On near optimal neural control of multiple-input nonlinear systems

It has been a common consensus that general techniques for stabilization of nonlinear systems are available only for some special classes of nonlinear systems. Control design for nonlinear systems with uncertain components is usually carried out on a per system basis, especially when physical control constraints, and certain control performance measures such as optimum time control are imposed. Elegant adaptive control techniques are difficult to apply to this type of problems. A new neural network based control design is proposed and presented in this paper to deal with a special class of uncertain nonlinear systems with multiple inputs. The desired system dynamics are analyzed and utilized in the process of the proposed intelligent control design. The theoretical results are provided to justify the design procedures. The simulation study is conducted on a second-order bilinear system with two inputs and uncertainties on its parameters. The simulation results indicate that the proposed design approach is effective.     

Theoretical analysis of unconstrained nonlinear model predictive control

Model predictive control (MPC) is a well-established controller design strategy for linear process models. Because many chemical and biological processes exhibit significant nonlinear behaviour, several MPC techniques based on nonlinear process models have recently been proposed. The most significant difference between these techniques is the computational approach used to solve the nonlinear model predictive control (NMPC) optimization problem. Consequently, analysis of NMPC techniques is often connected to the computational approach employed. In this paper, a theoretical analysis of unconstrained NMPC is presented that is independent of the computational approach. A nonlinear discrete-time, state-space model is used to predict the effects of future inputs on future process outputs. It is shown that model inverse, pole-placement, and steady-state controllers can be obtained by suitable selection of the control and prediction horizons. Moreover, the NMPC optimization problem can be modified to yield nonlinear internal model control (NIMC). The computational requirements of NIMC are considerably less than NMPC, but the NIMC approach is currently restricted to nonlinear models with well-defined and stable inverses. The NIMC controller is shown to provide superior servo and regulatory performance to a linear IMC controller for a continuous stirred tank reactor.     

Supervisory multiple regime control

The objective of this work is to identify a control algorithm that is capable of handling nonlinear behaviour (operating point dependent) witnessed in most industrial processes. To this end, the proposed solution is that of a supervisory multiple model control scheme, SMMC. This work demonstrates that the multiple model methodology can be recast into a Supervisory approach, whereby the supervisor is employed as a selector. This selector (supervisor) identifies the appropriate local-controller from a fixed family set. Unlike other supervisory techniques a multiple model observer (MMO) is proposed for the selection mechanism. Switching between local-controllers is accomplished bumplessly through a multiple model bumpless transfer scheme. Consequently, producing a continuous control signal as the process transverses between different operating regimes. The key issue in this application is the unique interaction between the local-controllers and the supervisor. This interaction is necessary to ensure global stability is maintained at all times, especially during switching. In short, the SMMC scheme enables the implementation of linear control theory, which is well accepted in industry, to standard nonlinear processes. The SMMC approach warrants the control design to extend beyond normal operating conditions that breakdown when standard linear control techniques are applied. The above notion is applied to a pilot-scale binary distillation column. In this example the column's distinct operating points describe the nonlinear behaviour. The results illustrate that as the distillation column shifted between different operating points the SMMC self-regulates accordingly. This self-regulation ensures that global stability and performance are maintained at an optimum. The entire SMMC design was implemented within a PC Windows-NT environment that was interfaced to an industrial DCS system.     

Stabilisation of nonlinear chemical processes via dynamic power-shaping passivity-based control

It is well known that energy-balancing passivity-based control is stymied by the presence of pervasive dissipation. To overcome this problem in electrical circuits, some authors have used power-shaping techniques, where stabilisation is achieved by shaping a function akin to power instead of energy. Some extensions of the techniques to general nonlinear systems, yielding static state-feedback control laws, have also been reported. In this article, we extend these techniques to dynamic feedback control and apply them to nonlinear chemical processes. The stability analysis is carried out using the shaped power function as Lyapunov function. The proposed technique is illustrated with two nonlinear chemical process examples.     

