Disturbance Observer-based Robust Control and Its Applications: 35th Anniversary Overview

Disturbance Observer has been one of the most widely used robust control tools since it was proposed in 1983. This paper introduces the origins of Disturbance Observer and presents a survey of the major results on Disturbance Observer-based robust control in the last thirty-five years. Furthermore, it explains the analysis and synthesis techniques of Disturbance Observer-based robust control for linear and nonlinear systems by using a unified framework. In the last section, this paper presents concluding remarks on Disturbance Observer-based robust control and its engineering applications.Comment: 12 pages, 4 figure

PID Tuning: Analytical approach based on the weighted Sensitivity problem

[EN] The PID controller is the most common option in the realm of control applications and is dominant in the process control industry. Among the related analytical methods, Internal Model Control (IMC) has gained remarkable industrial acceptance due to its robust nature and good set-point responses. However, the traditional application of IMC results in poor load disturbance rejection for lag-dominant and integrating plants. This work presents an IMC-like design method which avoids this common pitfall and is devised to work well for plants of modest complexity, for which analytical PID tuning is plausible. For simplicity, the design only focuses on the closed-loop sensitivity function. The approach provides model-based tuning of single-loop PID controllers in terms of the robustness/performance and servo/regulator trade-offs. Although the robustness/performance compromise is commonly considered, it is not so common to also take into account, for example, the conflict between input and output disturbances, referred also as the servo/regulator trade-off. As interested in providing a unified tuning approach, it is shown how the proposed methodology allows to deal with different process dynamics in a unified way.[ES] El controlador PID es la opción más común en el ámbito de las aplicaciones de control, siendo la opción predominante en el control de procesos industriales. Entre los métodos analíticos más usuales utilizados para su diseño, el Control por Modelo Interno (IMC) ha ganado una notable aceptación industrial debido a su naturaleza robusta y buenas respuestas ante cambios de consigna. Sin embargo, la aplicación tradicional del IMC da como resultado un bajo rendimiento para el rechazo de perturbaciones en carga para plantas integradoras y/o con largas constantes de tiempo. Este trabajo presenta un método de diseño, basado en IMC, que evita esta deficiencia y está diseñado para funcionar bien en plantas de complejidad moderada para las cuales, por otro lado, el ajuste analítico de un controlador PID es plausible. Por simplicidad, el diseño solo se centra en la función de sensibilidad en lazo cerrado. El enfoque proporciona un ajuste basado en modelo en términos de los compromisos robustez/rendimiento y de servo/regulación. Aunque comúnmente se considera el compromiso robustez/rendimiento, no es tan común tener en cuenta también, por ejemplo, el conflicto entre las perturbaciones de entrada y salida, también conocido como el compromiso servo/regulación. Con el objetivo de proporcionar un enfoque de ajuste unificado, se muestra como la metodología propuesta permite tratar diferentes dinámicas de proceso de manera unificada.Los autores desean agradecer al Ministerio de Economía y Competitividad bajo las subvenciones DPI-2016-77271-R y PID2019-105434RB-C33 por la ayuda que han supuesto en la elaboración de los trabajos que han conducido a los desarrollos aquí presentados.Vilanova, R.; Alcántara, S.; Pedret, C. (2021). Sintonía de controladores PID: un enfoque analítico basado en el moldeo de la función de sensibilidad. Revista Iberoamericana de Automática e Informática industrial. 18(4):313-326. https://doi.org/10.4995/riai.2021.15422OJS313326184Alcántara, S., Vilanova, R., Pedret, C., 2013. PID control in terms of robustness/performance and servo/regulator trade-offs: A unifying approach to balanced autotuning. Journal of Process Control 23 (4), 527 - 542. https://doi.org/10.1016/j.jprocont.2013.01.003Alcántara, S., Pedret, C., Vilanova, R., 2010. On the model matching approach to PID design: Analytical perspective for robust Servo/Regulator tradeoff tuning. Journal of Process Control 20 (5), 596 - 608. https://doi.org/10.1016/j.jprocont.2010.02.011Alcántara, S., Pedret, C., Vilanova, R., Skogestad, S., 2011a. Generalized Internal Model Control for balancing input/output disturbance response. Industrial & Engineering Chemistry Research 50 (19), 11170-11180. https://doi.org/10.1021/ie200717zAlcántara, S., Vilanova, R., Pedret, C., 2020. PID Tuning: A Modern Approach via the Weighted Sensitivity Problem (1st ed.). CRC Press. https://doi.org/10.1201/9780429325335-1Alcántara, S., Vilanova, R., Pedret, C., Skogestad, S., 2012. A look into robustness/performance and servo/regulation issues in PI tuning. In: Proc. of the IFAC Conf. on Advances in PID Control PID'12. https://doi.org/10.3182/20120328-3-IT-3014.00031Alcántara, S., Zhang, W., Pedret, C., Vilanova, R., Skogestad, S., 2011b. IMC-like analytical H-inf design with S/SP mixed sensitivity consideration: Utility in PID tuning guidance. Journal of Process Control 21 (6), 976 - 985. https://doi.org/10.1016/j.jprocont.2011.04.007Alfaro, V. M., Vilanova, R., 2013a. Performance and Robustness Considerations for Tuning of Proportional Integral/Proportional Integral Derivative Controllers with Two Input Filters. Industrial & Engineering Chemistry Research 52, 18287-18302. https://doi.org/10.1021/ie4012694Alfaro, V. M., Vilanova, R., 2013b. Robust tuning of 2DoF five-parameters PID controllers for inverse response controlled processes. Journal of Process Control 23, 453-462. https://doi.org/10.1016/j.jprocont.2013.01.005Alfaro, V. M., Vilanova, R., September 