Discrete-Time First-Order Plus Dead-Time Model-Reference Trade-off PID Control Design

The present study proposes a novel proportional-integral-derivative (PID) control design method in discrete time. In the proposed method, a PID controller is designed for first-order plus dead-time (FOPDT) systems so that the prescribed robust stability is accomplished. Furthermore, based on the control performance, the relationship between the servo performance and the regulator performance is a trade-off relationship, and hence, these items are not simultaneously optimized. Therefore, the proposed method provides an optimal design method of the PID parameters for optimizing the reference tracking and disturbance rejection performances, respectively. Even though such a trade-off design method is being actively researched for continuous time, few studies have examined such a method for discrete time. In conventional discrete time methods, the robust stability is not directly prescribed or available systems are restricted to systems for which the dead-time in the continuous time model is an integer multiple of the sampling interval. On the other hand, in the proposed method, even when a discrete time zero is included in the controlled plant, the optimal PID parameters are obtained. In the present study, as well as the other plant parameters, a zero in the FOPDT system is newly normalized, and then, a universal design method is obtained for the FOPDT system with the zero. Finally, the effectiveness of the proposed method is demonstrated through numerical examples.

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Optimal Robust PID Control for First- and Second-Order Plus Dead-Time Processes

Applied Sciences ◽

10.3390/app9091934 ◽

2019 ◽

Vol 9 (9) ◽

pp. 1934 ◽

Cited By ~ 8

Author(s):

Takao Sato ◽

Itaru Hayashi ◽

Yohei Horibe ◽

Ramon Vilanova ◽

Yasuo Konishi

Keyword(s):

Control System ◽

Pid Control ◽

Dead Time ◽

Design Method ◽

Second Order ◽

Process Models ◽

Second Step ◽

Reference Tracking ◽

First Order ◽

Pid Tuning

The present study proposes a new design method for a proportional-integral-derivative (PID) control system for first-order plus dead-time (FOPDT) and over-damped second-order plus dead-time (SOPDT) systems. What is presented is an optimal PID tuning constrained to robust stability. The optimal tuning is defined for each one of the two operation modes the control system may operate in: servo (reference tracking) and regulation (disturbance rejection). The optimization problem is stated for a normalized second-order plant that unifies FOPDT and SOPDT process models. Different robustness levels are considered and for each one of them, the set of optimal controller parameters is obtained. In a second step, suitable formulas are found that provide continuous values for the controller parameters. Finally, the effectiveness of the proposed method is confirmed through numerical examples.

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Analytical PID control design in time domain with performance‐robustness trade‐off

Electronics Letters ◽

10.1049/el.2018.1345 ◽

2018 ◽

Vol 54 (13) ◽

pp. 815-817 ◽

Cited By ~ 3

Author(s):

S. Tavakoli ◽

M. Safaei

Keyword(s):

Time Domain ◽

Pid Control ◽

Control Design ◽

Trade Off ◽

Performance Robustness

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Time-Varying Polar Decomposition by Continuous-Time Model and Discrete-Time Algorithm of Zeroing Neural Network Using Zhang Time Discretization (ZTD)

10.1109/icicip53388.2021.9642222 ◽

2021 ◽

Author(s):

Zanyu Tang ◽

Liangjie Ming ◽

Yunong Zhang ◽

Runhao Shi

Keyword(s):

Neural Network ◽

Discrete Time ◽

Continuous Time ◽

Polar Decomposition ◽

Time Discretization ◽

Time Algorithm ◽

Time Varying ◽

Continuous Time Model ◽

Time Model

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Dynamic Precompensation for the Discrete Time Control Design of Continuous Time Generalized State Space Systems

Intelligent Automation & Soft Computing ◽

10.1080/10798587.1998.10750735 ◽

1998 ◽

Vol 4 (3) ◽

pp. 253-260

Author(s):

Dimitri Lefebvre ◽

Frédéric Rotella

Keyword(s):

State Space ◽

Discrete Time ◽

Continuous Time ◽

Control Design ◽

Space Systems ◽

Time Control ◽

State Space Systems ◽

Generalized State Space ◽

Generalized State

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Dividend Moments in the Dual Risk Model: Exact and Approximate Approaches

Astin Bulletin ◽

10.2143/ast.38.2.2033347 ◽

2008 ◽

Vol 38 (02) ◽

pp. 399-422 ◽

Cited By ~ 19

Author(s):

Eric C.K. Cheung ◽

Steve Drekic

Keyword(s):

