State-Space Interpretation of Model Predictive Control

A model predictive control technique based on a step response model is developed using state estimation techniques. The standard step response model is extended so that integrating systems can be treated within the same framework. Based on the modified step response model, it is shown how the state estimation techniques from stochastic optimal control can be used to construct the optimal prediction vector without introducing significant additional numerical complexity. In the case of integrated or double integrated white noise disturbances filtered through general first-order dynamics and white measurement noise, the optimal filter gain is parametrized explicitly in terms of a single parameter between 0 and 1, thus removing the requirement for solving a Riccati equation and equipping the control system with useful on-line tuning parameters. Parallels are drawn to the existing MPC techniques such as Dynamic Matrix Control (DMC), Internal Model Control (IMC) and Generalized Predictive Control (GPC)

Multivariable nonlinear advanced control of copolymerization processes

A reliable multivariable model of a process is a fundamental prerequisite for the design of an efficient control strategy. Though, such a model is often very hard to obtain via a first-principles approach. The development of two fuzzy model-based multivariable nonlinear predictive control schemes and their implementation on a copolymerization process are described in this paper. Multi-input/single-output models are developed using fuzzy logic and combined to form a parallel system model for simulation and online prediction. The behavior of the outlined controllers were compared to the dynamic matrix control (DMC) and to a typical nonlinear model-based predictive control (NMPC) for regulatory problem and the obtained results showed the effectiveness of the proposed structures

On fractional predictive PID controller design method

A new method of designing fractional-order predictive PID controller with similar features to model based predictive controllers (MPC) is considered. A general state space model of plant is assumed to be available and the model is augmented for prediction of future output. Thereafter, a structured cost function is defined which retains the design objective of fractional-order predictive PI controller. The resultant controller retains inherent benefits of model-based predictive control but with better performance. Simulations results are presented to show improved benefits of the proposed design method over dynamic matrix control (DMC) algorithm. One major contribution is that the new controller structure, which is a fractional-order predictive PI controller, retains combined benefits of conventional predictive control algorithm and robust features of fractional-order PID controller

Reglas de diseño para la sintonía de controladores predictivos dynamic matrix control (DMC)