2013c. Simple robust tuning of 2DoF PID controllers from a performance/robustness trade-off analysis. Asian Journal of Control 15 (5), 1-14. https://doi.org/10.1002/asjc.653Alfaro, V. M., Vilanova, R., 2016. Model-Reference Robust Tuning of PID Controllers. Springer International Publishing AG, Gewerbestrasse 11, 6330 Cham, Switzerland, ISBN 978-3-319-28213-8.Alfaro, V. M., Vilanova, R., Méndez, R., Lafuente, J., 2010. Performance/Robustness Tradeoff Analysis of PI/PID Servo and Regulatory Control Systems. In: Proc. of the IEEE International Conference on Industrial Technology. https://doi.org/10.1109/ICIT.2010.5472662Arrieta, O., Vilanova, R., 2012. Simple servo/regulation proportional-integralderivative (pid) tuning rules for arbitrary ms-based robustness achievement. Industrial & Engineering Chemistry Research 51 (6), 2666-2674. https://doi.org/10.1021/ie201655cArrieta, O., Vilanova, R., Rojas, J. D., Meneses, M., 2016. Improved pid controller tuning rules for performance degradation/robustness increase trade-off. Electrical Engineering 98 (3), 233-243. https://doi.org/10.1007/s00202-016-0361-xArrieta, O., Visioli, A., Vilanova, R., 2010. PID autotuning for weighted servo/regulation control operation. Journal of Process Control 20 (4), 472 -480. https://doi.org/10.1016/j.jprocont.2010.01.002Astrom, K., Hagglund, T., 2004. Revisiting the Ziegler-Nichols step response method for PID control. J. Process Control 14, 635-650. https://doi.org/10.1016/j.jprocont.2004.01.002Astrom, K., Hagglund, T., 2005. Advanced PID control. ISA - The Instrumentation, Systems, and Automation Society.Chien, I. L., Fruehauf, P. S., 1990. Consider IMC tuning to improve controller performance. Chemical Engineering Progress 86 (10), 33 - 41.Dehghani, A., Lanzon, A., Anderson, B., 2006. H1 design to generalize internalmodel control. Automatica 42 (11), 1959 - 1968.Grimholt, C., Skogestad, S., 2012. Optimal PI Control and Verifcation of the SIMC Tuning Rule. In: Proc. of the IFAC Conf. on Advances in PID Control PID'12. https://doi.org/10.3182/20120328-3-IT-3014.00003Horn, I. G., Arulandu, J. R., Gombas, C. J., VanAntwerp, J. G., Braatz, R. D., 1996. Improved Filter Design in Internal Model Control. Industrial & Engineering Chemistry Research 35 (10), 3437 - 3441. https://doi.org/10.1021/ie9602872Huba, M., 2012. Setpoint Versus Disturbance Responses of the IPDT Plant. In: Proc. of the IFAC Conf. on Advances in PID Control PID'12. https://doi.org/10.3182/20120328-3-IT-3014.00070J.Shi, W.S.Lee, 2004. Set Point Response and Disturbance Rejection Tradeoff for Second-Order Plus Dead Time Processes. In: Asian Control Conference.Kristiansson, B., Lennartson, B., 1998. Optimal PID controllers for unstable and resonant plants. In: Proc. of the IEEE Conference on Decision and Control. pp. 4380-4381.Kurokawa, R., Sato, T., Vilanova, R., Konishi, Y., 2019. Discrete-time firstorder plus dead-time model-reference trade-off pid control design. Applied Sciences 9 (16). https://doi.org/10.3390/app9163220Kurokawa, R., Sato, T., Vilanova, R., Konishi, Y., 2020. Design of optimal pid control with a sensitivity function for resonance phenomenon-involved second-order plus dead-time system. Journal of the Franklin Institute 357 (7), 4187-4211. https://doi.org/10.1016/j.jfranklin.2020.03.015Leva, A., Maggio, M., 2012. Model-Based PI(D) Autotuning. In: PID Control in the Third Millennium. Lessons Learned and New Approaches. Springer. https://doi.org/10.1007/978-1-4471-2425-2_2Mercader, P., Astrom, K. J., Baños, A., Hagglund, T., 2017a. Robust pid design based on qft and convex?concave optimization. IEEE Transactions on Control Systems Technology 25 (2), 441-452. https://doi.org/10.1109/TCST.2016.2562581Mercader, P., Baños, A., 2017. A pi tuning rule for integrating plus dead time processes with parametric uncertainty. ISA Transactions 67, 246-255. https://doi.org/10.1016/j.isatra.2017.01.025Mercader, P., Baños, A., Vilanova, R., 2017b. Robust proportional-integral-derivative design for processes with interval parametric uncertainty. IET Control Theory & Applications 11 (7), 016-1023. https://doi.org/10.1049/iet-cta.2016.1239Mercader, P., Soltesz, K., Baños, A., 2017c. Robust pid design by chance-constrained optimization. Journal of the Franklin Institute 354 (18), 8217-8231. https://doi.org/10.1016/j.jfranklin.2017.10.017Meza, G. R., Ferragud, X. B., Saez, J. S., Dur, J. M. H., 2016. Controller Tuning with Evolutionary Multiobjective Optimization: A Holistic Multiobjective Optimization Design Procedure, 1st Edition. Springer Publishing Company, Incorporated.Middleton, R. H., Graebe, S. F., 1999. Slow stable open-loop poles: to cancel or not to cancel. Automatica 35 (5), 877-886. https://doi.org/10.1016/S0005-1098(98)00220-9Morari, M., Zafiriou, E., 1989. Robust Process Control. Prentice-Hall International.Panagopoulos, H., Astrom, K. J., 2000. PID control design and H1 loop shaping. International Journal of Robust and Nonlinear Control 10 (15), 1249-1261. https://doi.org/10.1002/1099-1239(20001230)10:153.0.CO;2-7Pedret, C., Vilanova, R., Moreno, R., Serra, I., 2002. A refinement procedure for PID controller tuning. Computers & Chemical Engineering 26 (6), 903- 908. https://doi.org/10.1016/S0098-1354(02)00011-XRivera, D. E., Morari, M., Skogestad, S., 1986. Internal model control: PID controller design. Industrial & Engineering Chemistry Process Design and Development 25 (1), 252 - 265. https://doi.org/10.1021/i200032a041Rodriguez, C., September 2020. Revisiting the simplified imc tuning rules for low-order controllers: Novel 2dof feedback controller. IET Control Theory & Applications 14, 1700-1710(10). https://doi.org/10.1049/iet-cta.2019.0821Ruscio, D. D., 2010. On Tuning PI Controllers for Integrating Plus Time Delay Systems. 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Control of open-loop unstable processes with time delay using PI/PID controllers specified using tuning rules: An outline survey

