Control design for time-delay systems based on quasi-direct pole placement

Michiels, Wim; Vyhlídal, Tomáš; Zı́tek, Pavel

doi:10.1016/j.jprocont.2009.11.004

Cited by 70 publications

(48 citation statements)

References 12 publications

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“…The whole methodology has been tested on an attractive example of a skater on a swaying bow described by an unstable LTI TDS model. The procedure is similar to the algorithm introduced in (Michiels et al, 2010); however, there are some substantial differences between them. Firstly, the presented approach is made in input-output space of meromorphic Laplace transfer functions, whereas the one in (Michiels et al, 2010) deals purely with state space.…”

Section: Resultsmentioning

confidence: 99%

“…The procedure is similar to the algorithm introduced in (Michiels et al, 2010); however, there are some substantial differences between them. Firstly, the presented approach is made in input-output space of meromorphic Laplace transfer functions, whereas the one in (Michiels et al, 2010) deals purely with state space. Second, in the cited literature, a number poles less then a number of free controller parameters is set exactly and the rest of the spectrum is pushed to the left as much as possible.…”

Section: Resultsmentioning

confidence: 99%

“…Moreover, we suggest unambiguously how the prescribed poles (and zeros) positions are to be chosen -based on model overshoots. Last but not least, in (Michiels et al, 2010), the gradient sampling algorithm (Burke et al, 2005) on the spectral abscissa was used while SOMA together with more complex cost function is considered in this chapter. The presented approach is limited to retarded SISO LTI-TDS without distributed delays only.…”

Section: Resultsmentioning

confidence: 99%

See 2 more Smart Citations

Implementation of a New Quasi-Optimal Controller Tuning Algorithm for Time-Delay Systems

Pekař¹,

Prokop²

2011

MATLAB for Engineers - Applications in Control, Electrical Engineering, IT and Robotics

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Implementation of a New Quasi-Optimal Controller Tuning Algorithm for Time-Delay Systems

Pekař¹,

Prokop²

2011

MATLAB for Engineers - Applications in Control, Electrical Engineering, IT and Robotics

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“…The use of pole-placement (pole-assignment, root-locus) tuning algorithms can be a possible way how to solve the setting problem, see e.g. [7][8][9]. However, these algorithms deal with poles only ignoring closed-loop zeros and/or they have been derived for state-space controllers.…”

Section: Introductionmentioning

confidence: 99%

“…controller parameter setting) is obtained using the Quasi-Continuous Shifting Algorithm (QCSA) [7], [8] which is followed by the use of an advanced numerical optimization algorithm. The method was independently developed in [9]; however, there are some essential differences -the reader is referred e.g. to [10] for details.…”

Section: Introductionmentioning

confidence: 99%

PPSA: A Tool for Suboptimal Control of Time Delay Systems: Revision and Open Tasks

Pekař

Navrátil

2014

Advances in Intelligent Systems and Computing

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Abstract. During the development of algebraic controller design in a special ring for time delay systems (TDSs) a problem of a suitable free controller parameters setting appeared. The first author of this contribution recently suggested a natural idea of placing the dominant characteristic numbers (poles) and zeros of the infinite-dimensional feedback control system on the basis of the desired overshoot for a simple finite-dimensional matching model and shifting of the rest of the spectrum. However, the original procedure called the Pole-Placement Shifting based controller tuning Algorithm (PPSA) was not developed and described entirely well. The aim of this paper is to revise the idea of the PPSA and suggest a possible ways how to improve or extend the algorithm. A concise illustrative example is attached to clarify the procedure for the reader as well.

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An approach to compute and design the delay margin of a large‐scale matrix delay equation

Ramírez

Koh

Sipahi

2018

Intl J Robust & Nonlinear

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A methodology to compute and design the delay margin (DM) of large-scale linear time-invariant systems is presented. Different from existing work, this methodology is scalable; does not impose restrictions on the system to be able to invoke simultaneous triangularization or simultaneous diagonalization; and sheds light on how the finite number of delay-free system eigenvalues can be effectively utilized to compute or design the DM. KEYWORDSdelay margin, delay margin design, time-delay systems INTRODUCTIONThe presence of time delays in feedback control systems has attracted tremendous interest in engineering, mathematics, and physics communities for over six decades. [1][2][3][4][5][6] The main reason for this is that delays can dramatically affect the dynamics of control systems. Notably, they can cause poor performance and even instability; and this must be properly dealt with either through controller design or through system design. Virtually, in all control applications, delays exist because it takes time to transmit information, sense information, formulate a proper decision, and execute such decisions. Widely studied problems include machine tool chatter, 7,8 teleoperation, 9,10 human reaction times in driving 11,12 and when operating an aircraft, 13,14 power networks, 15,16 population dynamics, 17,18 supply chain networks, 19,20 and gene regulatory networks. 21,22 In the pursuit of addressing the fundamental stability analysis and control design needs, one faces numerous challenges and opportunities. For example, the presence of delays makes the system infinite dimensional. In linear time-invariant (LTI) systems, this means that one has to deal with infinitely many poles, and thus, standard tools available for finite-dimensional problems are immediately ruled out as prospects to analyze stability and/or design controllers. Moreover, the presence of delay is not necessarily detrimental to the dynamics. An appropriate amount of delay can render improved disturbance rejection capabilities, 23 can increase stability margins, 24 can be deliberately introduced as part of a controller to enhance the performance of a closed-loop system, 25-28 or can provide stability. 29,30 One of the widely studied problems in the context of time-delay systems is the problem of computing the delay margin * (DM) of a system. An LTI system is stable for all delays from zero up to the DM ∈ [0, * ), which implies that when the delay value is equal to the DM = * , the system has at least one pole on the imaginary axis of the complex plane. 1 Many techniques have been developed to calculate the DM of LTI systems. Efforts in this direction possibly go back to 31 where the authors developed an approach to create "stability maps" of LTI systems with delay. These maps represent, on the plane of the delay and a parameter of interest, the boundaries along which the system can have imaginary poles ∓ j and which side of the boundaries indeed correspond to the stable operation of the system. Approaches to obtain similar maps have also been deve...

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Control design for time-delay systems based on quasi-direct pole placement

Cited by 70 publications

References 12 publications

Implementation of a New Quasi-Optimal Controller Tuning Algorithm for Time-Delay Systems

Implementation of a New Quasi-Optimal Controller Tuning Algorithm for Time-Delay Systems

PPSA: A Tool for Suboptimal Control of Time Delay Systems: Revision and Open Tasks

An approach to compute and design the delay margin of a large‐scale matrix delay equation

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