scholarly journals Singularly Perturbation Method Applied To Multivariable PID Controller Design

2015 ◽  
Vol 2015 ◽  
pp. 1-22 ◽  
Author(s):  
Mashitah Che Razali ◽  
Norhaliza Abdul Wahab ◽  
P. Balaguer ◽  
M. F. Rahmat ◽  
Sharatul Izah Samsudin
Keyword(s):  
Perturbation Method ◽  
Pid Controller ◽  
Closed Loop ◽  
Controller Design ◽  
Control Strategies ◽  
High Reliability ◽  
Treatment Plant ◽  
Computation Time ◽  
Singularly Perturbed ◽  
Singularly Perturbation

Proportional integral derivative (PID) controllers are commonly used in process industries due to their simple structure and high reliability. Efficient tuning is one of the relevant issues of PID controller type. The tuning process always becomes a challenging matter especially for multivariable system and to obtain the best control tuning for different time scales system. This motivates the use of singularly perturbation method into the multivariable PID (MPID) controller designs. In this work, wastewater treatment plant and Newell and Lee evaporator were considered as system case studies. Four MPID control strategies, Davison, Penttinen-Koivo, Maciejowski, and Combined methods, were applied into the systems. The singularly perturbation method based on Naidu and Jian Niu algorithms was applied into MPID control design. It was found that the singularly perturbed system obtained by Naidu method was able to maintain the system characteristic and hence was applied into the design of MPID controllers. The closed loop performance and process interactions were analyzed. It is observed that less computation time is required for singularly perturbed MPID controller compared to the conventional MPID controller. The closed loop performance shows good transient responses, low steady state error, and less process interaction when using singularly perturbed MPID controller.

An Intelligent Controller Design Approach for MIMO Coupled Tank System

2018 ◽  
Vol 7 (1) ◽  
pp. 8
Author(s):  
Mohd Hafiz Jali ◽  
Ahmad Firdaus Azhar ◽  
Rozaimi Ghazali ◽  
Chong Chee Soon
Keyword(s):  
Pid Controller ◽  
Closed Loop ◽  
Fuzzy Logic Controller ◽  
Controller Design ◽  
Proportional Integral Derivative ◽  
Cross Sectional ◽  
Intelligent Controller ◽  
Pump Flow Rate ◽  
Tank System ◽  
Better Than

Nowadays, versatilities of controllers have been developed to control the Coupled Tank System (CTS) such as proportional, integral, derivative (PID), fuzzy, fuzzy PID and neuro network. This paper focused on the control of the pump flow rate, in and out of the tank against the cross-sectional area of the CTS’s tank. The main objective of this paper is to design a CTS by using MATLAB since the Fuzzy Logic Controller (FLC) is widely utilized in the control of engineering applications in the industrial. Therefore, the FLC will be utilized to control and improve the performance of the CTS. The conventional PID controller will be applied, which reacts as a benchmark in the performance of the FLC. Parameters such as steady state error, settling time, and maximum overshoot will be part of the simulation results. As a result of the dynamic response executed in the closed-loop environment, it can be concluded that the FLC is capable of performing better than the conventional PID controller.

Chilled Water Temperature Control of HVAC System Using GPC Based Controller

2012 ◽  
Vol 151 ◽  
pp. 626-631
Author(s):  
Qiang Ma ◽  
Jian Gang Lu ◽  
Qin Min Yang ◽  
Jin Shui Chen ◽  
You Xian Sun
Keyword(s):  
Predictive Control ◽  
Pid Controller ◽  
Closed Loop ◽  
Controller Design ◽  
Simulation Environment ◽  
Closed Loop System ◽  
Satisfactory Performance ◽  
Chilled Water ◽  
The Stability ◽  
Theoretical Results

This work proposes a generalized predictive control (GPC) based controller for the temperature of HVAC chilled water supply. In this paper, several models of evaporator are firstly introduced, wherein an identified black-box model is selected for the purpose of controller design. Based on this model, a GPC based controller is employed to obtain a satisfactory performance even with the presence of disturbance. The theoretical results show the stability of the closed-loop system and the performance of this scheme is compared with that of traditional PID controller under simulation environment.