[SPA] El control dinámico matricial nació a finales de la década de los 70 como respuesta a necesidades específicas de la industria de procesos que los métodos de control de aquella época no podían ofrecer: Un control multivariable que tuviera en cuenta restricciones. Desde entonces se ha expandido con fuerza en la industria. Sin embargo, a pesar de este éxito, esta técnica de control aún carece de un método claro de sintonía con las características que demandan los usuarios: Que sea fácil de utilizar, apto para multivaraible, que no necesite un extenso conocimiento de la planta más allá del modelo de respuesta a escalón (necesario para usar el DMC) y que proporcione unas prestaciones aceptables que sirvan como base para un ajuste en detalle. Para conseguir este objetivo, se ha optado por utilizar una técnica propia de la teoría de sistemas: Un exhaustivo análisis del efecto de los parámetros del DMC en los polos y ceros en lazo cerrado. Para ello ha sido necesario poder expresar una planta controlada por un algoritmo en un sistema de bloques mediante un equivalente LTI, que convierte al DMC en un sistema de bloques en lazo cerrado del que se puedan extraer funciones de transferencia y, consecuentemente, polos y ceros. Este equivalente LTI se ha empleado tanto para sistemas SISO como MIMO. La base para sistemas SISO de este equivalente ya existe en la literatura. Pero para sistemas MIMO ha sido necesario desarrollar una formulación específica en este trabajo que permita obtener el equivalente en lazo cerrado para llevar a cabo el estudio de polos y ceros. Sin embargo, la utilidad de este equivalente no se limita al cálculo de polos y ceros, sino que es una útil herramienta que puede ser utilizada en futuros estudios del DMC como los de estabilidad y robustez. Como ejemplo de su utilidad, se ha usado para demostrar que el DMC actúa como un desacoplador para sistemas multivariable. El uso de esta herramienta de la teoría de sistemas con el DMC ha permitido obtener una serie de reglas de diseño que han sido puestas a prueba de varias formas: Mediante simulación del control DMC de varios benchmark (SISO y MIMO) extraídos de la literatura, mediante el control DMC por simulación de un modelo altamente no lineal previamente usado por otros investigadores en sus trabajos y mediante el control de una maqueta térmica (un sistema físico real) En los casos anteriores, el método propuesto ha sido comparado con otras técnicas de ajuste existentes, obteniéndose resultados que demuestran que el método obtenido supone una mejora respecto a los existentes. Los resultados demuestran que las reglas desarrolladas cumplen con los objetivos fijados: Son sencillas de usar y entender, son válidas tanto para sistemas MIMO como SISO, no requieren un conocimiento del sistema más allá del necesario para usar el DMC (solo el modelo de respuesta a escalón), no es necesario poseer fuertes conocimientos matemáticos ni de teoría de control para comprenderlas y proporcionan un control aceptable como un primer ajuste que puede ser refinado posteriormente.[ENG] Dynamic Matrix Control (DMC) has widely expanded in Industry in the last 30 years. Despite this success, this control technique still lacks of a set of design rules for the choice of tuning parameters with the requirements of the practitioners. These are: easy to carry out, without the need of an exhaustive knowledge of the dynamics beyond the step tests, but able to provide an acceptable performance as startup tuning. To achieve this, an exhaustive study of the closed loop system poles and zeros (using DMC controller) has been made as an indicator of the time response. The transformation of the system using the LTI equivalent has allowed the development of a set of tuning rules that fulfill the required characteristics for SISO and MIMO plants. In the case of MIMO systems it has been necessary to develop in this work a specific formulation that allows obtaining the closed loop equivalent. Following the results obtained for the DMC proposed tuning rules, the method has been put to test studying DMC control performance in some cases: Simulation of several SISO and MIMO widely used benchmarks extracted from the bibliography, control of a real thermal system, simulation of highly non‐linear MIMO system. In all cases there has been a performance comparison with some already used techniques with successful results improving existing methods. The set of provided rules matches with the required characteristics: They are easy to understand and use, they do not require advanced knowledge of mathematics and control theory and provide an acceptable Controlled Output for a start up first tuning.Escuela Internacional de Doctorado de la Universidad Politécnica de CartagenaUniversidad Politécnica de CartagenaPrograma Oficial de Doctorado en Tecnologías Industriale

A systematic approach to the tuning of multivariable Dynamic Matrix Control (DMC) controllers

Traditionally the tuning of DMC-type multivariable controllers is done by trial and error. The APC engineer would choose arbitrary starting values and test the performance on a simulated controller. The engineer would then either increase the values to suppress movement more, or decrease them to have the manipulated variables move faster. When the controller performs acceptably in simulation, then the tuning is improved during the commissioning of the controller on the plant. This is a time consuming and unscientific exercise and therefore often does not get the required attention, leading to unacceptable controller behaviour during commissioning and sub-optimal control once commissioning is completed. This dissertation presents a new method to obtain move suppression factors for DMC type multivariable controllers. The challenge in choosing move suppressions lies in the multivariable nature of the controller. Changing the move suppression on one manipulated variable will not only change the performance of that manipulated variable, it will also change the performance of every other manipulated variable with models to the same controlled variables. In the same way, changing the steady state cost of a manipulated variable or the equal concern error of a controlled variable will also affect the behaviour of every other manipulated variable with shared models. There have been attempts to calculate the required move suppression factors mathematically. Some methods used an approach that is based on the premise that move suppression factors that present a well-conditioned controller matrix will provide a well behaved controller in terms of tuning. Some other methods focussed on providing parameters that will cause desirable controlled variable response, either by determining tuning parameters offline, or by re-tuning the controller in real time. The method described in this paper uses a Nelder Mead (Nelder and Mead, 1965) search algorithm to search for move suppressions that will provide acceptable control behaviour. Acceptable behaviour is defined by characterising the dynamic move plan calculated by the controller for each of the manipulated variables, or by characterising the controlled variable path that will result from the manipulated variable moves. The search algorithm can change the move suppressions, the steady state costs, or the move suppression multipliers as used in DMC type controllers. CopyrightDissertation (MEng)--University of Pretoria, 2012.Chemical Engineeringunrestricte

