Advanced methods of process computer control for industrial processes

In recent years, the requirements for the performance of multilevel process control, including feedforward and feedback control, monitoring and optimization have increased. Applying process computers and micro computers, the functions of analog equipment and hardwired logic devices cannot only be replaced. Extended or quite new methods can be realized improving the performance of multilevel process control. These advanced methods for process control are characterized by: more sophisticated, better adjusted control algorithms, forecasting of process variables, estimation of not directly measurable variables, computer aided design of algorithms and adaptive or selftuning algorithms. The basis of these advanced methods are mathematical models of the processes and their signals, often gained by the process computer itself during on-line operation.The present paper discusses first how process models in open and closed loop can be obtained by on-line identification methods. Then, based on these models, the computer aided design of control algorithms, adaptive control algorithms and adaptive steady-state on-line optimization will be regarded. Monitoring of not direct measurable variables will be mentioned. For some methods, practical results with real and simulated processes are shown. Interactive process computer software packages are used which can easily be transferred to other process computers.     

Digital parameter-adaptive control of an air-conditioning plant

Two parameter-adaptive (self-tuning) control algorithms for multivariable systems are described. The algorithms are designed on the basis of linear input-output system models by the combination of recursive parameter estimation and control algorithms: a parameter-adaptive deadbeat controller and a parameter-adaptive optimal state controller. These controllers are applied to a two-input two-output air-conditioning pilot plant, which consists of an air heater and an air humidifier and whose output variables are the temperature and the relative humidity of the air measured at the air outlet. The air-conditioning plant is a nonlinear system and its linearized static and dynamic behaviour is strongly dependent on the operating point characterized mainly by the output variables and by the air flow rate through the plant. The results of the real-time control experiments indicate that it is possible to use the self-tuning features of the parameter-adaptive controllers to stabilize the controlled system after a short adaption phase and to achieve at least a satisfactory control performance for time varying air flow rates and for time varying setpoints of the output variables.     

Parameter adaptive control algorithms—A tutorial

An introduction is given to adaptive (self-tuning) control algorithms with recursive parameter estimation, which have obtained increasing attention in recent years. These algorithms result from combinations of recursive parameter estimation algorithms and easy to design control algorithms. Firstly a short review is given on proper recursive parameter estimation methods, including their application in a closed loop. This is followed by the design equations for various control algorithms and ways for d.c.-value estimation and for offset compensation. Various explicit and implicit combinations can be designed with different properties of the resulting adaptive control algorithms for both deterministic and stochastic disturbances. Their convergence properties are discussed. Simulation examples are presented and examples for the adaptive control of an air conditioner and a pH-process are shown. The introduction of a third feedback level for coordination and supervision is considered. Finally further problems are discussed.     

On-line identification scheme using adaptive filters

An on-line scheme for identifying a linear process is proposed which consists of a linear time-varying filter and a parameter update algorithm. The disturbances affecting the process, its input and its output, belong to a general class of signals which are a mixture of stochastic and deterministic signal processes generated by some linear time-invariant system excited by white noise and the Dirac delta function, respectively. The process and the disturbance signal models are not restricted to be asymptotically stable. Either a probing input signal or a normal operating input signal can be employed. The probing signal consists of a finite number of sinusoidal signals (exponentially increasing sinusoidal signals for unstable processes) of distinct frequencies. When a normal operating signal is used, an adaptive scheme is employed to tune the parameters of the filters to the distinct frequency components of the signal. The convergence of the parameter estimates to their true value is established.     