LMI-Based Decentralized PID Controller Design With Application to the Shape Control of Magnetic Fluid Deformable Mirrors

2010 ◽  
Author(s):  
Zhizheng Wu ◽  
Azhar Iqbal ◽  
Foued Ben Amara
Keyword(s):  
Adaptive Optics ◽  
Output Feedback ◽  
Pid Controller ◽  
Control Algorithm ◽  
Closed Loop ◽  
Controller Design ◽  
Design Method ◽  
Pid Controller Design ◽  
Static Output ◽  
Adaptive Optics System

In this paper, a decentralized robust PID controller design method is proposed for multi-input multi-output systems. The system model is first decoupled in the low frequency range, and only the diagonal entries in the DC-decoupled plant model are retained. To deal with the resulting unmodeled high frequency dynamics, a decentralized robust PID controller design method is proposed, where the robust stability and transient response performance of the resulting closed loop system are formulated as a multi-objective H∞/H2 static output feedback problem. The desired parameters of the PID controller are determined by solving a static output feedback problem using linear matrix inequalities (LMIs). Finally, the performance of the proposed control algorithm is experimentally evaluated on the adaptive optics system involving a prototype magnetic fluid deformable mirror (MFDM). The experimental results illustrate the effectiveness of the proposed control algorithm for the MFDM surface shape tracking in the closed loop adaptive optics system.

Multivariable PID Using Singularly Perturbed System

2014 ◽  
Vol 67 (5) ◽  
Author(s):  
Mashitah Che Razali ◽  
Norhaliza Abdul Wahab ◽  
Sharatul Izah Samsudin
Keyword(s):  
Controller Design ◽  
Treatment Plant ◽  
Original System ◽  
Singularly Perturbed ◽  
Order System ◽  
Singularly Perturbed System ◽  
Modeling And Control ◽  
Dynamic Matrix ◽  
Perturbed System ◽  
The Stability

The paper investigates the possibilities of using the singularly perturbation method in a multivariable proportional-integral-derivative (MPID) controller design. The MPID methods of Davison, Penttinen-Koivo and Maciejowski are implemented and the effective of each method is tested on wastewater treatment plant (WWTP). Basically, this work involves modeling and control. In the modeling part, the original full order system of the WWTP was decomposed to a singularly perturbed system. Approximated slow and fast models of the system were realized based on eigenvalue of the identified system. The estimated models are then used for controller design. Mostly, the conventional MPID considered static inverse matrix, but this singularly perturbed MPID considers dynamic matrix inverse. The stability of the singularly perturbed system is established by using Bode analysis, whereby the bode plot of the model system is compared to the original system. The simulation results showed that the singularly perturbed method can be applied into MPID. The three methods of MPID have been compared and the Maciejowski shows the best closed loop performance.

Optimal PID controller design with Kalman filter for Qball-X4 quad-rotor unmanned aerial vehicle

2016 ◽  
Vol 39 (12) ◽  
pp. 1785-1797 ◽  
Author(s):  
Feng Pan ◽  
Lu Liu ◽  
Dingyu Xue
Keyword(s):  
Mathematical Model ◽  
Kalman Filter ◽  
Unmanned Aerial Vehicle ◽  
Pid Controller ◽  
Closed Loop ◽  
Controller Design ◽  
Absolute Error ◽  
Pid Controller Design ◽  
Aerial Vehicle ◽  
Set Up

In this paper, we used a Qball-X4 quad-rotor unmanned aerial vehicle (UAV) which was developed by the Quanser Company as the experimental platform. First, a fundamental mathematical model of the Qball-X4 quad-rotor UAV was built and a simulation model was set up based on the proposed mathematical model; then, a double closed-loop optimal proportional–integral–derivative (PID) controller based on integral of time multiplied by absolute error (ITAE) indices was designed according to the model structure. In consideration of the possible system error and data delay, we designed a corresponding Kalman filter, which can estimate the target trajectory and be put before the proposed PID controller to ensure their validity. Finally, simulation results of the system with presented PID controller and Kalman filter were shown to verify their effectiveness.

Substructural Multiobjective H∞ Controller Design for Large Flexible Structures: A Divide-and-Conquer Approach Based on Linear Matrix Inequalities

2005 ◽  
Vol 219 (5) ◽  
pp. 319-334 ◽  
Author(s):  
O Toker ◽  
M Sunar
Keyword(s):  
Linear Matrix Inequalities ◽  
Closed Loop ◽  
Controller Design ◽  
Flexible Structures ◽  
Computation Time ◽  
Divide And Conquer ◽  
Control Technique ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Static Condensation

