Multivariable predictive control with filtered variables in prediction equations

The paper is focused on an implementation of a multivariable predictive controller with a colouring filter C in a disturbance model. The filter is often essential for practical applications of predictive control based on input-output models. It is commonly considered as a design parameter because it has direct effects on closed loop performance. In this paper a computation of predictions for the case with the colouring filter is introduced. The computation is based on a particular model of the controlled system in the form of matrix fraction which is commonly used for description of a range of multivariable processes. Performance of closed loop system with and without the colouring filter in the disturbance model was compared.Ministry of Education, Youth and Sports of the Czech Republic within the National Sustainability Programme [LO1303 (MSMT-7778/2014)]; European Regional Development Fund under the project CEBIA-Tech [CZ.1.05/2.1.00/03.0089]; Programme EEA and Norway Grants [NF-CZ07-ICP-4-345-2016]ERDF, European Regional Development Fund; CZ.1.05/2.1.00/03.0089, ERDF, European Regional Development Fun

Predictive control dead-time processes

One of the possible approaches to control of dead-time processes is application of predictive control methods. In technical practice often occur higher order processes when a design of an optimal controller leads to complicated control algorithms. One of the possibilities of control of such processes is their approximation by lower-order model with dead-time (time-delay). The first part of the paper deals with a design of an algorithm for predictive control of high-order processes which are approximated by a second-order model of the process with time-delay. The second part of the paper deals with a design of an analogical algorithm for predictive control of multivariable processes with time-delay. The predictive controllers are based on the recursive computation of predictions which was extended for the time-delay system. The designed control algorithms were verified by simulation. © 2017, World Scientific and Engineering Academy and Society. All rights reserved

Adaptive LQ cascade control of a tubular chemical reactor

The paper deals with adaptive LQ cascade control design of a tubular chemical reactor with an exothermic consecutive reaction. The control is performed in primary and secondary control-loops where the primary controlled output of the reactor is the concentration of a main reaction product and the secondary output is the mean temperature of the reactant. A common control input is the coolant flow rate. The controller in the primary control-loop is a nonlinear P-controller with the gain calculated using simulated or measured steady-state characteristics of the reactor. The controller in the secondary control-loop is a LQ adaptive controller. The proposed method is verified by control simulations

Statistical analysis of modified predictive control of non-minimum phase system

Testing statistical hypothesis in comparison of corresponding pairs of signals in control has not been widely used both in practice and research. In this paper, pairs of signals obtained during control before and after a modification of a control algorithm are paired tested by quantitative methods. In previous research, the authors used this type of mathematical analysis with regards to the control quality in an analysis of signals in multivariable MPC with a modified optimization strategy. The control quality was slightly influenced in favour of the decreasing the computational complexity of the MPC control algorithm. In this paper, results of a predictive control of a non-minimum phase system with an elimination of the undershoot are analysed in detail. The control algorithm was modified by a particular setting of control constraints. The aim of this modification was suppression of the undershoot. The quality of control with the original and modified control algorithms is analysed by testing hypothesis. Particular signals are compared using the testing hypotheses on the statistically significant differences. © 2019, World Scientific and Engineering Academy and Society. All rights reserved

Modifications of optimization algorithms applied in multivariable predictive control

Non-linear optimization, particularly quadratic programming (QP), is a mathematical method which is widely applicable in model predictive control (MPC). It is significantly important if constraints of variables are considered in MPC and the optimization task is then computationally demanding. The result of the optimization is a vector of future increments of a manipulated variable. The first element of this vector is applied in the next sampling period of MPC in the framework of a receding horizon strategy. In practical realization of a multivariable MPC, the optimization is characterized by higher computational complexity. Therefore, reduction of the computational complexity of the optimization methods has been widely researched. Besides the generally used numerical Hildreth’s method of QP, a possible suitable modification is based on precomputing operations proposed by Wang, L. This general optimization strategy is further modified. Two modifications, which could be applied separately each, were interconnected in this paper. The first modification was published previously; however, its application can be more efficient in connection with the second proposed approach, which modifies precomputing operations. Decreasing of the computational complexity of the optimization by using of the proposal is discussed and analyzed by measurements of floating point operations and control quality criterions using hypotheses tests – paired T-test and Wilcoxon test. © 2018, World Scientific and Engineering Academy and Society. All rights reserved

Continuous-time and discrete multivariable decoupling controllers

The paper is focused on a design and implementation of a decoupling multivariable controller. The controller was designed in both discrete and continuous-time versions. The control algorithm is based on polynomial theory and pole - placement. A decoupling compensator is used to suppress interactions between control loops. The controller integrates an on - line identification of an ARX model of a controlled system and a control synthesis on the basis of the identified parameters. The model parameters are recursively estimated using the recursive least squares method

Polynomial digital control of a series equal liquid tanks

Time-delays are mainly caused by the time required to transport mass, energy or information, but they can also be caused by processing time or accumulation. Typical examples of such processes are e.g. pumps, liquid storing tanks, distillation columns or some types of chemical reactors. In many cases time-delay is caused by the effect produced by the accumulation of a large number of low-order systems. Several industrial processes have the time-delay effect produced by the accumulation of a great number of low-order systems with the identical dynamic. The dynamic behavior of series these low-order systems is expressed by high-order system. One of possibilities of control of such processes is their approximation by low-order model with time-delay. The paper is focused on the design of the digital polynomial control of a set of equal liquid cylinder atmospheric tanks. The designed control algorithms are realized using the digital Smith Predictor (SP) based on polynomial approach by minimization of the Linear Quadratic (LQ) criterion. The LQ criterion was combined with pole assignment

Predictive control of multivariable time-delay systems

In technical practice often occur multivariable processes with time delay. Time-delays are mainly caused by the time required to transport mass, energy or information, but they can also be caused by processing time or accumulation. In a multivariable system each input may influence all system outputs. The design of a controller for such a system must be quite sophisticated if the system is to be controlled adequately. One of the possible approaches to control of multivariable time-delay processes is application of predictive control methods. The paper deals with design of an algorithm for predictive control of multivariable processes with time-delay. The predictive controller is based on the recursive computation of predictions which was extended for the time-delay system. The control of a multivariable system with two steps of time-delay was verified by simulation. © The Authors, published by EDP Sciences, 2017

Self-tuning control: Laboratory real-time education

The combination of the automatic control theory courses and practical implementation of the designed controller algorithms in real-time conditions is very important for training of the control engineers. This contribution presents a MATLAB-Toolbox for design, simulation verification and especially real-time implementation of single input - single output (SISO) discrete self-tuning controllers. The proposed adaptive controllers what are included into a Toolbox can be divided into three groups. The first group covers PID adaptive algorithms using traditional Ziegler-Nichols method for the setting of the controller parameters, the second group of described controllers is based on the pole placement design and the third group contains the controllers derived on the other approaches (dead-beat, minimum variance etc.). The controllers are implemented as an encapsulated SIMULINK blocks and thus allows users simple integration into existing SIMULINK schemas. The process of developing real-time applications using MATLAB Real-Time Workshop and several control courses is also presented. The MATLAB-Toolbox is very successfully used in Adaptive Control Course in education practice for design and verification of self-tuning control systems in real-time. It is suitable for design and verification of the industrial controllers, too. The MATLAB-Toolbox is available free ofcharge at Internet site - bttp:llwww.utb.cz/stctooll. Copyright © IFAC Advances in Control Education Oulu, Finland, 200