Search

This paper is devoted to the analysis of fundamental limitations regarding closed-loop control performance of discrete-time nonlinear systems subject to hard constraints (which are nonlinear in state and manipulated input variables). The control performance for the problem of interest is quantified by the decline (decay) of the generalized energy of the controlled system. The paper develops (upper and lower) barriers bounding the decay of the system’s generalized energy, which can be achieved over a set of asymptotically stabilizing feedback laws. The corresponding problem is treated without the loss of generality, resulting in a theoretical framework that provides a solid basis for practical implementations. To enhance understanding, the main results are illustrated in a simple example.

A mathematical analysis highlighting the decomposition structure of the least-cost reservoir filling problem under time–invariant conditions is provided. It is shown, without loss of generality, that time invariance and unidimensionality of the state variable (for describing the evolution of the hydrodynamic system) are sufficient in order to achieve full (spatial and temporal) decomposition. Using this result, the role of specific energy in finding least–cost operational schedules for reservoir filling in a general “physically meaningful” hydrodynamic system is discussed.

Automatic calibration of physical plant models in the context of monitoring and control of industrial processes is considered. A structure integrating a physical model and estimated FIR filters is proposed. In addition, a finite state FIR structure is proposed to complement the calibrated physical model with a data-driven mapping. The approach is illustrated in simulations using the van der Vusse CSTR benchmark.

Combustion power plants currently face major performance challenges, which require robust control design methods. Extensive relative gain analysis was conducted in this paper to generate plantwide control structures for a full-scale once-through circulating fluidized bed boiler. No such study has been reported before for steam boilers. The partial relative gain was employed to generate decentralized control structures based on integral controllability with integrity. The approach provided feasible control structures and verified that basic turbine-following boiler control is preferable in terms of controllability. The steady-state results were extended with the dynamic relative gain array for higher frequencies, which revealed that boiler-following control becomes feasible for faster disturbances. The results highlight the complex interactions between steam pressure and output electrical power control, as well as the loop interactions caused by the feedwater flow in the once-through steam path.

Integrated control and process design (ICPD) practices focus on an interaction between process and control design. The paper investigates ICPD design in circulating fluidized bed (CFB) power plants, which face increasing load change, efficiency and emission requirements. The state of ICPD research is examined and a classification of its methodologies is provided. The applicability of ICPD to large-scale CFB boilers is discussed for the first time based on this classification. Two ICPD case studies with a simple steam path mass storage model are presented for an industrial CFB boiler, with the aim of illustrating possibilities and challenges related to boiler ICPD. The steam mass storage amounts of the boiler superheating and evaporation sections are modified based on the dynamic relative gain array and closed-loop process optimization to generate processes with improved constant pressure mode output power setpoint tracking performance.

Oxy combustion has been introduced in power plants for facilitated CO2 capture and storage (CCS). Existing process controls for air-fired circulating fluidized bed (CFB) boilers are not necessarily optimal for oxy-firing. New degrees of freedom and alternative structures for control should be carefully analyzed for performance and flexibility. In this paper, the application of self-optimizing control (SOC) and partial relative gain (PRG) methods is presented for the early phases of control structure design. Controlled variable (CV) candidate sets are studied using the SOC concept. For the proposed CV sets, PRG analysis is used to reveal possible SISO loops with manipulated variables (MVs). Structures with promising results from both analyses were discovered.

The problem of curse-of-dimensionality in finite state and action Markov decision processes is considered using iterative clustering of closed-loop data and repeated discretization of the state space process model. The performance of the control design approach is demonstrated using a multi-input van der Vusse continuous stirred tank reactor control benchmark. It is demonstrated that the finite state description provides a simple implementation of Bayesian state estimation using cell filters, and dynamic programming gives means to conduct optimization of closed-loop performance of a nonlinear stochastic multidimensional chemical plant.

