Autotuning for delay systems using meromorphic functions

The paper presents an autotuning method for time delay systems. The novelty in principles is a new combination of biased-relay feedback identification and an algebraic control design method for timedelay systems. The estimation of the controlled process is based on an asymmetrical limit cycle data experiment. Then, a stable transfer function with a dead-time term is identified. The controller is designed through solutions of Diophantine equations in the ring of stable and proper retarded quasipolynomial meromorphic functions. Controller parameters are tuned through a pole-placement problem as a desired multiple root of the characteristic closed loop equation. First and second order identification gives Smith-like feedback controllers with the realistic PI and PID structure. The design principle also offers a scalar tuning parameter m 0 > 0 which can be adjusted by a suitable principle or an optimization method. The developed approach is illustrated by examples in the Matlab + Simulink environment

Time delay systems - meromorphic functions control approach

The paper brings an engineering acceptable approach for anisochronic controllers. The method is based on algebraic tools in the ring of RQ-meromorphic functions and it was developed for a wide class of delayed systems. This contribution deals with so-called anisochronic systems which include delays also in dynamics. Both stable and unstable systems are assumed. The control synthesis consists in the solution of the Bèzout identity and Youla-Kučera parameterization resulting in the Smith-like control structure. A final controller can be tuned by a suitable choice of a scalar real parameter. Among many others tuning methods, the equalization method is adopted. The approach is suitable also for high order dynamics approximation and autotuning procedures. First order stable and unstable simulation examples are presented. Copyright © 2007 IFAC

Reléový test pro anizochronní modely - řešení v časové oblasti

Anisochronic models are characteristic for containing state delays. These models have some practical and attractive features; e.g. they enable to fit the dynamics of systems with very high order. This contribution utilizes an idea of anisochronic models identification based on limit cycle information obtained from relay feedback test is investigated. Unlike conventional approaches connected with the frequency analysis of a plant transfer function, the proposed alternative methodology is based on computation with functional differential equation only, i.e. in time domain. Plant parameters to be identified are obtained analytically. In addition, parameter estimation is also improved using autotune variable (ATV+) technique which required an additional delay element. An illustrative example where parameters of a tenth order system are approximated by a first order anisochronic model is presented.Anizochronní modely jsou význačné tím, že obsahují zpoždění stavových veličin. Tyto modely mají některé zajímavé vlastnosti – například umožňují vystihnout dynamiku konvenčních soustav vyšších řádů a dále matematické modely mnoha procesů vedou právě na anisochronní modely. V tomto příspěvku je prezentována myšlenka identifikace těchto modelů pomocí reléového experimentu. Narozdíl od tradičního pojetí je zde uveden postup pro odhad parametrů modelu přímo z diferenciální rovnice, tedy v časové oblasti. Reléový test je dále vylepšen pomocí metody ATV+ využívající umělého zpoždění. Ilustrační příklad, kde je systém 10. řádu aproximován anizochronním modelem 1. řádu, demonstruje uvedenou metodiku

PID and PID-like controller design by pole assignment within D-stable regions

This paper presents a new PID and PID-like controller design method that permits the designer to control the desired dynamic performance of a closed-loop system by first specifying a set of desired D-stable regions in the complex plane and then running a numerical optimisation algorithm to find the controller parameters such that all the roots of the closed-loop system are within the specified regions. This method can be used for stable and unstable plants with high order degree, for plants with time delay, for controller with more than three design parameters, and for various controller configurations. It also allows a unified treatment of the controller design for both continuous and discrete systems. Examples and comparative simulation results are pro-vided to illustrate its merit

Improved cascade control structure for enhanced performance

In conventional single feedback control, the corrective action for disturbances does not begin until the controlled variable deviates from the set point. In this case, a cascade control strategy can be used to improve the performance of a control system particularly in the presence of disturbances. In this paper, an improved cascade control structure and controller design based on standard forms, which was initially given by authors, is suggested to improve the performance of cascade control. Examples are given to illustrate the use of the proposed method and its superiority over some existing design methods

Asymmetric system model parameters identification framework via relay feedback

This paper proposes an innovative framework of a parameter estimation procedure based on the well-established relay-feedback experiment paradigm. The novelty consists in consideration of asymmetric dynamics and non-equal static gains of the identified system. A different system behavior after changing the input variable polarity near the operating point is rarely considered or even omitted within relay-based parameter identification tests, in contrast to the common use of asymmetry in the nonlinear relay element. The thing is that many existing relay-based identification techniques in the frequency domain use integrations, assuming that the system output operating point coincides with the setpoint value (i.e., the offset between them is zero). However, this is not true for asymmetric dynamic systems, which yields considerably erroneous parameter estimation as the integration result is highly sensitive to the baseline value. The resulting iterative numerical optimization-based algorithm is built-up using a chain of natural assumptions and step-by-step thought experiments. The proposed framework is applied to the well-established exponential decaying method in this paper. Some computation aspects of the algorithm are discussed. A comparative numerical study illustrates the efficacy of the proposed strategy, where several frequency-fitting-based and descriptive-function-based competitive approaches are considered

Algebraic principles as a tool for energy saving

This paper discusses algebraic approaches of control design for a set of Single Input - Single Output (SISO) delayed systems that are further developed and discussed. The first principle utilises a special ring RQM, - a set of RQ-meromorphic functions. The second one is based on a ring of proper and stable rational functions RPS and can be considered as a special case. Controller parameters are derived through the general solution of linear Diophantine equations in the appropriate ring. A final controller can be tuned by the scalar real parameter m0>0. The methodology is illustrated by a comparison with another approach, some analyses of a tuning parameter and example. The simulations are performed in the Matlab environment. Copyright © 2020, AIDIC Servizi S.r.l

Closed-Loop Identification Applied to a DC Servomechanism: Controller Gains Analysis

Usually, when parameter identification is applied, there are some gains related to the identification algorithm whose value must be carefully adjusted in order to obtain a good performance of the algorithm. However, when performing closed loop identification, there are some other constants that in general are not taken into account for the identification algorithm: the controller gains, which may appear inside the identification algorithm, specifically in the regressor vector, which is very important for the parameter convergence according to the persistence of excitation condition. Therefore, the effect of these gains on the estimated parameters should be analyzed so that better estimates can be obtained. This paper addresses the behavior of the parameter estimates for a closed-loop identification methodology applied to a DC servomechanism with a bounded perturbation signal and a PD controller. It is shown that, with this perturbation, the parameter estimates converge to a region whose size can be modified not only by varying the identification algorithm gains but also by modifying the P and D controller gains in a suitable way