Sets of stabilising PID controllers for second-order integrating processes with time delay

AbstractThe processes which contain at least one pole at the origin are known as integrating systems. The process output varies continuously with time at certain speed when they are disturbed from the equilibrium operating point by any environment disturbance/change in input conditions and thus they are considered as non-self-regulating. In most occasions this phenomenon is very disadvantageous and dangerous. Therefore it is always a challenging task to efficient control such kind of processes. Depending upon the number of poles present at the origin and also on the location of other poles in transfer function different types of integrating systems exist. Stable first order plus time delay systems with an integrator (FOPTDI), unstable first order plus time delay systems with an integrator (UFOPTDI), pure integrating plus time delay (PIPTD) systems and double integrating plus time delay (DIPTD) systems are the classifications of integrating systems. By using a well-controlled positioning stage the advances in micro and nano metrology are inevitable in order satisfy the need to maintain the product quality of miniaturized components. As proportional-integral-derivative (PID) controllers are very simple to tune, easy to understand and robust in control they are widely implemented in many of the chemical process industries. In industries this PID control is the most common control algorithm used and also this has been universally accepted in industrial control. In a wide range of operating conditions the popularity of PID controllers can be attributed partly to their robust performance and partly to their functional simplicity which allows engineers to operate them in a simple, straight forward manner. One of the accepted control algorithms by the process industries is the PID control. However, in order to accomplish high precision positioning performance and to build a robust controller tuning of the key parameters in a PID controller is most inevitable. Therefore, for PID controllers many tuning methods are proposed. the main factors that lead to lifetime reduction in gain loss of PID parameters are described in This paper and also the main methods used for gain tuning based on optimization approach analysis is reviewed. The advantages and disadvantages of each one are outlined and some future directions for research are analyzed.

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The MID property for a second-order neutral time-delay differential equation

2020 24th International Conference on System Theory, Control and Computing (ICSTCC) ◽

10.1109/icstcc50638.2020.9259685 ◽

2020 ◽

Author(s):

Amina Benarab ◽

Islam Boussaada ◽

Karim Trabelsi ◽

Guilherme Mazanti ◽

Catherine Bonnet

Keyword(s):

Differential Equation ◽

Time Delay ◽

Delay Differential Equation ◽

Second Order ◽

Delay Differential

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Enhanced Two-Degrees-of-Freedom Control Strategy for Second-Order Unstable Processes with Time Delay

Industrial & Engineering Chemistry Research ◽

10.1021/ie051046+ ◽

2006 ◽

Vol 45 (10) ◽

pp. 3604-3614 ◽

Cited By ~ 46

Author(s):

A. Seshagiri Rao ◽

M. Chidambaram

Keyword(s):

Time Delay ◽

Control Strategy ◽

Degrees Of Freedom ◽

Second Order ◽

Two Degrees Of Freedom ◽

Unstable Processes

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Complementary Sensitivity Design of PID Controllers for Arbitrary-Order Transfer Functions With Time Delay

ASME 2008 Dynamic Systems and Control Conference, Parts A and B ◽

10.1115/dscc2008-2205 ◽

2008 ◽

Cited By ~ 4

Author(s):

Tooran Emami ◽

John M. Watkins

Keyword(s):

Time Delay ◽

Transfer Functions ◽

Linear Time ◽

Order System ◽

Pid Controllers ◽

Single Input Single Output ◽

Linear Time Invariant ◽

Single Output ◽

Plant Transfer ◽

Time Invariant

A graphical technique for finding all proportional integral derivative (PID) controllers that stabilize a given single-input-single-output (SISO) linear time-invariant (LTI) system of any order system with time delay has been solved. In this paper a method is introduced that finds all PID controllers that also satisfy an H∞ complementary sensitivity constraint. This problem can be solved by finding all PID controllers that simultaneously stabilize the closed-loop characteristic polynomial and satisfy constraints defined by a set of related complex polynomials. A key advantage of this procedure is the fact that it does not require the plant transfer function, only its frequency response.

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