An algorithm for steady-state system optimization and parameter estimation

In this paper an algorithm is described which uses a steady-state mode! to determine the optimum operating point of a process. The model, which is not required to be an accurate representation of the real process, contains parameters to be estimated and the algorithm involves an iterative procedure between the two problems of system optimization and parameter estimation. Lagrangian analysis is employed to account for the interaction between the two problems, resulting in a procedure which may be regarded as a modified two-step approach in which the optimization objective index includes an extra term. The extra term contains a comparison between model and real process output derivatives and ensures that the optimal steady-state operating condition is achieved in spite of model inaccuracies.

The algorithm is shown to perform satisfactorily in a digital simulation study concerned with determining food flow rate and temperature controller set points to maximize the net rate of return from an exothermic chemical reactor using a simplified non-linear model for system optimization and parameter estimation. The simulation is employed to investigate the convergence properties of the algorithm and to study the effects of measurement errors.     

Online set-point optimisation cooperating with predictive control of a yeast fermentation process: A neural network approach

Online set-point optimisation which cooperates with model predictive control (MPC) and its application to a yeast fermentation process are described. A computationally efficient multilayer control system structure with adaptive steady-state target optimisation (ASSTO) and a suboptimal MPC algorithm are presented in which two neural models of the process are used. For set-point optimisation, a steady-state neural model is linearised online and the set-point is calculated from a linear programming problem. For MPC, a dynamic neural model is linearised online and the control policy is calculated from a quadratic programming problem. In consequence of linearisation of neural models, the necessity of online nonlinear optimisation is eliminated. Results obtained in the proposed structure are comparable with those achieved in a computationally demanding structure with nonlinear optimisation used for set-point optimisation and MPC.     

Dynamic Ant Colony Optimisation

Ant Colony optimisation has proved suitable to solve static optimisation problems, that is problems that do not change with time. However in the real world changing circumstances may mean that a previously optimum solution becomes suboptimal. This paper explores the ability of the ant colony optimisation algorithm to adapt from the optimum solution for one set of circumstances to the optimal solution for another set of circumstances. Results are given for a preliminary investigation based on the classical travelling salesman problem. It is concluded that, for this problem at least, the time taken for the solution adaption process is far shorter than the time taken to find the second optimum solution if the whole process is started over from scratch.     

Neighbouring-extremal control for singular dynamic optimisation problems. Part II: multiple-input systems

Dynamic optimisation provides a unified framework for improving process operations while taking operational constraints into account. In the presence of uncertainty, measurements can be incorporated into the optimisation framework for tracking the optimum. For non-singular control problems, neighbouring-extremal (NE) control can be used to force the first-order variation of the necessary conditions of optimality (NCO) to zero along interior arcs. An extension of NE control to singular control problems has been proposed in the companion paper for single-input problems. In this article, a generalisation to multiple-input systems is presented. In order for these controllers to be tractable from a real-time optimisation perspective, an approximate NE feedback law is proposed, whose application guarantees, under mild assumptions, that the first-order variation of the NCO converges to zero exponentially. The performance of multi-input NE control is illustrated by the case study of a steered car.     

工业过程稳态优化控制算法的鲁棒性分析

本文旨在讨论稳态优化算法最优性的鲁棒性问题。为此，对稳态优化控制算法进行了统一数学描述，利用集合间的Ｈａｕｓｄｏｒｆｆ半距离和Ｄｉｎｉ导数，引入了标志算法抗干扰性能强弱的灵敏度指标。在此基础上研究了线性模型且具有二次性能指标控制问题ＩＳＯＰＥ（系统优化与参数估计相结合）算法的鲁棒性。     

An efficient optimum Latin hypercube sampling technique based on sequencing optimisation using simulated annealing

This paper proposes a new optimal Latin hypercube sampling method (OLHS) for design of a computer experiment. The new method is based on solving sequencing and continuous optimisation using simulated annealing. There are two sets of design variables used in the optimisation process: sequencing and real number variables. The special mutation operator is developed to deal with such design variables. The performance of the proposed numerical strategy is tested and compared with three established OLHS methods, namely genetic algorithm (GA), enhanced stochastic evolutionary algorithm (ESEA) and successive local enumeration (SLE). Based on 30 test problems with various design dimensions and numbers of sampling points, the proposed method gives the best results. The method can generate an optimum set of sampling points within reasonable computing time; therefore, it can be considered as a powerful tool for design of computer experiments.     

Multivariate batch to batch optimisation of fermentation processes incorporating validity constraints

This paper presents an innovative optimisation technique, which utilises an adaptive Multiway Partial Least Squares (MPLS) model to track the dynamics of a batch process from one batch to the next. Utilising this model, an optimisation algorithm solves a quadratic cost function that identifies operating conditions for the subsequent batch that should increase yield. Hard constraints are shown to be required when solving the cost function to ensure that batch conditions do not vary too greatly from one batch to the next. Furthermore, validity constraints are imposed to prevent the PLS model from extrapolating significantly when determining new operating conditions. The capabilities of the proposed technique are illustrated through its application to two benchmark fermentation simulations, where its performance is shown to compare favourably with alternative batch-to-batch optimisation techniques.     

