameters were calculated using PID Output Feedback and ITAE polynomial methods. The best ITAE polynomial PID controllers were then be combined with a Fuzzy Logic Controller to form a Hybrid-ITAE system. Simulation and experimental stages were carried out in two conditions, namely no load and loaded. Simulation and experimental results showed that Hybrid-ITAE (l = 0.85) was the best controller for no-load simulation conditions. For loaded simulation Hybrid-ITAE (l=1) was a better controller. In no-loads experiment, the best controller was Hybrid PID-Ziegler Nichols, while for loaded condition the best controller was Hybrid PID-Ziegler Nichols.

scholarly journals Determining configuration parameters for proportionally integrated differentiating controllers by arranging the poles of the transfer function on the complex plane

2021 ◽  
Vol 5 (2 (113)) ◽  
pp. 80-93
Author(s):  
Mykhailo Horbiychuk ◽  
Nataliia Lazoriv ◽  
Liudmyla Chyhur ◽  
Іhor Chyhur
Keyword(s):  
Control System ◽  
Transfer Function ◽  
Characteristic Equation ◽  
Complex Plane ◽  
Transfer Functions ◽  
Control Process ◽  
Pid Controllers ◽  
Algebraic Equations ◽  
Automated Control ◽  
Linear Algebraic Equations

This paper reports a solution to the problem of determining the configuration parameters of PID controllers when arranging the poles of the transfer function of a linear single-circuit automated control system for a predefined set of control objects. Unlike known methods in which the task to find the optimal settings of a PID controller is formed as a problem of nonlinear programming, in this work a similar problem is reduced to solving a system of linear algebraic equations. The method devised is based on the generalized Viète theorem, which establishes the relationship between the parameters and roots of the characteristic equation of the automatic control system. It is shown that for control objects with transfer functions of the first and second orders, the problem of determining the configuration parameters of PID controllers has an unambiguous solution. For control objects with transfer functions of the third and higher orders, the generated problem is reduced to solving the redefined system of linear algebraic equations that has an unambiguous solution when the Rouché–Capelli theorem condition is met. Such a condition can be met by arranging one of the roots of the characteristic equation of the system on a complex plane. At the same time, the requirements for the qualitative indicators of the system would not always be met. Therefore, alternative techniques have been proposed for determining the configuration parameters of PID controllers. The first of these defines configuration parameters as a pseudo solution to the redefined system of linear algebraic equations while the second produces a solution for which the value of the maximum residual for the system of equations is minimal. For each case, which was used to determine the settings of PID controllers, such indicators of the control process as overshooting and control time have been determined

A Unified Approach for H∞ Complementary Sensitivity Design of PID Controllers Applied to a DC Motor With Communication Delay

2009 ◽  
Author(s):  
T. Emami ◽  
J. M. Watkins
Keyword(s):  
Transfer Function ◽  
Frequency Response ◽  
Discrete Time ◽  
Continuous Time ◽  
Dc Motor ◽  
Communication Delay ◽  
Time Shift ◽  
Pid Controllers ◽  
Unified Approach ◽  
Experimental Frequency

In this paper a graphical technique is introduced for finding all continuous-time and discrete-time proportional integral derivative (PID) controllers that satisfy the discrete-time H∞ complementary sensitivity constraint of an arbitrary order transfer function with time delay. These problems can be solved by finding all achievable PID controllers that simultaneously stabilize the closed-loop characteristic polynomial and satisfy constraints defined by a set of related complex polynomials. The key advantage of this procedure is that this method depends only on the frequency response of the system. If the plant transfer function is given, the procedure is still appropriate. The delta operator is used to describe the discrete-time controllers because it not only possesses numerical properties superior to the discrete-time shift operator, but also converges to the continuous-time controller as the sampling period approaches zero. A unified approach allows us to use the same procedure for discrete-time and continuous-time complementary sensitivity design of PID controllers. The method is demonstrated by using the experimental frequency response of a DC motor with communication delay for H∞ complementary sensitivity design of PID controllers.

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