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

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 redictions 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

Convenient optimization strategy implemented in multivariable predictive control

A significantly important part of model predictive control (MPC) with constraints is a solution of an optimization task. 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. One suitable principle of precomputing operations was proposed by Wang, L. This general optimization strategy is further modified in this paper. Decreasing of the computational complexity of the optimization by using of the proposed modification is discussed

Statistical analysis of control quality of MPC using testing hypothesis

Methods of the statistical induction have a significant role in the quantitative research. In a wide spectrum of research areas, the methods based on testing hypotheses have been frequently used. However, in the area of the process control, testing hypothesis has not been widely considered as an established tool for signal analyses, although signals in control loops are suitable for analysis by means of quantitative statistical methods due to their stochastic character. Particularly, a statistical paired comparison can be applied for analysis of control quality achieved with different control algorithms. This comparison can be based on a paired comparison of corresponding signals obtained with different or modified control algorithms. The aim of this paper is a proposal of incorporation of testing hypothesis to analysis of control quality. The analysis was performed on a strictly defined significance level 0.001, which is a standardly used value in technical applications. As an example was demonstrated analysis of control quality achieved with two versions of a predictive controller. Finally, achieved results of paired comparison using testing hypothesis are discussed

Convenient optimization strategy implemented in multivariable predictive control

A significantly important part of model predictive control (MPC) with constraints is a solution of an optimization task. 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. One suitable principle of precomputing operations was proposed by Wang, L. This general optimization strategy is further modified in this paper. Decreasing of the computational complexity of the optimization by using of the proposed modification is discussed

Applied quadratic programming with principles of statistical paired tests

In applied research areas, various types of mathematical disciplines have been advantageously connected together with wide corresponding applications. As an applied proposal of this connection, a numerical optimization method of the quadratic programming particularly modified by a principle of statistical hypothesis testing can be seen in this paper. With regards to a computational complexity, algorithms of multivariable Model Predictive Control (MPC) can be considered as procedures with a higher computational complexity caused by the multi-variability, higher horizons and included constraints conditions. A wide spectrum of modifications has been proposed in the optimization subsystem of MPC controller yet; however, approaches based on including the hypotheses testing have not been widely considered in applied optimization method. A number of operations should be decreased; however, a control quality may be slightly influenced with regards to this aim. Therefore, the proposed modification is advantageous in an applied form of the quadratic programming technique where necessary information for following steps of a process control are provided. Achieved results are discussed in order to the incorporating of the principle of hypotheses testing in the modified numerical method of the applied quadratic programming. © 2019, Springer Nature Switzerland AG