Reduction of stable differential–algebraic equation systems via projections and system identification

Most large-scale process models derived from first principles are represented by nonlinear differential–algebraic equation (DAE) systems. Since such models are often computationally too expensive for real-time control, techniques for model reduction of these systems need to be investigated. However, models of DAE type have received little attention in the literature on nonlinear model reduction. In order to address this, a new technique for reducing nonlinear DAE systems is presented in this work. This method reduces the order of the differential equations as well as the number and complexity of the algebraic equations. Additionally, the algebraic equations of the resulting system can be replaced by an explicit expression for the algebraic variables such as a feedforward neural network. This last property is important insofar as the reduced model does not require a DAE solver for its solution but system trajectories can instead be computed with regular ODE solvers. This technique is illustrated with a case study where responses of several different reduced-order models of a distillation column with 32 differential equations and 32 algebraic equations are compared.     

Control of an anaerobic digester through normal form of fold bifurcation

Nonlinear dynamics is ubiquitous in engineering systems. As some parameters are varied bifurcations arise in the state variables. Generically, when one parameter changes, Hopf and fold bifurcations are found. Other ones can also be present due to special systems characteristics, such as symmetries. Knowing in advance the significant bifurcation scenario, a novel approach to control can be considered. We compute the normal form corresponding to such a bifurcation and we take this model as the nominal model of the plant. Then we design a nonlinear control which takes advantage of the precise bifurcation scenario. This general method is applied, in this paper, to an anaerobic digester. We will control the process with an adaptive controller.Specifically, we want to compare with the case that the nominal plant is considered as a linear model, such as it is typical in adaptive control techniques. Our proposed method has more benefits in signal control effort, faster convergence rate and low error.This paper shows how the combination of appropriated nonlinear dynamic techniques such as bifurcations and normal forms, and nonlinear control, can give rise to an improvement of the traditional methodology.     

Nonlinear prediction of manufacturing systems through explicit and implicit data mining

Many processes in the industrial realm exhibit stochastic and nonlinear behavior. Consequently, an intelligent system must be able to ndapt to nonlinear production processes as well as probabilistic phenomena. To this end, an intelligent manufacturing system may draw on techniques from disparate fields, involving knowledge in both explicit and implicit form.In order for a knowledge based system to control a manufacturing process, an important capability is that of prediction: forecasting the future trajectory of a process as well as the consequences of the control action. This paper presents a comparative study of explicitaand implicit methods to predict nonlinear chaotic behavior. The evaluated models include statistica; procedures as well as neural networks and case based reasoning. The concepts are crystallized through a case study in the prediction of chaotic processes adulterated by various patterns of noise.     

Single screw extrusion control: A comprehensive review and directions for improvements

Polymer extrusion is usually a complex process, particularly due to the coupled nature of process parameters, and hence highly prone to fluctuations. Although a number of different approaches have been attempted in research/industry over the last few decades for extrusion control, it is still experiencing some problems in achieving consistent product quality. Presently, most of the polymer processing extruders are equipped with PID controllers mainly for the control of the screw speed and barrel temperatures in their set limits. It seems that only both of these controllers are commonly used as the major aids of process control to achieve the required melt quality. Although, the quality of the melt output (i.e., a thermally homogeneous melt output which is constant in quantity and quality over the time) is the key variable in polymer extrusion, only a few control techniques are available which make control decisions by observing the actual melt flow quality. Therefore, the development of new control strategies which consider the actual melt quality, perhaps incorporating industrially popular nonlinear techniques such as artificial intelligence, should be highly valuable. In this work, a critical evaluation is made on the state-of-the-art of the previous control approaches in polymer extrusion in industry and research while identifying their limitations. Then, some of the possible directions for future research and also to develop an advanced process control strategy are presented by eliminating a few of the existing limitations.     

Adaptive predictive control of combustor NOx emissions

The design and implementation for the active control of oxides of nitrogen (NO_x) emissions from gas turbine combustors is considered in this paper. Predictive control techniques with both fixed and adaptive parameters are employed. An on-line parameter estimation algorithm provides good modelling of the nonlinear characteristics of the combustor NO_x process. To obtain a comparison with other control techniques, an optimal PID controller is detailed. The actuator that controls the gas flow to the combustor is an electromagnetic shaker. Gain-scheduling control is applied to provide accurate position tracking of the shaker whose characteristics vary between different operating points. These control strategies are implemented using the SIMULINK/dSPACE controller development environment. Their performance is evaluated on an atmospheric test rig fitted with a commercial combustor.     