Model-based optimization tools for demand side management using supermarket refrigeration systems are considered. A model for medium-sized supermarket freezer and cooler temperatures is developed, as well as for the CO 2 compressor cycle power consumption. Model parameters are estimated from measured data. The formulation of an optimization problem vs. various electricity markets is briefly discussed, and an illustrative numerical simulation of demand side management optimization in a supermarket is provided. The developed model provides a feasible tool for including the supermarket thermal capacity dynamics into the optimization problem.

This paper contributes to the field of Lyapunov stability theory where positive definite radially unbounded functions – which can be interpreted as generalized energy for the system of interest – play a central role. Given a discrete–time LTI system subject to hard constraints, which are affine in state and control variables, upper and lower barriers are developed which bound the fastest possible decay of generalized energy over the set of admissible control policies for which the closed–loop system is asymptotically stable on a compact polyhedral set including the origin. It is shown that the lower barrier is a greatest feasible lower bound of the fastest possible decay of generalized energy over any set of admissible control policies. A simple example is given to illustrate the main results.

A wealth of control designs and experience are available for traditional air combustion in circulating fluidized bed (CFB) boilers. For the novel process of oxy combustion (for facilitated CO 2 capture) input gas compositions and flows can be adjusted independently, which decouples fluidization and oxygen carrying tasks and introduces new degrees of freedom and alternatives for control. The self-optimizing control approach (as formulated by Skogestad and colleagues in the 2000s) was used with steady-state approximations of a validated dynamic model for a pilot-size CFB combustor to study how the added degrees of freedom should be used. Instead of centralized online optimization of setpoints, self-optimizing control searches for a set of controlled variables which can be kept at constant setpoints despite disturbances and measurement errors, resulting in performance with acceptable steady-state loss. Results for air firing support method validity by suggesting the common practice in control; keeping power, flue gas O 2 and primary air/fuel feed ratio constant. For oxy firing, various control structures could satisfactorily compensate for studied disturbances and errors. Results suggest direct oxidant O 2 % control or simpler feed-forward solutions in line with current industrial CFB control, or alternatively using the added degrees of freedom for controlling variables such as furnace temperatures. Differences in, e.g. controllability, dynamic performance and implementation cost are relevant in further studies. The results serve as a first step in oxy-CFB control studies, suggesting candidate structures for dynamic analysis.

Oxy combustion in circulating fluidized bed (CFB) boilers was investigated in this paper. Oxy combustion is a carbon capture and storage technology, which uses oxygen and recirculated flue gas (RFG) instead of air as an oxidant. Air and oxy combustion were compared through physical considerations and simulations, focusing on process dynamics, transients and control. The oxidant specific heat capacity and density are elevated in oxy combustion, which leads to slower temperature dynamics. Flue gas recirculation introduces internal feedback dynamics to the process. The possibility to adjust the RFG and oxygen flows separately gives an additional degree of freedom for control. In the simulations, “direct” and “sequenced” switches between air- and oxy-firing were compared. Fast “direct” switches with simultaneous ramping of all inputs should be preferred due to the resulting smooth temperature responses. If these process input changes are unfeasible, the fuel should be altered after the gaseous flows (“sequenced” method).

Simulation-based non-linear active suspension control design for MacPherson systems is considered. A nonlinear dynamic model for the MacPherson suspension system is derived. The model nonlinearities and the dynamic behaviour of the system is illustrated by simulations. The design of controllers and state estimators using finite state Markov models is briefly outlined, and applied for nonlinear active suspension control system. The study illustrates the potential of the finite Markov chains approach in non-linear active suspension control, emphasizing the possibility to move computational load due to simulations to off-line design.

This paper proposes a (tube based) robust MPC approach for the class of “well-designed” water distribution systems subject to water demand uncertainties. The underlying mathematical problem is formulated within a robust decision making framework where the operational decision (which is obtained using feedback) is cost efficient and feasible under a range of water demand realizations. An application to the efficient pump scheduling of the water distribution system of the city of Sopron (Hungary) is presented.

The choice of a pump schedule has a great influence on the cost efficiency of a system, when the energy consumption charge changes during the day. The pump scheduling problem for a sub-system of a regional water network is considered, and the formulation of the problem as a MDP is given. The system under stochastic demand is modelled and an optimal controller is designed. Two implementations are considered: a direct application of MDP control actions, and local PI-controllers with a feedforward part. The experimental section shows computer simulations illustrating the considered approaches.

