PLC Implementation of Piecewise Affine PI Controller Applied to Industrial Systems with Constraints

In this paper, the design of a piecewise affine proportional integral (PWA-PI) controller algorithm based on invariant set and multiparametric programming for constrained systems is proposed. We implemented the algorithm in a programmable logic controller (PLC) to control an industrial constrained level plant and analyze its behavior. Structured text routines were programmed and validated while controlling two systems with PLC. The results show that the constraints on the error, integral of the error, system output and control action are respected because PWA-PI controllers are tuned from the solution of an optimization problem. The evaluated performance indexes (such as mean square error, Goodhart, overshoot and settling time) show that PWA-PI can be adjusted for better performance than proportional integral (PI) controller tuned by Ziegler–Nichols (Z–N) rules. In the analyzed cases, a settling time of 108 s was obtained, whereas PI controller with Z–N rules presented a 179 s settling time. All of the analyzed performance indexes that we used to evaluate both controllers show PWA-PI as a better controller for constrained systems.

[1]  Karl Johan Åström,et al.  PID Controllers: Theory, Design, and Tuning , 1995 .

[2]  J. Hennet,et al.  (A, B)-Invariant Polyhedral Sets of Linear Discrete-Time Systems , 1999 .

[3]  Iluminada Baturone,et al.  High-Speed and Low-Cost Implementation of Explicit Model Predictive Controllers , 2019, IEEE Transactions on Control Systems Technology.

[4]  G. P. C. Weinkeller,et al.  Predictive Control via Multi-Parametric Programming Applied to the Dynamic Model of a Robotic Wheelchair , 2012, 2012 Brazilian Robotics Symposium and Latin American Robotics Symposium.

[5]  Carlos E. T. Dorea,et al.  Static output feedback control design for constrained linear discrete-time systems using data cluster analysis , 2018 .

[6]  J. G. Ziegler,et al.  Optimum Settings for Automatic Controllers , 1942, Journal of Fluids Engineering.

[7]  Eyal Dassau,et al.  Design and Evaluation of a Robust PID Controller for a Fully Implantable Artificial Pancreas , 2015, Industrial & engineering chemistry research.

[8]  J. L. Brown.  Output Correlation Function for a Half-wave Smooth Limiter† , 1965 .

[9]  G. Smith,et al.  Numerical Solution of Partial Differential Equations: Finite Difference Methods , 1978 .

[10]  Dmitriy Zelentsov,et al.  Neural Network Algorithm for Accuracy Control in Modelling of Structures with Changing Characteristics , 2018 .

[11]  Carlos E. T. Dorea,et al.  PID Control for Electric Vehicles Subject to Control and Speed Signal Constraints , 2018, J. Control. Sci. Eng..

[12]  Keith J. Burnham,et al.  Bilinear self-tuning control of a high temperature heat treatment plant , 1994 .

[13]  Nikolaos Athanasopoulos,et al.  A novel approach to the computation of the maximal controlled invariant set for constrained linear systems , 2009, 2009 European Control Conference (ECC).

[14]  P. R. Krishnaswamy,et al.  Estimation of time delay time constant parameters in time, frequency, and laplace domains , 1978 .

[15]  Wei Xing Zheng,et al.  Complete Stability of Neural Networks With Nonmonotonic Piecewise Linear Activation Functions , 2015, IEEE Transactions on Circuits and Systems II: Express Briefs.

[16]  Ju Zhang,et al.  Grid k-d tree approach for point location in polyhedral data sets – application to explicit MPC , 2018, Int. J. Control.

[17]  Hu Biaobiao,et al.  Using a Two-Level Structure to Manage the Point Location Problem in Explicit Model Predictive Control , 2016 .

[18]  Jun Liu,et al.  Computing maximal invariant sets for switched nonlinear systems , 2016, 2016 IEEE Conference on Computer Aided Control System Design (CACSD).

[19]  Martin Mönnigmann,et al.  Optimization-free robust MPC around the terminal region , 2018, Autom..

[20]  Robert Shorten,et al.  Stability Criteria for Switched and Hybrid Systems , 2007, SIAM Rev..

[21]  D. Puangdownreong.  Optimal PID Controller Design for DC Motor Speed Control System with Tracking and Regulating Constrained Optimization via Cuckoo Search , 2017 .

[22]  Felix Weber,et al.  Robust force tracking control scheme for MR dampers , 2015 .

[23]  F. Blanchini.  Ultimate boundedness control for uncertain discrete-time systems via set-induced Lyapunov functions , 1994, IEEE Trans. Autom. Control..

[24]  Franco Blanchini,et al.  Set invariance in control , 1999, Autom..

[25]  Muhammad Zeeshan,et al.  Adaptive fuzzy multivariable controller design based on genetic algorithm for an air handling unit , 2015 .

[26]  Michael Short,et al.  A Microcontroller-Based Adaptive Model Predictive Control Platform for Process Control Applications , 2017 .

[27]  Jianbin Qiu,et al.  Reliable Output Feedback Control for Piecewise Affine Systems With Markov-Type Sensor Failure , 2018, IEEE Transactions on Circuits and Systems II: Express Briefs.

[28]  B. R. Chahar,et al.  Flood control in an urban drainage system using a linear controller , 2017 .

[29]  J. Hennet,et al.  Feedback control of linear discrete-time systems under state and control constraints , 1988 .

[30]  Moonyong Lee,et al.  Analytical design of an industrial two-term controller for optimal regulatory control of open-loop unstable processes under operational constraints. , 2018, ISA transactions.

[31]  Manfred Morari,et al.  Multi-Parametric Toolbox 3.0 , 2013, 2013 European Control Conference (ECC).

[32]  Raad Z. Homod,et al.  Analysis and optimization of HVAC control systems based on energy and performance considerations for smart buildings , 2018, Renewable Energy.

[33]  Alberto Bemporad,et al.  The explicit linear quadratic regulator for constrained systems , 2003, Autom..

[34]  Franco Blanchini,et al.  Set-theoretic methods in control , 2007 .

[35]  C. Pinheiro,et al.  Implementation of a Rough Controller with Proportional–Integral Action to Control a Nonlinear System , 2017 .

[36]  J. Hennet,et al.  On invariant polyhedra of continuous-time linear systems , 1993, IEEE Trans. Autom. Control..