Nonlinear system identification for predictive control using continuous time recurrent neural networks and automatic differentiation

In this paper, a continuous time recurrent neural network (CTRNN) is developed to be used in nonlinear model predictive control (NMPC) context. The neural network represented in a general nonlinear state-space form is used to predict the future dynamic behavior of the nonlinear process in real time. An efficient training algorithm for the proposed network is developed using automatic differentiation (AD) techniques. By automatically generating Taylor coefficients, the algorithm not only solves the differentiation equations of the network but also produces the sensitivity for the training problem. The same approach is also used to solve the online optimization problem in the predictive controller. The proposed neural network and the nonlinear predictive controller were tested on an evaporation case study. A good model fitting for the nonlinear plant is obtained using the new method. A comparison with other approaches shows that the new algorithm can considerably reduce network training time and improve solution accuracy. The CTRNN trained is used as an internal model in a predictive controller and results in good performance under different operating conditions.     

继电反馈多模型控制及应用

作为简单、鲁棒的设计方法,基于继电反馈的PID控制器巳广泛应用于工业过程控制。它可以由继电反馈引起的振荡近似估计过程临界信息进行控制器的设计。多模型控制是解决系统时变、非线性、参数不确定性等复杂问题得一种有效方法。该文将继电反馈控制与多模型控制相结合,对时变、非线性的电厂主汽温系统过进行控制。首先在各个工况点应用继电反馈方法设计子控制器。然后在系统整个运行区间进行多模型自适应控制以克服非线性、时变对系统的影响。仿真表明本方法所建立的控制系统具有良好的控制品质及较强的自适应能力。     

Predictive LPV control of a liquid–gas separation process

The problem of controlling a liquid–gas separation process is approached by using LPV control techniques. An LPV model is derived from a nonlinear model of the process using differential inclusion techniques. Once an LPV model is available, an LPV controller can be synthesized. The authors present a predictive LPV controller based on the GPC controller [Clarke D, Mohtadi C, Tuffs P. Generalized predictive control – Part I. Automatica 1987;23(2):137–48; Clarke D, Mohtadi C, Tuffs P. Generalized predictive control – Part II. Extensions and interpretations. Automatica 1987;23(2):149–60]. The resulting controller is denoted as GPC–LPV. This one shows the same structure as a general LPV controller [El Gahoui L, Scorletti G. Control of rational systems using linear-fractional representations and linear matrix inequalities. Automatica 1996;32(9):1273–84; Scorletti G, El Ghaoui L. Improved LMI conditions for gain scheduling and related control problems. International Journal of Robust Nonlinear Control 1998;8:845–77; Apkarian P, Tuan HD. Parametrized LMIs in control theory. In: Proceedings of the 37th IEEE conference on decision and control; 1998. p. 152–7; Scherer CW. LPV control and full block multipliers. Automatica 2001;37:361–75], which presents a linear fractional dependence on the process signal measurements. Therefore, this controller has the ability of modifying its dynamics depending on measurements leading to a possibly nonlinear controller. That controller is designed in two steps. First, for a given steady state point is obtained a linear GPC using a linear local model of the nonlinear system around that operating point. And second, using bilinear and linear matrix inequalities (BMIs/LMIs) the remaining matrices of GPC–LPV are selected in order to achieve some closed loop properties: stability in some operation zone, norm bounding of some input/output channels, maximum settling time, maximum overshoot, etc., given some LPV model for the nonlinear system. As an application, a GPC–LPV is designed for the derived LPV model of the liquid–gas separation process. This methodology can be applied to any nonlinear system which can be embedded in an LPV system using differential inclusion techniques.     