An iterative approach to the optimal co-design of linear control systems

This paper investigates the optimal co-design of both physical plants and control policies for a class of continuous-time linear control systems. The optimal co-design of a specific linear control system is commonly formulated as a nonlinear non-convex optimisation problem (NNOP), and solved by using iterative techniques, where the plant parameters and the control policy are updated iteratively and alternately. This paper proposes a novel iterative approach to solve the NNOP, where the plant parameters are updated by solving a standard semi-definite programming problem, with non-convexity no longer involved. The proposed system design is generally less conservative in terms of the system performance compared to the conventional system-equivalence-based design, albeit the range of applicability is slightly reduced. A practical optimisation algorithm is proposed to compute a sub-optimal solution ensuring the system stability, and the convergence of the algorithm is established. The effectiveness of the proposed algorithm is illustrated by its application to the optimal co-design of a physical load positioning system.     

Shape optimisation of continuum structures via evolution strategies and fixed grid finite element analysis

Evolution strategies (ES) are very robust and general techniques for finding global optima in optimisation problems. As with all evolutionary algorithms, ES apply evolutionary operators and select the most fit from a set of possible solutions. Unlike genetic algorithms, ES do not use binary coding of individuals, working instead with real variables. Many recent studies have applied evolutionary algorithms to structural problems, particularly the optimisation of trusses. This paper focuses on shape optimisation of continuum structures via ES. Stress analysis is accomplished by using the fixed grid finite element method, which reduces the computing time while keeping track of the boundary representation of the structure. This boundary is represented by b-spline functions, circles, and polylines, whose control points constitute the parameters that govern the shape of the structure. Evolutionary operations are applied to each set of variables until a global optimum is reached. Several numerical examples are presented to illustrate the performance of the method. Finally, structures with multiple load cases are considered along with examples illustrating the results obtained.     

Adaptive on-line steady-state optimization of slow dynamic processes

A software package OLIOPT was developed for the on-line optimization of the steady-state behaviour of slow dynamic processes in a relatively short time period. In the starting phase, the independently variable inputs are changed according to a special test signal. A nonlinear dynamic process model is identified on-line. Based on the static part of the model and the known inputs, the gradients of the performance index are calculated. An optimization algorithm changes the inputs towards their optimal values. On-line identification of the nonlinear model continues and the prediction of the optimum improves. In the last phase, the inputs take their optimal values and the process follows, feedforward controlled, to its optimal steady-state. The method is suited for industrial processes with one or more variable inputs, where a small gain in efficiency turns out to give a relatively large financial return. Results are shown for the on-line optimization of a thermal pilot process.     

A variable structure MRAC with expected transient and steady-state performance

A new output feedback variable structure model reference adaptive control (VS-MRAC) scheme is proposed in this paper for uncertain plants with relative degree one. The scheme is based on the existing VS-MRAC structure together with a high gain switching mechanism to adjust the variable structure control signal. The main features of the scheme are that (1) the pre-specified transient and steady-state performance specifications for tracking error can be guaranteed, (2) it does not require the plant high frequency gain sign to be known a priori, (3) the usual assumption for MRAC system that the reference model is strictly positive real (SPR) is not needed and (4) the plant input disturbance, which is assumed to be unknown but bounded, can be completely rejected.     

Application of neural networks to temperature control in thermal power plants

In a thermal power plant with once-through boilers, it is important to control the temperature at the middle point where water becomes steam. However, there are many problems in the design of such a control system, due to a long system response delay, dead-zone and saturation of the actuator mechanisms, uncertainties in the system model and/or parameters, and process noise. To overcome these problems, an adaptive controller has been designed using neural networks, and tested extensively via simulations.

One of the key problems in designing such a controller is to develop an efficient training algorithm. Neural networks are usually trained using the output errors of the network, instead of using the output errors of the controlled plant. However, when a neural network is used to control a plant directly, the output errors of the network are unknown, since the desired control actions are unknown. This paper proposes a simple training algorithm for a class of nonlinear systems, which enables the neural network to be trained with the output errors of the controlled plant. The only a priori knowledge of the controlled plant is the direction of its output response. Due to its simple structure and algorithm, and good performance, the proposed controller has high potential for handling difficult problems in process-control systems.     

双层结构预测控制研究进展

现代工业大系统的优化控制采用递阶结构,其中以预测控制为代表的先进过程控制已经成为重要的一级.目前,主流的工业预测控制技术均采用双层结构,即包含稳态优化层和动态控制层.双层结构预测控制技术可以有效解决复杂工业过程常见的多目标优化、多变量控制的难点问题.本文简要总结了双层结构预测控制的算法,并从控制输入与被控输出稳态关系入手分析了多变量预测控制稳态解的相容性和唯一性,说明了稳态优化的重要性.针对双层结构预测控制与区间预测控制的性能比较、稳态模型的奇异性以及闭环系统动态特性等提出了一些见解,并指出了需要重点研究的主题.     

