Piotr M. Marusak

Advantages of an easy to design fuzzy predictive algorithm in control systems of nonlinear chemical reactors

Advantages of a fuzzy predictive control algorithm are discussed in the paper. The fuzzy predictive algorithm is a combination of a DMC (Dynamic Matrix Control) algorithm and Takagi-Sugeno fuzzy modeling, thus it inherits advantages of both techniques. The algorithm is numerically effective. It is in fact generalization of the standard DMC algorithm widely used in the industry, thus the existing implementations of the DMC algorithm can be extended using the presented fuzzy approach. A simple and easy to apply method of fuzzy predictive control algorithms synthesis is presented in the paper. It can be easy applied also in the case of Multiple Input Multiple Output (MIMO) control plants. Moreover, information about measured disturbance can be included in the algorithms in an easy way. The advantages of the fuzzy predictive control algorithm are demonstrated in the example control systems of two nonlinear chemical reactors: the first one-with inverse response and the second one-a MIMO plant with time delay.

Multilayer and integrated structures for predictive control and economic optimisation

Abstract The problem of co-operation of model predictive control (MPC) algorithms with nonlinear economic optimisation is considered. It is important when dynamics of disturbances is comparable with dynamics of the process, thus when application of the classical multilayer approach may be not efficient. Two main approaches are discussed and their features studied. The first one consists in approximate linear, linear-quadratic or piecewise-linear formulations of the target set-point optimisation depending on problem properties. The idea of the second approach consists in integrating the economic optimisation and manipulated variables calculation by MPC algorithm into one optimisation problem. The nonlinear steady-state model used in economic optimisation is approximated on-line. The resulting optimisation problem is then integrated with the MPC optimisation task and a computationally efficient quadratic programming problem is obtained.

Software Implementation of Explicit DMC Algorithm with Improved Dependability

The paper presents an approach to improve the dependability of software implementation of the explicit DMC (Dynamic Matrix Control) Model Predictive Control (MPC) algorithm. The investigated DMC algorithm is implemented for a control system of a rectification column - a process with strong cross-couplings and significant time delays. The control plant has two manipulated inputs and two outputs. The fault sensitivity of the proposed implementation is verified in experiments with a software implemented fault injector. The experimental results prove the efficiency of proposed software improvements.

Efficient model predictive control algorithm with fuzzy approximations of nonlinear models

Model predictive control (MPC) algorithms are widely used in practical applications. They are usually formulated as optimization problems. If the model used for prediction is linear (or linearized on-line) then the optimization problem is standard, quadratic one. Otherwise, it is a nonlinear, in general, non-convex optimization problem. In the latter case the numerical problems may occur and time needed to calculate the control signals cannot be determined. Therefore approaches based on linear or linearized models are preferred in practical applications. In the paper a new algorithm is proposed, with prediction which employs heuristic fuzzy modeling. The algorithm is formulated as quadratic optimization problem but offers performance very close to that of MPC algorithm with nonlinear optimization. The efficiency of the proposed algorithm is demonstrated in the control system of the nonlinear control plant with inverse response - a chemical CSTR reactor.

Effective Dual-Mode Fuzzy DMC Algorithms with On-Line Quadratic Optimization and Guaranteed Stability

Effective Dual-Mode Fuzzy DMC Algorithms with On-Line Quadratic Optimization and Guaranteed Stability Dual-mode fuzzy dynamic matrix control (fuzzy DMC-FDMC) algorithms with guaranteed nominal stability for constrained nonlinear plants are presented. The algorithms join the advantages of fuzzy Takagi-Sugeno modeling and the predictive dual-mode approach in a computationally efficient version. Thus, they can bring an improvement in control quality compared with predictive controllers based on linear models and, at the same time, control performance similar to that obtained using more demanding algorithms with nonlinear optimization. Numerical effectiveness is obtained by using a successive linearization approach resulting in a quadratic programming problem solved on-line at each sampling instant. It is a computationally robust and fast optimization problem, which is important for on-line applications. Stability is achieved by appropriate introduction of dual-mode type stabilization mechanisms, which are simple and easy to implement. The effectiveness of the proposed approach is tested on a control system of a nonlinear plant—a distillation column with basic feedback controllers.