The ability of PI and PID controllers to compensate many practical processes has led to their wide acceptance in industrial applications. The requirement to choose two or three controller parameters is conveniently done using tuning rules. Starting with a general discussion of industrial practice, the paper provides a survey of tuning rules for continuous time PI and PID control of open-loop unstable time-delayed single-input, single-output (SISO) processes

Optimal Robust PID control for first- and second-order plus dead-time processes

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

An Active Disturbance Rejection Control Solution for Electro-Hydraulic Servo Systems

The intriguing history of disturbance cancellation control is reviewed in this thesis first, which demonstrates that this unique control concept is both reasonable and practical. One novel form of disturbance cancellation, ADRC (Active Disturbance Rejection Control), attracts much attention because of its good disturbance rejection ability and simplicity in implementation. Hydraulic systems tend to have many disturbances and model uncertainties, giving us a great motivation to find out a good control method. In this thesis, electro-hydraulic servo control problem is reformulated to focus on the core problem of disturbance rejection. An ADRC solution is developed and evaluated against the industry standard solution, with promising result

Using controller tuning formulae to improve performance

The proportional integral derivative (PID) controller is the most dominant form of automatic controller in industrial use today. With this device, it is necessary to adjust the controller parameters according to the nature of the process. Thus, for effective control of a HVDC system, for example, specific values need to be chosen for the P, I and D parameters, which will be different for the values required to control, for example, an induction motor drive. This tailoring of controller to process is known as controller tuning. Controller tuning is easily and effectively performed using tuning rules (i.e. formulae for controller tuning, based on process information). Such tuning rules allow the easy set up of controllers to achieve optimum performance at commissioning. Importantly, they allow ease of re-commissioning if the characteristics of the process change. The paper communicates the results of recent work in the collation of industry-relevant PI and PID controller tuning rules, which may be applied to a variety of applications in power electronics, machines and drives

