Iterative Design of Centralized PID Controllers Based on Equivalent Loop Transfer Functions and Linear Programming

Garrido, Juan; Ruz, Mario L.; Morilla, Fernando; Vázquez, Francisco

doi:10.1109/access.2021.3139214

Cited by 6 publications

(11 citation statements)

References 34 publications

(63 reference statements)

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“…The problem with these open-loop transfer functions is that they do not capture the interactions and dynamics with the other loops when they are closed. In [39], the concept of an equivalent open-loop transfer function (ELTF) for centralized control was introduced. This function represents the transfer function between an output and its error signal when the loop is open and the rest of the loops remain closed.…”

Section: Preliminariesmentioning

confidence: 99%

“…Furthermore, as the polar trace lies below the line r, the minimum values of other classical robustness margins, such as gain margin Am, phase margin ϕm, or maximum sensitivity margin Ms, all depicted in Figure 3, are guaranteed. More details on the relationship between these classical robustness margins and the values of Lm and α can be found in [39,40]. The robustness As demonstrated in [39], ELTFs can be expressed as a function of controllers in the same column, which can be designed in isolation in an iterative process if the other control columns are known.…”

Section: Preliminariesmentioning

confidence: 99%

“…In our previous paper [39], we proposed an iterative method to design multivariable PID controls for stable and square linear systems based on their frequency response and the concept of equivalent loop transfer function (ELTF). In that study, ELTFs enabled the calculation of the elements for each column of the controller matrix separately using a linear optimization problem if the linear margin proposed in [40] was used as a robustness specification.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Design of Multivariable PID Control Using Iterative Linear Programming and Decoupling

Garrido,

Garrido-Jurado,

Vázquez

et al. 2024

Electronics

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The design of multivariable process control systems is specially complicated when there are strong interactions between the different control loops, and even more with multiple time delays. This paper proposes an iterative design method of centralized proportional-integral-derivative (PID) controllers for stable linear systems. The methodology is based on the linear parameterization of equivalent loop transfer functions (ELTFs) for centralized control. These functions capture the dynamics of the other loops and, from a prior design, allow solving the design problem at each iteration with linear programming that shapes the Nyquist plot of the ELTFs in the frequency domain, which also avoids the need for approximations. Two optimizations are proposed: (I) maximizing integral gains by fulfilling linear robustness margins in each ELTF and (II) maximizing linear robustness margins by fulfilling minimum bandwidths in each loop. In both optimizations, static decoupling and decoupling at a frequency close to the bandwidth of each loop are included as constraints, which improves the decoupling performance and the procedure convergence. The effectiveness of the method is verified in three simulation examples (square and non-square) and a lab experimental process. The proposed designs achieve a similar or better response when compared to that achieved by other authors.

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Section: Preliminariesmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Design of Multivariable PID Control Using Iterative Linear Programming and Decoupling

Garrido,

Garrido-Jurado,

Vázquez

et al. 2024

Electronics

Self Cite

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“…A model predictive controller based on linear quadratic Gaussian regulator for achieving the design criteria of the quadruple tank system is described in [ 21 ]. A multivariable controller is designed based on the equivalent loop transfer function in [ 22 ]. The controller was able to reduce the loop interactions through iterative procedure.…”

Section: Introductionmentioning

confidence: 99%

Frequency Domain Specifications Based Robust Decentralized PI/PID Control Algorithm for Benchmark Variable-Area Coupled Tank Systems

K.R.¹,

Mahapatra²

2022

Sensors

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A decentralized PI/PID controller based on the frequency domain analysis for two input two output (TITO) coupled tank systems is exploited in this paper. The fundamentals of the gain margin and phase margin are used to design the proposed PI/PID controller. The basic objective is to keep the tank at the predetermined level. To satisfy the design specifications, the control algorithm is implemented for decoupled subsystems by employing a decoupler. First-order plus dead time (FOPDT) models are obtained for the decoupled subsystems using the model-reduction technique. In addition, the control law is realized by considering the frequency domain analysis. Further, the robustness of the controller is verified by considering multiplicative input and output uncertainties. The proposed method is briefly contrasted with existing techniques. It is envisaged that the proposed control algorithm exhibits better servo and regulatory responses compared to the existing techniques.

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“…One of the most known tuning methods is the Ziegler-Nichols’s method presented in 1942 [ 14 ], which provides fast and simple rule-based tuning [ 13 , 15 ], although there are many other design methods such as the internal model control [ 16 , 17 ] or gain margin, phase margin, and gain crossover frequency methods [ 18 , 19 ]. Garrido et al [ 20 ] proposed a method for the iterative design of centralized PID controllers based on equivalent loop transfer functions and linear programing. Euzébio et al [ 21 ] proposed a nonlinear optimization algorithm to minimize the disturbance effects in coupled loops in decentralized PID controllers.…”

Section: Introductionmentioning

confidence: 99%

Optimal PID Control of a Brushed DC Motor with an Embedded Low-Cost Magnetic Quadrature Encoder for Improved Step Overshoot and Undershoot Responses in a Mobile Robot Application

Bitriá

Palacín

2022

Sensors

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The development of a proportional–integral–derivative (PID) control system is a simple, practical, highly effective method used to control the angular rotational velocity of electric motors. This paper describes the optimization of the PID control of a brushed DC motor (BDCM) with an embedded low-cost magnetic quadrature encoder. This paper demonstrates empirically that the feedback provided by low-cost magnetic encoders produces some inaccuracies and control artifacts that are not usually considered in simulations, proposing a practical optimization approach in order to improve the step overshoot and undershoot controller response. This optimization approach is responsible for the motion performances of a human-sized omnidirectional mobile robot using three motorized omnidirectional wheels.

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Iterative Design of Centralized PID Controllers Based on Equivalent Loop Transfer Functions and Linear Programming

Abstract: Date of publication xxxx 00, 0000, date of current version xxxx 00, 0000.

Cited by 6 publications

References 34 publications

Design of Multivariable PID Control Using Iterative Linear Programming and Decoupling

Design of Multivariable PID Control Using Iterative Linear Programming and Decoupling

Frequency Domain Specifications Based Robust Decentralized PI/PID Control Algorithm for Benchmark Variable-Area Coupled Tank Systems

Optimal PID Control of a Brushed DC Motor with an Embedded Low-Cost Magnetic Quadrature Encoder for Improved Step Overshoot and Undershoot Responses in a Mobile Robot Application

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