Model Predictive Control

This project thesis provides a brief overview of Model Predictive Control (MPC).A brief history of industrial model predictive control technology has been presented first followed by a some concepts like the receding horizon, moves etc. which form the basis of the MPC. It follows the Optimization problem which ultimately leads to the description of the Dynamic Matrix Control (DMC).The MPC presented in this report is based on DMC. After this the application summary and the limitations of the existing technology has been discussed and the next generation MPC, with an emphasis on potential business and research opportunities has been reviewed. Finally in the last part we generate Matlab code to implement basic model predictive controller and introduce noise into the model. We have also taken up some case studies like Swimming pool water temperature control and helicopter flight control etc. by applying the MPC controller on these models

Model Predictive Control Strategy for Industrial Process

Model Predictive control (MPC) is shown to be particularly effective for the self-tuning control of industrial processes. It makes use of a truncated step response of the process and provides a simple explicit solution in the absence of constraints. Here we use Dynamic Matrix Control (DMC). DMC uses a set of basis functions to form the future control sequence. The industrial success of DMC has mainly come from its application to high dimension multivariable system without constraints. Here main objective of DMC controller is to drive the output as close to the set point as possible in a least square sense with the possibility of the inclusion of a penalty term on the input moves. Therefore, the manipulated variables are selected to minimize a quadratic objective that can consider the minimization of future error. Implementation of the internal model control is also shown here. The control strategy is to determine the best model for the current operating condition and activate the corresponding controller. Internal model control (IMC) continues to be a powerful strategy in complex, industrial processes control application. This structure provides a practical tool to influence dynamic performance and robustness to modeling error transparently in the design. It is particularly appropriate for the design and implementation of controllers for linear open loop stable system. A simulated example of the control of nonlinear chemical process is shown. The nonlinear chemical process study in this work is the exothermic stirred tank reactors system with the first order reaction. The reaction is assumed to be perfectly mixed and no heat loss occurs within the system. Using internal model control and dynamic matrix control has simulated control of the total process in CSTR. Simulation example provided to show the effectiveness of the proposed control strategy

Robust stability conditions for remote SISO DMC controller in networked control systems

A two level hierarchy is employed in the design of Networked Control Systems (NCSs) with bounded random transmission delay. At the lower level a local controller is designed to stabilize the plant. At the higher level a remote controller with the Dynamic Matrix Control (DMC) algorithm is implemented to regulate the desirable set-point for the local controller. The conventional DMC algorithm is not applicable due to the unknown transmission delay in NCSs. To meet the requirements of a networked environment, a new remote DMC controller is proposed in this study. Two methods, maximum delayed output feedback and multi-rate sampling, are used to cope with the delayed feedback sensory data. Under the assumption that the closed-loop local system is described by one FIR model of an FIR model family, the robust stability problem of the remote DMC controller is investigated. Applying Jury's dominant coefficient lemma and some stability results of switching discrete-time systems with multiple delays; several stability criteria are obtained in the form of simple inequalities. Finally, some numerical simulations are given to demonstrate the theoretical results

Design and Application of Offset-Free Model Predictive Control Disturbance Observation Method

Model predictive control (MPC) with its lower request to the mathematical model, excellent control performance, and convenience online calculation has developed into a very important subdiscipline with rich theory foundation and practical application. However, unmeasurable disturbance is widespread in industrial processes, which is difficult to deal with directly at present. In most of the implemented MPC strategies, the method of incorporating a constant output disturbance into the process model is introduced to solve this problem, but it fails to achieve offset-free control once the unmeasured disturbances access the process. Based on the Kalman filter theory, the problem is solved by using a more general disturbance model which is superior to the constant output disturbance model. This paper presents the necessary conditions for offset-free model predictive control based on the model. By applying disturbance model, the unmeasurable disturbance vectors are augmented as the states of control system, and the Kalman filer is used to estimate unmeasurable disturbance and its effect on the output. Then, the dynamic matrix control (DMC) algorithm is improved by utilizing the feed-forward compensation control strategy with the disturbance estimated