How to design externally positive feedback loops – an open problem of control theory

2020 ◽  
Vol 68 (5) ◽  
pp. 301-311
Author(s):  
Alexander Schwab ◽  
Jan Lunze

AbstractThis paper addresses the properties of externally positive systems and summarises existing conditions and design approaches that achieve externally positive closed-loop dynamics. The output variable of such systems is always nonnegative for any nonnegative input which is a very useful property in various control tasks. This paper investigates the problem of rendering control loops externally positive by an appropriate choice of a feedback. It shows that there is currently no general design procedure for that purpose and the question of when such a controller exists has not been clarified yet. It is also shown that there are plants for which there is no controller that leads to an externally positive control loop.

2017 ◽  
Author(s):  
◽  
Nelendran Pillay

Controller performance assessment (CPA) is concerned with the design of analytical tools that are utilized to evaluate the performance of process control loops. The objective of the CPA is to ensure that control systems operate at their full potential, and also to indicate when a controller design is performing unsatisfactorily under current closed loop conditions. Such monitoring efforts are imperative to minimize product variability, improve production rates and reduce wastage. Various studies conducted on process control loop performance indicate that as many as 60% of control loops often suffer from some kind of performance problem. It is therefore an important task to detect unsatisfactory control loop behavior and suggest remedial action. Such a monitoring system must be integrated into the control system life span as plant changes and hardware issues become apparent. CPA is well established for linear systems. However, not much research has been conducted on CPA for nonlinear systems. Traditional CPA analytical tools depend on the theoretical minimum variance control law that is derived from models of linear systems. In systems exhibiting dominant nonlinear behavior, the accuracy of linear based CPA is compromised. In light of this, there is a need to broaden existing CPA knowledge base with comprehensive benchmarking indices for the performance analysis of nonlinear process control systems. The research efforts presented in this thesis focuses on the development and analysis of such CPA tools for univariate nonlinear process control loops experiencing the negative effects of dominant nonlinearities emanating from the process. Two novel CPA frameworks are proposed; first a model based nonlinear assessment index is developed using an open loop model of the plant in an artificial neural network NARMAX (NNARMAX) representation. The nonlinear control loop is optimized offline using a proposed Nelder Mead-Particle Swarm Optimization (NM-PSO) hybrid search to determine global optimal control parameters for a gain scheduled PID controller. Application of the benchmark in real-time utilizes a synthetic process output derived from the NNARMAX system which is compared to the actual closed loop performance. In the case where no process model is available, a second method is presented. An autonomous data driven approach based on Multi-Class Support Vector Machines (MC- SVMs) is developed and analyzed. Unlike the model based method, the closed loop performance is classified according to five distinct class groups. MC-SVM classifier requires minimal process loop information other than routine operating closed loop data. Several simulation case studies conducted using MATLAB™ software package demonstrate the effectiveness of the proposed performance indices. Furthermore, the methodologies presented in this work were tested on real world systems using control loop data sets from a computer interfaced full scale pilot pH neutralization plant and pulp and paper industry.


10.14311/742 ◽  
2005 ◽  
Vol 45 (4) ◽  
Author(s):  
M. Hrouzek

This paper offers a concise survey of the most commonly used feedback loops for atomic force microscopes. In addition it proposes feedback control loops in order to minimize the effect of thermal noise on measurements of weak forces, and to improve the manipulability of the AFM. Growing requirements to study and fabricate systems of ever-shrinking size mean that ever-increasing performance of instruments like atomic force microscopes (AFM) is needed. A typical AFM consists of a micro-cantilever with a sharp tip, a sample positioning system, a detection system and a control system. Present day commercial AFMs use a standard PI controller to position the micro-cantilever tip at a desired distance from the sample. There is still a need for studies showing the optimal way to tune these controllers in order to achieve high closed-loop positioning performance. The choice of other controller structures, more suitable for dealing with the robustness/performance compromise can also be a solution. 


Author(s):  
Volodymyr Drevetskyi ◽  
Ivan Kovela ◽  
Vitalii Kutia

It was proposed a method of comparative estimation of process control loops based on a complex of direct and indirect performance measurers taking into account stability margins. It was presented a comparison algorithm for complex performance parameter considering the influence of stability margins of a control loop on its properties. Features of the method of comparative estimation of process control systems performance have been considered as an example for the closed loop feedback control system with PI controller (4 variations) and the second order plus transport delay plant.