A classification of techniques for the compensation of time delayed processes. Part 2: Structurally optimised controllers

Following on from Part 1, Part 2 of the paper considers the use of structurally optimised controllers to compensate time delayed processes

A unified approach for proportional-integral-derivative controller design for time delay processes

Abstract−An analytical design method for PI/PID controller tuning is proposed for several types of processes with time delay. A single tuning formula gives enhanced disturbance rejection performance. The design method is based on the IMC approach, which has a single tuning parameter to adjust the performance and robustness of the controller. A simple tuning formula gives consistently better performance as compared to several well-known methods at the same degree of robustness for stable and integrating process. The performance of the unstable process has been compared with other recently published methods which also show significant improvement in the proposed method. Furthermore, the robustness of the controller is investigated by inserting a perturbation uncertainty in all parameters simultaneously, again showing comparable results with other methods. An analysis has been performed for the uncertainty margin in the different process parameters for the robust controller design. It gives the guidelines of the M s setting for the PI controller design based on the process parameters uncertainty. For the selection of the closed-loop time constant, (τ c ), a guideline is provided over a broad range of θ/τ ratios on the basis of the peak of maximum uncertainty (M s ). A comparison of the IAE has been conducted for the wide range of θ/τ ratio for the first order time delay process. The proposed method shows minimum IAE in compared to SIMC, while Lee et al. shows poor disturbance rejection in the lag dominant process. In the simulation study, the controllers were tuned to have the same degree of robustness by measuring the M s , to obtain a reasonable comparison

Performance analysis of robust stable PID controllers using dominant pole placement for SOPTD process models

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this recordThis paper derives new formulations for designing dominant pole placement based proportionalintegral-derivative (PID) controllers to handle second order processes with time delays (SOPTD). Previously, similar attempts have been made for pole placement in delay-free systems. The presence of the time delay term manifests itself as a higher order system with variable number of interlaced poles and zeros upon Pade approximation, which makes it difficult to achieve precise pole placement control. We here report the analytical expressions to constrain the closed loop dominant and nondominant poles at the desired locations in the complex s-plane, using a third order Pade approximation for the delay term. However, invariance of the closed loop performance with different time delay approximation has also been verified using increasing order of Pade, representing a closed to reality higher order delay dynamics. The choice of the nature of non-dominant poles e.g. all being complex, real or a combination of them modifies the characteristic equation and influences the achievable stability regions. The effect of different types of non-dominant poles and the corresponding stability regions are obtained for nine test-bench processes indicating different levels of open-loop damping and lag to delay ratio. Next, we investigate which expression yields a wider stability region in the design parameter space by using Monte Carlo simulations while uniformly sampling a chosen design parameter space. The accepted data-points from the stabilizing region in the design parameter space can then be mapped on to the PID controller parameter space, relating these two sets of parameters. The widest stability region is then used to find out the most robust solution which are investigated using an unsupervised data clustering algorithm yielding the optimal centroid location of the arbitrary shaped stability regions. Various time and frequency domain control performance parameters are investigated next, as well as their deviations with uncertain process parameters, using thousands of Monte Carlo simulations, around the robust stable solution for each of the nine test-bench processes. We also report, PID controller tuning rules for the robust stable solutions using the test-bench processes while also providing computational complexity analysis of the algorithm and carry out hypothesis testing for the distribution of sampled data-points for different classes of process dynamics and non-dominant pole types.KH acknowledges the support from the University Grants Commission (UGC), Govt. of India under its Basic Scientific Research (BSR) schem

The estimation and compensation of processes with time delays

The estimation and compensation of processes with time delays have been of interest to academics and practitioners for several decades. A full review of the literature for both model parameter and time delay estimation is presented. Gradient methods of parameter estimation, in open loop, in the time and frequency domains are subsequently considered in detail. Firstly, an algorithm is developed, using an appropriate gradient algorithm, for the estimation of all the parameters of an appropriate process model with time delay, in open loop, in the time domain. The convergence of the model parameters to the process parameters is considered analytically and in simulation. The estimation of the process parameters in the frequency domain is also addressed, with analytical procedures being defined to provide initial estimates of the model parameters, and a gradient algorithm being used to refine these estimates to attain the global minimum of the cost function that is optimised. The focus of the thesis is subsequently broadened with the consideration of compensation methods for processes with time delays. These methods are reviewed in a comprehensive manner, and the design of a modified Smith predictor, which facilitates a better regulator response than does the Smith predictor, is considered in detail. Gradient algorithms are subsequently developed for the estimation of process parameters (including time delay) in closed loop, in the Smith predictor and modified Smith predictor structures, in the time domain; the convergence of the model parameters to the process parameters is considered analytically and in simulation. The thesis concludes with an overview of the methods developed, and projections regarding future developments in the topics under consideration