Synthesis of PI Controller with a Simple Set-Point Filter for Unstable First-Order Time Delay Processes and Integral plus Time Delay Plant

Gerov, Radmila; Jovanović, Zoran

doi:10.5755/j01.eie.24.2.20629

Cited by 10 publications

(7 citation statements)

References 12 publications

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“…where A and A d are the constant matrices assuming the dimensions 2x2, S k is the complex solution matrix (13) of the same dimensions, k is the ordinal number of the branch of the Lambert W function, [11]- [12], [15]- [16] and 00 01 ,. 00…”

Section: Fig 2 Conventional 1-dof Controller Control Systemmentioning

confidence: 99%

“…The gain parameters of the PD controller could be received, alongside the alreadymentioned way, based on the received gain of the PI controller for the IPTD processes [11]- [12]. In order to make an analogy between 1-DOF PD controller system for DIPTD processes and 1-DOF PI controller system for IPTD processes, let us assume that the control system shown in Fig.…”

Section: Fig 2 Conventional 1-dof Controller Control Systemmentioning

confidence: 99%

“…In this paper, a PD controller for the DIPTD systems is designed according to the existing Proportional-integral (PI) controller for IPTD processes [11]- [12]. It is well known that the application of the PD controller with DIPTD processes, in case of disturbance, yields the off-set of the output signal.…”

Section: Introductionmentioning

confidence: 99%

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Tuning Pd and Pid Controllers via the Lambert W Function for Double Integrator Plus Dead Time Processes

Gerov

Jovanović

2019

FU Aut Cont Rob

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The paper explores the Proportional-derivative controller for a double integrator plus dead time processes, which is a challenging control problem, that is designed based on the existing Proportional-integrative controller for integrator plus dead time processes. The PD controller is extended with an integral action and an ideal PID controller is received. The parameters of both controllers are received by using the pole placement technique, whereby the transcendent characteristics equation of the closed loop system is solved by using the Lambert W function. The paper also examines the influence of the desired poles of the system with a closed feedback as well as the influence of the disturbance and the change of the DIPTD processes parameters onto the received control system performances. The results received by simulation, and the quantitative indicators, show that the proposed control system has better performances in comparison to the control systems obtained by other methods in literature.

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Section: Fig 2 Conventional 1-dof Controller Control Systemmentioning

confidence: 99%

Section: Fig 2 Conventional 1-dof Controller Control Systemmentioning

confidence: 99%

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Tuning Pd and Pid Controllers via the Lambert W Function for Double Integrator Plus Dead Time Processes

Gerov

Jovanović

2019

FU Aut Cont Rob

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“…The synthesis of the PI controller was performed by using a pole placement method with the features of the Lambert W function [14]. Using the analytical solution form in terms of the matrix Lambert W function (LWF) [15]- [19] and the limitations of the matrix-like Lambert W function provided in [20], the characteristic system equation for the desired rightmost poles of the closed-loop system was solved and the PI controller parameters were set. The proposed method of controlling the speed of the DC motor was developed for one degree of freedom (1-DOF) and two degrees of freedom (2-DOF) PI controller.…”

Section: Introductionmentioning

confidence: 99%

The usage of Lambert W function for identification and speed control of a DC motor

Gerov

Jovanović

2019

FACTA U EE

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The paper proposes a new method of identifying the linear model of a DC motor. The parameter estimation is based on the closed-loop step response of the DC motor under a proportional controller. For the application of the method, a deliberate delay of the measured speed was introduced. The paper considers the speed regulation of the direct current motor with negligible inductance by applying 1-DOF and 2-DOF, proportional integral retarded controllers. The proportional and integral gain of the PI retarded controllers was received by using a pole placement method on the identified model. The Lambert W function was applied for the identification and in designing the controller with the purpose of finding the rightmost poles of the closed-loop as well as the boundary conditions for selecting the gain of the PI controller. The robustness of the calculated controllers was considered under the effect of an disturbance, uncertainty in each of the DC motor parameters as well as perturbations in time delay.

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“…In the industry, system identification is used for obtaining models for the purpose of control, i.e. for regulation, synthesis, and realization of various controller type such as Model Predictive Controllers (MPC) [9], Linear Quadratic Regulators (LQR) [10], PID controllers [11], PI controllers [12], etc. For finding the model parameters, different methods may be used, which, as a result of the identification, due to the tendency of the mathematical model to satisfy all the dynamic characteristics of the observed process, can produce a high-order model.…”

Section: Introductionmentioning

confidence: 99%

Parameter Estimation Method for the Unstable Time Delay Process

2019

APH

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The paper considers the evaluation of all the three parameters of the unstable first order process with time delay by using the process data received from the closed loop step response under proportional control. The new method of analysis of parameters identification is presented. One is required to read five parameters from the closed loop step response for the purpose of applying the method. For the selected proportional controller gain and the received process gain, the time constant and time delay of the unstable first-order plus time delay model is received by solving a characteristic system equation using the features of the Lambert W function. The suggested way of parameter estimation is simple and it yields better results than the well-documented methods in literature which the present method is compared with. Simulation results are given for linear system and a nonlinear bioreactor system.

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Synthesis of PI Controller with a Simple Set-Point Filter for Unstable First-Order Time Delay Processes and Integral plus Time Delay Plant

Cited by 10 publications

References 12 publications

Tuning Pd and Pid Controllers via the Lambert W Function for Double Integrator Plus Dead Time Processes

Tuning Pd and Pid Controllers via the Lambert W Function for Double Integrator Plus Dead Time Processes

The usage of Lambert W function for identification and speed control of a DC motor

Parameter Estimation Method for the Unstable Time Delay Process

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