ACTA IMEKO ◽  
2019 ◽  
Vol 8 (4) ◽  
pp. 62
Author(s):  
Na Wang ◽  
Balint Kiss

Several classes of weight handling equipment with nonlinear dynamics are exact linearizable by feedback. This implies that a controller ensuring exponential decay of the tracking error along a reference trajectory can be also designed. The control of both fully actuated robotic arms and underactuated crane-like systems can be addressed through this method. However, the value of model parameters such as the mass of the load or the friction coefficients must be known to calculate the actuated inputs in closed-loop. Uncertainty of these parameters may result in unstable closed-loop dynamics or in the deterioration of the tracking performance. This paper presents a design procedure to take into consideration such uncertainties using a serial pre-filter which is determined using H_infty techniques. The procedure is applied for a SCARA type robotic arm and for a two-dimensional overhead crane system. Simulation results show the applicability of the suggested method.


2021 ◽  
Vol 26 (1) ◽  
pp. 21
Author(s):  
Ahmad Taher Azar ◽  
Fernando E. Serrano ◽  
Nashwa Ahmad Kamal

In this paper, a loop shaping controller design methodology for single input and a single output (SISO) system is proposed. The theoretical background for this approach is based on complex elliptic functions which allow a flexible design of a SISO controller considering that elliptic functions have a double periodicity. The gain and phase margins of the closed-loop system can be selected appropriately with this new loop shaping design procedure. The loop shaping design methodology consists of implementing suitable filters to obtain a desired frequency response of the closed-loop system by selecting appropriate poles and zeros by the Abel theorem that are fundamental in the theory of the elliptic functions. The elliptic function properties are implemented to facilitate the loop shaping controller design along with their fundamental background and contributions from the complex analysis that are very useful in the automatic control field. Finally, apart from the filter design, a PID controller loop shaping synthesis is proposed implementing a similar design procedure as the first part of this study.


2015 ◽  
Vol 1084 ◽  
pp. 636-641
Author(s):  
Valeriy F. Dyadik ◽  
Nikolay S. Krinitsyn ◽  
Vyacheslav A. Rudnev

The article is devoted to the adaptation of the controller parameters during its operation as a part of a control loop. The possibility to identify the parameters of the controlled plant model in the closed control loop has been proved by a computer simulation. The described active identification method is based on the response processing of the closed loop control system to standard actions. The developed algorithm has been applied to determine the model parameters of the flaming fluorination reactor used for the production of uranium hexafluoride. Designed identification method improves the quality of the product and the efficiency of the entire production.


2021 ◽  
Vol 27 (1) ◽  
pp. 79-88
Author(s):  
Rafal Fawzi Faisal ◽  
Omar Waleed Abdulwahhab

This paper deals with a Twin Rotor Aerodynamic System (TRAS). It is a Multi-Input Multi-Output (MIMO) system with high crosscoupling between its two channels. It proposes a hybrid design procedure that combines frequency response and root locus approaches. The proposed controller is designated as PID-Lead Compensator (PIDLC); the PID controller was designed in previous work using frequency response design specifications, while the lead compensator is proposed in this paper and is designed using the root locus method. A general explicit formula for angle computations in any of the four quadrants is also given. The lead compensator is designed by shifting the dominant closed-loop poles slightly to the left in the s-plane. This has the effect of enhancing the relative stability of the closed-loop system by eliminating the oscillation in its transient part but at the expense of greater rise time. However, for some applications, long rise time may be an allowable price to get rid of undesired oscillation. To demonstrate the proposed hybrid controller's performance numerically, a new performance index, designated by Integral Reciprocal Time Absolute Error (IRTAE), is defined as a figure to measure the oscillation of the response in its transient part. The proposed controller enhances this performance index by 0.6771%. Although the relative enhancement of the performance index is small, it contributes to eliminating the oscillation of the response in its transient part. Simulation results are performed on the MATLAB/Simulink environment.


1986 ◽  
Vol 4 (1) ◽  
pp. 9-15
Author(s):  
Takahiro MASUDA ◽  
Akemi FUTAKAWA ◽  
Suguru ARIMOTO ◽  
Fumio MIYAZAKI

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