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.

A Unified Approach for Weighted Sensitivity Design of PID Controllers

2009 ◽  
Author(s):  
Tooran Emami ◽  
John M. Watkins
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Arbitrary Order ◽  
Shift Operator ◽  
Sampling Period ◽  
Time Shift ◽  
Pid Controllers ◽  
Unified Approach ◽  
Time Model ◽  
Graphical Technique

In this paper a graphical technique is introduced for finding all continuous-time or discrete-time proportional integral derivative (PID) controllers that satisfy a weighted 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. The delta operator is used to describe the controllers in a discrete-time model, 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 weighted sensitivity design of PID controllers.

scholarly journals Controller Design Using Laguerre Functions

2021 ◽  
Author(s):  
philip olivier
Keyword(s):  
Transfer Function ◽  
Discrete Time ◽  
Continuous Time ◽  
Controller Design ◽  
Laguerre Functions ◽  
Plant Transfer ◽  
Future Work

<div> <div> <div> <p>This paper presents a technique for designing controllers for rational plants using Laguerre functions. The inputs to the process are the a) the plant transfer function P(s), b) the target transfer function T(s) and c) the desired order of the controller. Future work will extend this process so it is applicable to 1) irrational continuous time plants and 2) to irrational discrete time plants. </p> </div> </div> </div>

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 Multivariable Unconstrained Pattern Search Method for Optimizing Digital PID Controllers Applied to Isolated Forward Converter

Energies ◽  
2020 ◽  
Vol 14 (1) ◽  
pp. 77
Author(s):  
Ghulam Abbas ◽  
Muhammad Usman Asad ◽  
Jason Gu ◽  
Salem Alelyani ◽  
Valentina E. Balas ◽  
...  
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Voltage Regulation ◽  
Search Method ◽  
Pattern Search ◽  
Pid Controllers ◽  
Digital Controllers ◽  
Forward Converter ◽  
Digital Redesign ◽  
Digital Pid

Most of the traditional PID tuning methods are heuristic in nature. The heuristic approach-based tuned PID controllers show only nominal performance. In addition, in the case of a digital redesign approach, mapping of the heuristically-designed continuous-time PID controllers into discrete-time PID controllers and in case of the direct digital design approach, mapping of the continuous-time plant (forward converter) into the discrete-time plant, results in frequency distortion (or warping). Besides this, nonlinear elements such as ADC and DAC, and delay in the digital control loop deteriorate the control performance. There is a need to tune conventionally-designed digital controllers to enhance performance. This paper proposes optimized discrete-time PID controllers for a forward DC–DC converter operating in continuous conduction mode (CCM). The considered conventional digital PID controllers designed on the basis of the digital redesign and direct digital approaches are tuned by one of the multivariable unconstrained pattern search methods named Hooke–Jeeves (H–J) search method to ensure excellent output voltage regulation performance against the changes in input voltage and load current. Numerical results show that the H–J-based optimized PID compensated forward converter system shows tremendous improvement in performance compared to its unoptimized counterpart and simulated annealing (SA)-based compensated system, thus justifying the applicability of the H–J method for enhancing the performance.

scholarly journals Additive Mixed Sensitivity Design of PID Controllers for Continuous-Time System with Uncertain Time-Delay

2021 ◽  
Vol 20 ◽  
pp. 303-311
Author(s):  
Tooran Emami
Keyword(s):  
Time Delay ◽  
Continuous Time ◽  
Time Delays ◽  
Dc Motor ◽  
Internal Communication ◽  
Pid Controllers ◽  
Time System ◽  
Communication Time ◽  
Uncertain Time ◽  
Continuous Time System

This paper presents an algorithm for all achievable coefficients of Proportional Integral Derivative (PID) controllers in an integral-derivative plane that stabilizes and satisfies additive mixed sensitivity constraint with an uncertain time delay for a continuous-time system. This algorithm solves the singularity problem of designing PID controllers in the integral and derivative plane and estimates achievable ranges of proportional gain of the PID controllers. A numerical cascaded ball and beam with unity feedback control of an SRV-DC motor and uncertain communication time delays in the system process demonstrate the application of this methodology. In this application, the additive weight bounds the additive errors for the cascaded ball and beam and the closed-loop SRV-DC motor system transfer function with the internal communication time delays

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