Energy efficiency is one of the main aspects in the Kraft pulping process. In Kraft pulping, the delignification of the pulp is mainly controlled by temperature and alkali. However, the quality is usually measured only in the blowline of the digester resulting in a control delay several hours. This affects to the quality control and also the energy efficiency of the plant. In this study, energy efficiency in the continuous Downflow Lo-Solids ® cooking application is studied using model-based approach. Temperature and alkali controls are considered and some suggestions are proposed.

The choice of a pump schedule has a great influence on the cost efficiency of a system, when the energy consumption charge changes during the day. The pump scheduling problem for a simplified regional water network is considered, and the formulation of the problem as a Markov decision process is given. The experimental section shows computer simulations and compares the results with a novel evolutionary approach based on neutral genetic algorithm techniques.

Cognition and control processes share many similar characteristics, and decisionmaking and learning under the paradigm of multiple models has increasingly gained attention in both fields. The controlled finite Markov chain (CFMC) approach enables to deal with a large variety of signals and systems with multivariable, nonlinear, and stochastic nature. In this article, adaptive control based on multiple models is considered. For a set of candidate plant models, CFMC models (and controllers) are constructed off-line. The outcomes of the CFMC models are compared with frequentist information obtained from on-line data. The best model (and controller) is chosen based on the Kullback–Leibler information. This approach to adaptive control emphasizes the use of physical models as the basis of reliable plant identification. Three series of simulations are conducted: to examine the performace of the developed Matlab-tools; to illustrate the approach in the control of a nonlinear nonminimum phase van der Vusse CSTR plant; and to examine the suggested model selection method for the adaptive control.

This paper deals with regulation control on the basis of genealogical decision trees (GDTs). GDTs are a population-based random search technique for solving sequential multimodal and multivariable trajectory tracking problems, when gradient information is not available or does not exist. A direct application of GDT results in an open-loop control. In this paper, feedback regulation based on GDT is considered. In the proposed scheme, GDTs are used for solving off-line a number of predictive control problems; a finite set of initial states is then constructed from these simulations, for each of which an optimal control sequence has been computed. Natural handling of missing state vector measurements is provided. Numerical examples dealing with the van der Vusse CSTR illustrate the feasibility and the efficiency of this feedback control algorithm. A discussion on alternative approaches and a numerical comparison with the Markov-decision-process-based optimal policy are provided. Copyright © 2008 John Wiley & Sons, Ltd.

A global optimization algorithm operating online in a stochastic multi-teacher environment is suggested. An application example introduces a new perspective for solving some optimization problems dealing with reliability. First, a hybrid scheme combining reinforcement-based learning automata and confidence probabilistics is developed for a single-teacher environment. The scheme is able to find the optimal solution with high confidence, yet providing a sequence of search actions that converge to the minimal loss. In addition, the suggested approach provides an on-line measure of the confidence to the current solution. Second, a multi-teacher environment is considered. A simple application of a database enables any single-teacher reinforcement algorithm to be used for updating the learning automaton action probability distribution. Two alternative approaches are suggested, where the former provides superior performance in terms of confidence and loss; the latter is able to deal with dependencies between the cost and the duration of the evaluation of the cost function. The performance of the learning schemes is studied in simulations on maintenance optimization, where an accumulated number of failures is optimized online for a deteriorating production system with preventive maintenance. The simulations indicate superior performance of the hybrid scheme. A significant speed-up is observed by taking advantage of information from processes running online in parallel, thus making the learning automata approach a much more feasible approach for solving engineering problems of practical interest.