Robust tracking of the heating value in an underground coal gasification process using dynamic integral sliding mode control and a gain-scheduled modified Utkin observer

In this paper, a model-based control and state reconstruction of an underground coal gasification (UCG) process is elaborated. In order to deploy model-based control strategies, a sophisticated model of the UCG process based on partial differential equations is approximated with a nonlinear control-oriented model that adequately preserves the fundamental dynamic characteristics of the process. A robust dynamic integral sliding mode control (DISMC) is designed based on the control-oriented model to track the desired heating value, which is one of the key indicators for evaluating the performance of an UCG process. Unknown states required for the model-based control are reconstructed using a gain-scheduled modified Utkin observer (GSMUO). In order to assess the robustness of the nonlinear control and estimation techniques, the water influx phenomenon is considered as an input disturbance. Moreover, the underlying UCG plant model is subjected to parametric variations as well as measurement noise. In order to guarantee the stability of the overall system, the boundedness of the internal dynamics is also proved. To make a fair comparison, the performance of the proposed controller is compared with an integral sliding mode control (ISMC) and a classical proportional-integral (PI) controller. Simulation results highlight the effectiveness of the proposed control scheme in terms of minimum control energy and improved tracking error. Moreover, the simulation study shows that the combination of DISMC and GSMUO exhibit robustness against an input disturbance, parametric uncertainties and measurement noise.     

Estimation and control of an α-olefin polymerization reactor

The research addressed in this paper is focused on the estimation and control of a nonlinear industrial polymerization process. The majority of the available estimation techniques are not easy to implement on-line due to the intensive computations involved. Therefore, there is a need for an estimation technique that is simple, yet capable of handling multi-rate sampled data with variable measurement dead times. For the polymerization system under study, one such estimator is presented. Estimation is implemented within a nonlinear model predictive control algorithm (NLMPC). The combined estimator-controller is shown to display good set-point tracking and disturbance rejection properties via simulations involving some practical control problems.     

A robust control scheme for nonlinear non-isothermal uncertain jacketed continuous stirred tank reactor

A Non-isothermal Jacketed Continuous Stirred Tank Reactor (CSTR) is extensively used in chemical as well as in other process industries to manufacture different products. The dynamics of non-isothermal CSTR are highly nonlinear and open-loop unstable in nature. Moreover, it may have parametric uncertainties, disturbances and un-modeled side reactions which may cause the reactor temperature to deviate from the reference value. This deviation may degrade quality of the product because the chemical reaction inside the CSTR depends on reactor temperature. For such a nonlinear, unstable and uncertain process, designing a control scheme with the ability to reject the effects of disturbances along with a good reference tracking capability is a challenging control engineering problem. In this work, a novel robust sliding mode control technique named as Improved Integral Sliding Mode Control (IISMC) has been presented for uncertain non-isothermal jacketed CSTR process. Moreover, a variety of recently developed sliding mode control techniques such as Classical Integral Sliding Mode Control (CISMC) and Super Twisted Algorithm based Sliding Mode Control (STA-SMC) have also been devised and compared with the proposed approach in order to investigate the effectiveness of the proposed scheme. A Lyapunov based analysis has also been provided to assure the robust stability of the closed loop process. Furthermore, in order to extend the state feedback approach to the output feedback scheme, two robust observers; High Gain Observer (HGO) and Extended High Gain Observer (EHGO), are also designed for the very process. They have also been compared with each other and have been investigated for robust stability using Lyapunov based approach. Finally, an output feedback control scheme using IISMC and EHGO has been presented and its performance has been examined and compared with the IISMC based state feedback approach. The simulation results show that the proposed control scheme effectively rejects the uncertainties and disturbances without leading the process to instability and offers good reference tracking capabilities.     