In this paper, a novel substructural approach is proposed and successfully implemented for H∞ robust controller design for large flexible structures. It is assumed that sensors and actuators are discrete and located at some nodal points of the structure. In general, a finite element method (FEM)-based modelling approach results in a matrix differential equation of large dimensions. As the dimension becomes larger and larger controller design algorithms require more and more computation time, and start to have numerical problems. To cope with these difficulties, there are many known techniques in the literature, including the decentralized- and substructural-type methods. In this paper, a substructural-type approach based on the static condensation principle is adopted and the H∞ optimal controller design problem for large flexible structures is studied. The key point in the present approach is that the static condensation is performed in the abstract state space. Geometric information about the flexible structure is utilized in deciding how to do the state decomposition, then H∞ optimal controllers are designed at the substructure level, and finally a global controller is assembled for the whole structure. To improve the convergence of the algorithm, a multi-objective H∞ optimization approach is adopted. More precisely, while forcing the closed-loop poles to be in a given convex region to ensure fast dynamics, and hence improve the convergence of the substructural iterations, the H∞ objective function is minimized to achieve maximum robustness. The main advantage of this approach is that both the H∞ objective and the constraints on closed-loop poles can be expressed as a convex problem and formulated as linear matrix inequalities (LMIs), which can be solved easily, e.g. by LMI Toolbox of MATLAB. Overall, the proposed approach results in a reduction in computation time and improvements in numerical reliability as the problem of large size is decomposed into several smaller-size problems. The accuracy and effectiveness of the substructural H∞ control technique are tested on benchmark problems, and effects of structural non-linearities are studied.

scholarly journals Limit Cycle Behavior of Smart Fluid Dampers Under Closed Loop Control

2005 ◽  
Vol 128 (4) ◽  
pp. 413-428 ◽  
Author(s):  
Neil D Sims
Keyword(s):  
Limit Cycle ◽  
Closed Loop ◽  
Controller Design ◽  
Nonlinear Models ◽  
Control Strategies ◽  
Nonlinear Behavior ◽  
Closed Loop Control ◽  
Loop Control ◽  
Fluid Dampers ◽  
Limit Cycle Behavior

Semiactive vibration dampers offer an attractive compromise between the simplicity and fail safety of passive devices, and the weight, cost, and complexity of fully active systems. In addition, the dissipative nature of semiactive dampers ensures they always remain stable under closed loop control, unlike their fully active counterparts. However, undesirable limit cycle behavior remains a possibility, which is not always properly considered during the controller design. Smart fluids provide an elegant means to produce semiactive damping, since their resistance to flow can be directly controlled by the application of an electric or magnetic field. However, the nonlinear behavior of smart fluid dampers makes it difficult to design effective controllers, and so a wide variety of control strategies has been proposed in the literature. In general, this work has overlooked the possibility of undesirable limit cycle behavior under closed loop conditions. The aim of the present study is to demonstrate how the experimentally observed limit cycle behavior of smart dampers can be predicted and explained by appropriate nonlinear models. The study is based upon a previously developed feedback control strategy, but the techniques described are relevant to other forms of smart damper control.

scholarly journals Adaptive Tracking PID and FOPID Speed Control of an Elastically Attached Load Driven by a DC Motor at Almost Step Disturbance of Loading Torque and Parametric Excitation

2021 ◽  
Vol 11 (2) ◽  
pp. 679
Author(s):  
Paweł Olejnik ◽  
Paweł Adamski ◽  
Damian Batory ◽  
Jan Awrejcewicz
Keyword(s):  
Pid Controller ◽  
Closed Loop ◽  
Control Method ◽  
Control Strategies ◽  
Absolute Error ◽  
System Response ◽  
Closed Loop Control ◽  
Loop Control ◽  
Adaptive Tracking Control ◽  
Adaptive Tracking

Adaptive tracking control of the speed of a very elastically attached circular load driven by a direct current motor accompanied with an adaptive conventional and a fractional-order Proportional Integral Derivative (PID) controller is studied. It refers to improving the closed-loop control system response of elastically coupled components of drivelines. The motor and the load mechatronic models and the block diagrams are constructed. Parameters of the PID controller in the model reference control are both constant, as well as vary in time. The adaptive control method is improved by the application of a new closed-loop control structure canceling error dynamics. A few competing control strategies are tested based on the application of two types low and high frequency stepwise increasing variations of loading torque and damping coefficient of motion. Moreover, the performance of the control strategies is verified by Integral Time-Weighted Absolute Error (ITAE) index, since their robustness is evaluated by applying a sine modulated triangle waves of selected electric parameters. Therefore, a dynamic forcing and parameter uncertainty is applied. Simulation results are compared for checking the proposed methods.

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