Controlled finite Markov chain (CFMC) approach can deal with a large variety of signals and systems with multivariable, non-linear and stochastic nature. In this paper, adaptive control based on multiple models is considered. For a set of candidate plant models, CFMC models (and controllers) are constructed off-line. The state transitions predicted by the CFMC models are compared with frequentist information obtained from on-line data. The best model (and controller) is chosen based on the Kullback–Leibler distance. This approach to adaptive control emphasizes the use of physical models as the basis of reliable plant identification. Three series of simulations are conducted: to examine the performance of the developed Matlab-tools; to illustrate the approach in the control of a non-linear non-minimum phase van der Vusse CSTR plant; and to examine the suggested model selection method for the adaptive control.

Polynomial artificial neural networks (PANN) have been shown to be powerful for forecasting nonlinear time series. The training time is small compared to the time used by other algorithms of artificial neural networks and the capacity to compute relations between the inputs and outputs represented by every term of the polynomial. In this paper a new structure of polynomial is presented that improves the performance of this type of network considering only non-integers exponents. The architecture adaptation uses genetic algorithm (GA) to find the optimal architecture for every example. Some examples of sunspots and chaotic time series are presented.

Plant-wide control in a circulating fluidized bed (CFB) power plant is considered. In particular, the self-optimizing control approach is used. The main contribution is applying the analysis in a pilot-sized CFB, which has not been reported before. This work focuses on conventional air-fired CFB combustion, for which a lot of experience on control design is already available. Therefore the results can be compared to practical knowledge from industrial practice. The work serves as an important step towards studying the control of oxy combustion in CFB, where the process is structurally similar but provides additional degrees of freedom for control design.

The goal of this paper is to design a new control algorithm for open-loop control of complex systems. This control approach is based on a genealogical decision tree for both regulation and tracking control problems. The idea behind this control strategy consists of associating Gaussian distributions to both the norms of the control actions and the tracking errors. This stochastic search model can be interpreted as a simple genetic particle evolution model with a natural birth and death interpretation. It converges on probability. A numerical example dealing with the control of a fluidized bed combustion power plant illustrates the feasibility and the performance of this control algorithm.

This paper considers identification of a multiple-input single-output Wiener model of a new type of superheater integrated to a CFB boiler. The static part is based on energy- and mass balances. Simultaneous estimation of model parameters in both static and dynamic parts was based on the industrial data from an 80 MW CFB boiler. The results indicate that the approach can be satisfactorily used to capture and describe the steam temperature in a wide range of variation in the input variables.

Identification and predictive control using a probabilistic CMC-ARX model is considered. The control problem is solved by maximizing the confidence in that the selected action results in a minimum cost. Bounds for the change in confidence of the optimal control action are derived, and a learning control algorithm is then suggested.

A new control algorithm for open-loop control of complex systems is suggested. The approach is based on a genealogical decision tree for tracking control problems. The idea behind this control strategy consists of associating Gaussian distributions to both the norms of the control actions and the tracking errors. This stochastic search model can be interpreted as a simple genetic particle evolution model with a natural birth and death interpretation. It converges in probability. A numerical example illustrates the feasibility and the performance of this control algorithm.

An improved version of the reinforcement scheme originally developed by McMurtry and Fu is presented. A projection procedure as well as a regularizing parameter are introduced to ensure the probability measure and uniqueness of the solution. To prevent degenerate situations where the realization of the function to be optimized is equal to zero, an auxiliary strictly positive regularizing parameter is introduced. A vector representation and a convergence analysis of this multimodal one-dimensional search technique are derived on the basis of the traditional convergence results on Robbins-Monro type of stochastic algorithms. Global maximization and minimization problems are discussed. Finally, some simulation results illustrate the performance and the feasibility of this self-learning optimization algorithm.

A distributed Wiener logic processor model structure is considered. Each fuzzy Wiener model consists of a succession of a linear dynamic part and a static steady-state (non-linear) logical part. The model structure and the necessary gradients required by gradient-based parameter estimation methods are given. Parameter projection and a modified threshold method are discussed. A simulation example illustrates the approach in the identification of a nonlinear, non-minimum phase CSTR process where a van der Vusse reaction takes place.