Robust adaptive finite‐time parameter estimation and control for robotic systems

This paper studies adaptive parameter estimation and control for nonlinear robotic systems based on parameter estimation errors. A framework to obtain an expression of the parameter estimation error is proposed first by introducing a set of auxiliary filtered variables. Then three novel adaptive laws driven by the estimation error are presented, where exponential error convergence is proved under the conventional persistent excitation (PE) condition; the direct measurement of the time derivatives of the system states are avoided. The adaptive laws are modified via a sliding mode technique to achieve finite‐time convergence, and an online verification of the alternative PE condition is introduced. Leakage terms, functions of the estimation error, are incorporated into the adaptation laws to avoid windup of the adaptation algorithms. The adaptive algorithm applied to robotic systems permits that tracking control and exact parameter estimation are achieved simultaneously in finite time using a terminal sliding mode (TSM) control law. In this case, the PE condition can be replaced with a sufficient richness requirement of the command signals and thus is verifiable a priori. The potential singularity problem encountered in TSM controls is remedied by introducing a two‐phase control procedure. The robustness of the proposed methods against disturbances is investigated. Simulations based on the ‘Bristol‐Elumotion‐Robotic‐Torso II’ (BERT II) are provided to validate the efficacy of the introduced methods. Copyright © 2014 John Wiley & Sons, Ltd.     

Digital parameter-adaptive control of processes with unknown dead time

Simultaneous estimation of process parameters and process time delay is achieved by applying a modification of the recursive least squares method. For an extended process model the order of the numerator polynomial is increased by an upper limit of the time delay. The estimation of the actual time delay $\text{d}\text{?}$ and the calculation of the final process model is done in every step by fitting the impulse response of a model with an assumed order $\text{m}\text{?}$ and time delay $\text{d}\text{?}$ to the impulse response of the estimated extended process model. By combining this method with a feedback control algorithm, parameter-adaptive control algorithms result, and they can be applied to processès with unknown parameters and unknown constant or time varying time delays.     

ROBUST ADAPTIVE CONTROL WITH MULTIPLE ESTIMATION MODELS FOR STABILIZATION OF A CLASS OF NON‐INVERSELY STABLE TIME‐VARYING PLANTS

This paper presents an indirect adaptive control scheme for nominally stabilizable non‐necessarily inversely stable continuous‐time systems with unmodelled dynamics. The control objective is the adaptive stabilization of the closed‐loop system with the achievement of a bounded tracking‐error between the system output and a reference signal given by a stable filter. The adaptive control scheme includes several estimation algorithms and a supervisor which selects the appropriate estimator at every certain time and keeping it operating for at least a minimum period of residence time. This selection is based on a performance criterion related to a measure of the estimation errors obtained with each estimator. In this way, the performance of the output signal is improved with regard to the performance achieved with a unique estimation algorithm. All the estimators are either of the least‐squares type or gradient type. However, any well‐posed estimation algorithm is potentially valid for application. These estimators include relative dead‐zones for robustness purposes and parameter ‘a posteriori’ modifications to ensure the controllability of the estimated models of the plant, which is crucial for proving the stabilizability of the plant via adaptive pole‐placement designs.     

pH值中和反应过程的无模型学习自适应控制

根据pH值处理过程的时变和非线性特性,将基于紧格式线性化的单入单出非线性离散时间系统的无模型学习自适应控制方法应用在带有时滞的pH值中和反应过程中。控制器的设计是无模型的,是直接基于称为伪偏导数的向量,此伪偏导数是通过一种新型参数估计算法,根据酸碱中和反应系统的输入输出信息在线导出的。此无模型控制方法非常适用于实际的模型参数难以辨识,且是时变的非线性系统。仿真控制验证了该方法对不确知动态的非线性pH值的控制具有鲁棒性强、响应速度快和控制精度高的优点,性能好于传统的PID控制。     

On-line time- and frequency-domain identification of unstable processes

An on-line scheme for identifying stable or unstable linear time-invariant processes subject to a class of deterministic and/or stochastic disturbances is proposed. The disturbances are restricted to be the outputs of some unknown linear time-invariant system. The identification scheme consists of: (a) a probing signal input which is a sum of sinusoids (or an exponentially increasing sum of sinusoids when the process is unstable or the disturbances are unbounded), (6) linear time-varying filters which have the properties of asymptotic stability, asymptotic signal tracking and asymptotic noise annihilation, and (c) a parameter update algorithm which uses the filtered input-output data. The frequency response of the process (at the probing signal frequencies) is also estimated. The proposed scheme is verified by simulation.     