Differential Equations ◽

Laplace Transform ◽

Size Distribution ◽

Discrete Time ◽

Continuous Time ◽

Risk Model ◽

Time Model ◽

Jump Size ◽

Time Of Ruin ◽

The Time Of Ruin

In the classical compound Poisson risk model, it is assumed that a company (typically an insurance company) receives premium at a constant rate and pays incurred claims until ruin occurs. In contrast, for certain companies (typically those focusing on invention), it might be more appropriate to assume expenses are paid at a fixed rate and occasional random income is earned. In such cases, the surplus process of the company can be modelled as a dual of the classical compound Poisson model, as described in Avanzi et al. (2007). Assuming further that a barrier strategy is applied to such a model (i.e., any overshoot beyond a fixed level caused by an upward jump is paid out as a dividend until ruin occurs), we are able to derive integro-differential equations for the moments of the total discounted dividends as well as the Laplace transform of the time of ruin. These integro-differential equations can be solved explicitly assuming the jump size distribution has a rational Laplace transform. We also propose a discrete-time analogue of the continuous-time dual model and show that the corresponding quantities can be solved for explicitly leaving the discrete jump size distribution arbitrary. While the discrete-time model can be considered as a stand-alone model, it can also serve as an approximation to the continuous-time model. Finally, we consider a generalization of the so-called Dickson-Waters modification in optimal dividends problems by maximizing the difference between the expected value of discounted dividends and the present value of a fixed penalty applied at the time of ruin.

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Speed Tracking Error and Rate Driven Event-Triggered PID Control Design Method for Automatic Train Operation System

2018 Chinese Automation Congress (CAC) ◽

10.1109/cac.2018.8623438 ◽

2018 ◽

Cited By ~ 2

Author(s):

Peichao Fu ◽

Shigen Gao ◽

Hairong Dong ◽

Bin Ning ◽

Qi Zhang

Keyword(s):

Pid Control ◽

Design Method ◽

Tracking Error ◽

Control Design ◽

Operation System ◽

Speed Tracking ◽

Train Operation ◽

Automatic Train Operation ◽

Event Triggered

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Birth and death processes with random environments in continuous time

Journal of Applied Probability ◽

10.1017/s0021900200097576 ◽

1981 ◽

Vol 18 (01) ◽

pp. 19-30 ◽

Cited By ~ 6

Author(s):

Robert Cogburn ◽

William C. Torrez

Keyword(s):

Discrete Time ◽

Random Environment ◽

Continuous Time ◽

Death Process ◽

Random Environments ◽

Birth And Death Process ◽

Time Model ◽

Birth And Death Processes ◽

Discrete Time Model ◽

Extinction Probabilities

A generalization to continuous time is given for a discrete-time model of a birth and death process in a random environment. Some important properties of this process in the continuous-time setting are stated and proved including instability and extinction conditions, and when suitable absorbing barriers have been defined, methods are given for the calculation of extinction probabilities and the expected duration of the process.

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Feedback Anticontrol of Discrete Chaos

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127498001236 ◽

1998 ◽

Vol 08 (07) ◽

pp. 1585-1590 ◽

Cited By ~ 130

Author(s):

Guanrong Chen ◽

Dejian Lai

Keyword(s):

Dynamical System ◽

Discrete Time ◽

State Feedback ◽

Design Method ◽

Control Design ◽

Rigorous Approach ◽

Discrete Time Dynamical System ◽

Discrete Chaos ◽

Simple Feedback ◽

Discrete Time Dynamical Systems

In this paper, a simple feedback control design method earlier proposed by us for discrete-time dynamical systems is proved to be a mathematically rigorous approach for anticontrol of chaos, in the sense that any given discrete-time dynamical system can be made chaotic by the designed state-feedback controller along with the mod-operations.

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Analytical Design of Fractional Order Proportional Integral Controller for Spherical Tank

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.573.279 ◽

2014 ◽

Vol 573 ◽

pp. 279-284 ◽

Cited By ~ 1

Author(s):

Neenu Elizabeth Cherian ◽

K. Sundaravadivu

Keyword(s):

Fractional Order ◽

Dead Time ◽

Transfer Functions ◽

Design Method ◽

Analytical Design ◽

Proportional Integral ◽

First Order ◽

Spherical Tank ◽

Proportional Integral Controller ◽

Fopi Controller

This paper presents an analytical design method for fractional order proportional integral (FOPI) controller for the spherical tank which is modelled as a first order plus dead time (FOPDT) process. The design is based on the Bode’s ideal transfer function and fractional calculus. By using frequency domain, the proposed FOPI tuning rules are directly derived for a generalized first order plus dead time process and then applied to the transfer functions obtained at various operating points of the spherical tank. The performance of the designed FOPI controller is compared with the conventional integer order proportional integral derivative (IOPID) controller in simulation.

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