This paper presents an algorithm for optimization. This algorithm is based on a team of learning stochastic automata. Each automaton is characterized by two actions providing a binary output (0 or 1). The action of the team of automata consists of a digital number which represents the environment input. The probability distribution associated which each automaton is adjusted using a modified version of the Bush-Mosteller reinforcement scheme. This adaptation scheme uses a continuous environment response and a time-varying correction factor. A normalization procedure is used in order to preserve the probability measure. The asymptotic properties of this optimization algorithm are presented. A numerical example illustrates the feasibility and the performance of this optimization algorithm.

State estimation and optimal control of a nonlinear stochastic MacPherson suspension system using finite state and action Markov chains is considered. A system model and optimal controller are iteratively constructed based on k-means clustering of closed loop data and re-discretisation of the continuous system state space. Bayesian estimation of measured and unmeasured states using a cell filter is considered, and the unscented Kalman filter is considered as an alternative implementation. The main contribution is the introduction of the finite state and action Markov chains to the optimal control design and state estimation in active suspension systems. The application for active suspension control is illustrated and discussed via simulations using a simplified nonlinear model of a MacPherson system including stochastic road and measurement noise.

The increasing challenges in district heating operational optimization are briefly discussed. The paper describes the first steps in a research project on minimization of short term operational costs in a full scale district heating system. Based on a test model describing a part of a real district heating network, and a chosen approximate dynamic programming technique, simulations are used to illustrate and validate the fundamentals of the modelling and optimization approaches. It is concluded that the considered methods provide an adequate set of tools for the design of optimal network loading. The project is currently continuing with building of a more realistic dynamic model of the full-scale energy network and its components.

Modelling of dynamic non-linear processes using the Wiener approach is considered. Models are constructed based on sampled measurements from the process, as well as a priori information of the characteristics of the process. Prior information is expressed by a set of constraints, which leads to an optimisation problem of parameter estimation under constraints. Modelling of a two-tank system Illustrates the performance of the approach

The identification of multiple-input single-output Wiener models is considered in this paper. The non-linear memoryless part is described by a parametrized steady state model. In this paper two representations for the linear dynamic part that preserve the unit steady state gain are discussed and compared: finite step response and transfer function with a feedback polynomial. The steps necessary for estimating the parameters of the Wiener model are presented. In the simulation examples with data from a pneumatic valve model, distillation column model and a pilot pump-valve system, the performance of the approach is examined, and the use of various kinds of non-linear black-box and grey-box structure for the modelling of the static part is illustrated.

This paper concerns process modelling using fuzzy neural networks. In distributed logic processors (DLP) the rule base is parameterised. The DLP derivatives required by gradient-based training methods are given, and the recursive prediction error method is used to adjust the model parameters. The power of the approach is illustrated with a modelling example where NOx-emission data from a full-scale fluidised-bed combustion district heating plant are used. The method presented in this paper is general, and can be applied to other complex processes as well.

Pulp and paper mills can be seen as big pumping plants, where mass is pumped from one step to another. The proper operation of the process in its different stages does not allow large deviations from given operation conditions, which makes it essential to monitor and control the flow rate and the consistency of the pulp. A structure is suggested for the modelling of pulp flow rate, and possibilities for using the pump-valve system as a flow meter are examined. The overall model structure consists of a Wiener model for pressure difference, a non-linear dynamic valve model, and a static mapping for flow rate. A full-scale pilot plant of pulp flow through a valve in a pipeline is used for experimentation. Linear dynamics and non-linearities due to the pump, valve and the pulp consistency are identified based on online measurements obtained from calibration tests. The results show that a simple model could be identified which, together with a valve model, can be further applied for the purposes of accurate flow control.

This paper considers the use of adaptive learning systems for multimodal functions optimization and process control. The learning system collects and processes the available data to achieve the desired control objective. The environment where the automaton operates corresponds to the function to be optimized (the process to be controlled) which is assumed to be unknown function of a single parameter x. The admissible region of x (control variable) is quantized into N levels. These levels are associated with the actions of the automaton. The set of these actions is further decomposed into nonempty subsets. The action set is changing from instant to instant. At each time an action set is selected according to a probability distribution. The action and the action set probabilities are adjusted using learning algorithms (reinforcement schemes). This optimization and control approach is tested using two numerical examples (multimodal function and a chemical reactor). However, the concept can be applied to other examples as well. Simulation results illustrate the feasibility and the performance of this adaptive automaton.