Actuator Fault Tolerance in Control Systems with Predictive Constrained Set-Point Optimizers

Actuator Fault Tolerance in Control Systems with Predictive Constrained Set-Point Optimizers Mechanisms of fault tolerance to actuator faults in a control structure with a predictive constrained set-point optimizer are proposed. The structure considered consists of a basic feedback control layer and a local supervisory set-point optimizer which executes as frequently as the feedback controllers do with the aim to recalculate the set-points both for constraint feasibility and economic performance. The main goal of the presented reconfiguration mechanisms activated in response to an actuator blockade is to continue the operation of the control system with the fault, until it is fixed. This may be even long-term, if additional manipulated variables are available. The mechanisms are relatively simple and consist in the reconfiguration of the model structure and the introduction of appropriate constraints into the optimization problem of the optimizer, thus not affecting the numerical effectiveness. Simulation results of the presented control system for a multivariable plant are provided, illustrating the efficiency of the proposed approach.

Efficient Model Predictive Control integrated with economic optimisation

This paper is concerned with a computationally efficient model predictive control (MPC) algorithm for control and set-point computation. The underlying idea consists in integrating the economic optimisation task and manipulated variables calculation by the MPC algorithm into one optimisation problem. The comprehensive nonlinear steady-state model of the process used in economic optimisation is approximated on-line taking into account current state of the plant and disturbance estimate or measurement. Linear and linear quadratic approximations are discussed. The resulting economic optimisation (with the approximate model) is then integrated with standard MPC optimisation problem in such a way that a computationally efficient quadratic programming problem is obtained.

ECONOMIC EFFICACY OF MULTILAYER CONSTRAINED PREDICTIVE CONTROL STRUCTURES: AN APPLICATION TO A MIMO NEUTRALISATION REACTOR

Abstract In the MIMO control system it is often sufficient for some of the output variables to be constrained instead of stabilised. Employing a predictive control algorithm, in which constraints can be easily taken into consideration, is natural in such cases. As a result, in comparison with the standard control problem formulation, in which all relevant output variables are stabilised, the obtained problem has more degrees of freedom. They can be used for improving process economic efficiency. It is demonstrated in the paper on the example of a highly nonlinear MIMO control plant. In order to use the aforementioned feature the multilayer structure with different number of manipulated inputs and controlled outputs is investigated.

Nonlinear extended output feedback control for CSTRs with van de Vusse reaction

Abstract This paper developed an output-feedback control system for regulation of continuous stirred tank reactors (CSTRs) with van de Vusse reaction. The reactors are often used as benchmark representatives of nonminimum-phase processes. Control of such nonlinear processes is difficult because they exhibit the inverse response. Linear controllers usually give unsatisfactory results in this case and thus nonlinear control approaches are more suitable. The proposed control system consists of a nonlinear observer and an extended nonlinear state feedback controller. The extension consists in adding the integrator to the controller for improving steady state performance of the control system. Stability of the control system including the observer dynamics is guaranteed, thanks to the existence of an input-to-state Lyapunov function. Simulation studies are conducted to illustrate the effectiveness of the proposed control system and its robustness.

On prediction generation in efficient MPC algorithms based on fuzzy hammerstein models

In the paper a novel method of prediction generation, based on fuzzy Hammerstein models, is proposed. Using this method one obtains the prediction described by analytical formulas. The prediction has such a form that the MPC (Model Predictive Control) algorithm utilizing it can be formulated as a numerically efficient quadratic optimization problem. At the same time, the algorithm offers practically the same performance as the MPC algorithm in which a nonlinear, non-convex optimization problem must be solved at each iteration. It is demonstrated in the control system of the distillation column - a nonlinear control plant with significant time delay.