Robust and reliable estimation via Unscented Recursive Nonlinear Dynamic Data Reconciliation

The quality of process data in a chemical plant significantly affects the performance and benefits gained from activities like performance monitoring, online optimization and control. Since many chemical processes often exhibit nonlinear dynamics, techniques like Extended Kalman Filter (EKF) and Nonlinear Dynamic Data Reconciliation (NDDR) have been developed to improve the data quality. There are various issues that arise with the use of either of these techniques: EKF cannot handle inequality or equality constraints, while the NDDR has high computational cost. Recently a recursive estimation technique for nonlinear dynamic processes has been proposed which combines the merits of EKF and NDDR techniques. This technique, named as Recursive Nonlinear Dynamic Data Reconciliation (RNDDR), provides state and parameter estimates that satisfy bounds and other constraints imposed on them. However, the estimate error covariance matrix in RNDDR is computed in the same manner as in EKF, that is, the effects of both nonlinearity and constraints are neglected in the computation of the estimate error covariance matrix.

A relatively new method known as the Unscented Kalman Filter has been developed for nonlinear processes, in which the statistical properties of the estimates are computed without resorting to linearization of the nonlinear equations. This leads to improved accuracy of the estimates. In this paper, we combine the merits of the Unscented Kalman Filter and the RNDDR to obtain the Unscented Recursive Nonlinear Dynamic Data Reconciliation (URNDDR) technique. This technique addresses all concerns arising due to the presence of nonlinearity and constraints within a recursive estimation framework, resulting in an efficient, accurate and stable method for real-time state and parameter estimation for nonlinear dynamic processes.     

An overview on fault diagnosis and nature-inspired optimal control of industrial process applications

Fault detection, isolation and optimal control have long been applied to industry. These techniques have proven various successful theoretical results and industrial applications. Fault diagnosis is considered as the merge of fault detection (that indicates if there is a fault) and fault isolation (that determines where the fault is), and it has important effects on the operation of complex dynamical systems specific to modern industry applications such as industrial electronics, business management systems, energy, and public sectors. Since the resources are always limited in real-world industrial applications, the solutions to optimally use them under various constraints are of high actuality. In this context, the optimal tuning of linear and nonlinear controllers is a systematic way to meet the performance specifications expressed as optimization problems that target the minimization of integral- or sum-type objective functions, where the tuning parameters of the controllers are the vector variables of the objective functions. The nature-inspired optimization algorithms give efficient solutions to such optimization problems. This paper presents an overview on recent developments in machine learning, data mining and evolving soft computing techniques for fault diagnosis and on nature-inspired optimal control. The generic theory is discussed along with illustrative industrial process applications that include a real liquid level control application, wind turbines and a nonlinear servo system. New research challenges with strong industrial impact are highlighted.     

一种空间飞行器姿态控制非线性模型的预测控制新算法

空间飞行器的姿态控制受到诸如带时延的非线性动态特性、模型和参数的不确定性等因素的影响 ,其控制相当复杂。传统的控制技术 (如PID控制 )对控制对象的过程模型要求较高 ,且不能解决过程控制中非线性、时变、控制输入的约束性等因素的影响 ,其控制所能达到的性能和效率也远不够满足当前飞行器的控制要求。该文将介绍一种新型的基于控制输入的函数空间最优化的模型预测控制算法 ,称为函数空间模型预测控制 (F -MPC)。该法可用于线性和非线性系统 ,对过程模型要求不高 ,能在控制输入约束条件存在的情况下通过在线优化使系统很好地跟踪期望轨迹 ,并且解决了PID控制所遇到的问题。同时 ,将该算法用于空间飞行器的姿态控制仿真 ,仿真结果表明控制效果很好。     

Wiener model based nonlinear predictive control

This paper addresses the problem of discrete-time nonlinear predictive control of W iener systems. Wiener-model-based nonlinear predictive control combines the advantages of linear-model-based predictive control and gain scheduling while retaining a moderate level of computational complexity. A clear relation is shown between an iteration in the optimization of the nonlinear control problem and the control problem of the underlying linear-model-based method. This relation has a simple form of gain scheduling, thus the properties of the nonlinear control system can be analysed from the comprehensible linear control aspect. Several disturbance rejection techniques are proposed and compared. The method was tested on a simulated model of a pH neutralization process. The performance was excellent also in the case of a considerable plant-tomodel mismatch. The method can be applied as a first next step in cases where the performance of linear control is unsatisfactory owing to process nonlinearity.