The paper concerns the estimation under constraints of the parameters of distributed logic processors (DLP). This optimization problem under constraints is solved using stochastic approximation techniques. DLPs are fuzzy neural networks capable of representing nonlinear functions. They consist of several logic processors, each of which performs a logical fuzzy mapping. A simulation example, using data collected from an industrial fluidized bed combustor, illustrates the feasibility and the performance of this training algorithm.

Wiener type of models consist of linear dynamics followed by a static non-linear part. In this paper, a restricted class of Wiener models is considered where the static mapping represents a steady-state model for the process. A Wiener model structure is suggested for the identification of a MISO steady-state static model with linear FIR (finite impulse response) dynamics for each input. Unit steady-state gain is obtained by using a reduced FIR model, consisting of a unit gain plus FSR (finite step response) dynamics. The necessary derivatives required by gradient-based parameter estimation techniques are given. Simulation examples with data from a distillation column model and a pump-valve system, using sigmoid neural networks to model the non-linearities, illustrate the behaviour of the approach.

A new algorithm for training the parameters of a distributed logic processor is suggested, based on learning automata. A fuzzy inference system is implemented on a multilayer perceptron platform. Various possibilities for assigning learning automata are discussed and two assignment strategies are proposed. The behaviour of the resulting algorithm is illustrated using flue-gas NO/sub x/ emission data measured from an industrial-size fluidised-bed combustor.

This paper concerns the process modelling based on fuzzy logic neural networks. Fuzzy systems are implemented in the form of distributed logic processors. Derivatives required by gradient descent training methods are given, and recursive prediction error training method is used to adjust the model parameters. The approach is illustrated with a modelling example where nitrogen emission (x) data from a fluidized-bed combustion district heating plant is used. The method presented in this paper is general, and can be applied to other complex processes as well.

This paper concerns the adaptive selection of the optimal order of linear regression models using a variable-structure stochastic learning automaton. The Alaike criterion is derived for stationary and non-stationary cases, and it is shown that the optimal order minimizes a loss function corresponding to the evaluation of this criterion. The order of the regression model belongs to a finite set. Each order value is associated with an action of the automaton. The Bush-Mosteller reinforcement scheme with normalized automaton input is used to adjust the probability distribution. Simulation results illustrate the feasibility and performance of this model order selection approach

Artificial neural networks are studied from process engineer's point of yiew. In engineering problems, uses of neural networks can be found from modelling of non-linear systems. In on-line process modelling, the problem of measurement data that has a low information content cannot be ignored. An attempt to collect recursively an infonnationrich training data set is made using a self-organising feature map preceding a multi-layer perceptron artificial neural network. The combined configuration is introduced and a case study is presented, where models for the fluidized-bed combustor flue gas NO x -content are made using data collected from a 25 MW district heating thermal power plant

This paper examines the application of a particle filtering-based optimization technique, the genealogical decision trees (GDT), to a finite horizon pump scheduling problem in a water distribution network. The GDT approach for trajectory tracking is first introduced, and a modified algorithm for minimization of costs during pump sequence optimization is then presented. Several variants of the algorithm are suggested, using the extended end constraint and neutrality. The performance of the optimization in various algorithm and parameter settings is examined in extensive simulations. It was observed that both the extended end constraint and neutrality improved the performance, however the deviation between solutions within a population and between different runs remained uncomfortably large. Finally, a comparison with a number of alternative up-to-date optimization techniques is provided. It was observed that the performance of GDT was adequate, compared with the best available approaches.

The adaptation made for the Polynomial Artificial Neural Networks (PANN) using not only integer exponentials but also fractional exponentials, have shown evidence of its better performance, especially, when it works with non-linear and chaotic time series. In this paper we show the comparison of the PANN improved model of fractional exponentials with a new logarithmic model. We show that this new model have even better performance than the last PANN improved model.