Distributed modifier-adaptation schemes for the real-time optimisation of uncertain interconnected systems

This paper proposes a set of distributed real-time optimisation schemes for the steady-state optimisation of parametrically and structurally uncertain systems that are composed of multiple interconnected subsystems. These schemes are derived in the framework of modifier adaptation and use uncertain system models of varying complexity. Consequently, each distributed modifier-adaptation scheme imposes different requirements on the available plant measurements, the communication network, and the control architecture. We prove that every scheme can converge to the plant optimum despite model uncertainty and compare the main features of each approach. Finally, we illustrate our findings via a numerical example.     

Convergence and optimality of modified two-step algorithm for integrated system optimization and parameter estimation

This paper investigates convergence and optimality properties of the modified two-step algorithm for on-line determination of the optimum steady-state operating point of an industrial process. Mild sufficient conditions are derived for the convergence and feasibility of the algorithm. It is shown that every point within the solution set of the algorithm satisfies first-order necessary conditions for optimality, and that every optimal solution belongs to this set. It is also shown that there are advantages to be gained by using a linear mathematical model of the process within the implementation of the algorithm.     

Sequencing optimisation for makespan improvement at wet-etch tools

The complex nature of wet-etch tools and their peculiar scheduling constraints pose a relevant challenge for the development and implementation of makespan optimisation strategies, especially when rigid scheduling rules have to be considered. In this paper, an optimisation model is developed for sequencing of wafer batches outside a wet-etch tool and scheduling of tool-internal handler moves. The scheduling algorithm is inspired by the control logics governing wet-etch tools operating in a real semiconductor manufacturing plant and proves effective in generating efficient and detailed schedules in short computational times. The mathematical formulation developed for the scheduling problem is based on generic and realistic assumptions for both the job flow and the material handling system. The sequencing module combines an exact optimisation approach, based on an efficient permutation concept, and a heuristics optimisation approach, based on genetic algorithms. The results obtained show that significant makespan reductions can be obtained by means of a mere sequencing optimisation. Using this optimisation strategy, variations to the scheduling logics, that are generally more difficult and expensive to implement, are avoided. A sensitivity analysis on genetic algorithm operators is also conducted and considerations on the best performing selection, cross-over and mutation operators are presented.     

Closed-loop control of crystal shape in cooling crystallization of l-glutamic acid

Recent simulation research has proved the principle that it is possible to exercise closed-loop control over the particle shape of the crystals produced from cooling crystallisation processes through tracking an optimum temperature or supersaturation profile which can be obtained through optimisation using a morphological population balance (M-PB) model. Here, attention is given to experimentally designing a closed-loop control system on a real crystallisation process to produce the desired shape for rod-like crystals. An optimization algorithm was applied to an M-PB model developed for l-glutamic acid crystallisation to find the optimal profiles of cooling temperature and supersaturation that lead to the desired shape of β-form rod-like product crystals. A closed-loop feedback control system was designed to control the solution temperature or concentration to track the optimum trajectory. On a 1-l crystalliser, it was demonstrated that crystals of different shape can be obtained using the developed closed-loop control methodology. Both supersaturation control and temperature control are compared with each other, and also with constant supersaturation strategy in performance in achieving the final product shape.     

Constrained self-adaptive differential evolution based design of robust optimal fixed structure controller

This paper presents a constrained Self-adaptive Differential Evolution (SaDE) algorithm for the design of robust optimal fixed structure controllers with uncertainties and disturbance. Almost all real world optimization problems have constraints which should be satisfied along with the best optimal solution for the problem. In evolutionary algorithms (EAs) the presence of constraints reduces the feasible region and complicates the search process. Therefore, a suitable method to handle the constraints must also be executed. In the SaDE algorithm, four mutation strategies and the control parameter CR are self-adapted. Self-adaptive Penalty (SP) method is introduced into the SaDE algorithm for constraint handling. The performance of SaDE algorithm is demonstrated on the design of robust optimal fixed structure controller of three systems, namely the linearized magnetic levitation system, F-8 aircraft linearized model and a SISO plant. For the comparison purpose, reported results of constrained PSO algorithm and five DE algorithms with different strategies and parameter values are taken into account. Statistical performance in 20 independent runs is considered to compare the performance of algorithms. From the obtained results, it is observed that SaDE algorithm is able to self-adapt the mutation strategy and the crossover rate and hence performs better than the other variants of DE and the constrained PSO algorithm. Better performance of SaDE is achieved by sustained maintenance of diversity throughout the evolutionary process thus producing better individuals consistently. This also aids the algorithm to escape from local optima thereby avoiding premature convergence.     

An extension to the modified two-step algorithm for steady-state system optimization and parameter estimation

This paper presents an extension to the modified two-step algorithm for determining the optimum steady-state operating condition of a system. The new version of the algorithm gives a faster convergent rate and ensures that the optimal condition is achieved in more general cases where system inequality constraints involving system outputs occur. The performance of the algorithm under noisy measurements is examined by simulation. Simple filter techniques are employed to attenuate errors in process measurements.