Practical issues in the implementation of self-tuning control

Implementation aspects of self-tuning regulators are discussed in the paper. There is a large discrepancy between simulation or academic algorithms and practical algorithms. In the idealized environment of simulations it is easy to get different types of adaptive algorithms to perform well. In practice the situation is quite opposite. The adaptive or self-tuning controller must be able to handle nonlinearities, unmodelled dynamics and unmodelled disturbances over a wide range of operating conditions. Some aspects of how to implement self-tuning controllers are discussed in the paper. This includes robustness, signal conditioning, parameter tracking, estimator wind-up, reset action and start-up. Different ways to use the prior knowledge about the process are also discussed.     

A new robust adaptive control algorithm for linear time-varying plants

Robustness is an important property of a control system. Robust adaptive control has been an active research area for more than a decade. Since it was shown that un-modelled dynamics or even a small bounded disturbance can cause most adaptive control algorithms to go unstable, various modifications of the adaptive control algorithms have been developed to counteract instability and improve robustness with respect to unmodelled dynamics and bounded disturbances. However, we know that most of the modified approaches to achieve robustness require knowledge of either the parameter of bounding function on the unmodelled dynamics, or the upper bound on the disturbances, or the bound on the norm of unknown matching controller/plant parameters, and such knowledge can hardly be obtained in practice. A new indirect adaptive control algorithm for linear time-varying plants is proposed to achieve robustness to a class of unmodelled dynamics, bounded disturbances and plant parameter time variations. A modified relative dead zone technique is used, so that knowledge of the parameters of the upper bounding function on the unmodelled dynamics and the disturbances is not required. The stability analysis and the robust performance of adoptively controlled time-varying systems are provided for the new scheme. A simulation example is given to show the effectiveness of the proposed algorithm.     

滞环非线性系统的加权自适应控制

本文通过引入一个非线性补偿环节和一个开关量函数,解决了滞环非线性系统的自适应 控制问题,并分别对滞环宽度已知和未知情况,建立了大范围渐近收敛和稳定的加权自适应控 制算法.这种算法具有渐近最优的控制效果,能用于非最小相位系统.仿真结果表明,该算法 具有良好的动态性能.     

Adaptive Nonsingular Terminal Sliding Mode Control Design for Near Space Hypersonic Vehicles

This paper presents an adaptive nonsingular terminal sliding mode approach for the attitude control of near space hypersonic vehicles (NSHV) in the presence of parameter uncertainties and external disturbances. Firstly, a novel nonsingular terminal sliding surface is developed and its finitetime convergence is analyzed. Then, an adaptive nonsingular terminal sliding mode control law is proposed, which is chattering free. In the proposed approach, all parameter uncertainties and external disturbances are lumped into one term, which is estimated by an adaptive uncertainty estimation for eliminating the boundary requirement needed in the conventional control design. Subsequently, stability of the closed-loop system is proven based on Lyapunov theory. Finally, the proposed approach is applied to the attitude control design for NSHV. Simulation results show that the proposed approach attains a satisfactory performance in the presence of parameter uncertainties and external disturbances.      

On-line identification of a heat exchanger with a process computer—A case study

For on-line identification and parameter estimation of industrial processes with process computers an identification program package was developed. Three appropriate identification methods can be selected: recursive least squares, recursive instrumental variables and recursive correlation analysis with least squares. The program package also includes: signal generation, determination of model order and time delay, data filtering for the elimination of low frequent disturbances, model verification and plotting of intermediate and final results. Practical results and comparisons with the identification package are shown for an industrial size steam-heated heat exchanger.     

Product property and production rate control of styrene polymerization

A multivariable multi-rate nonlinear model predictive control (NMPC) strategy is applied to styrene polymerization. The NMPC algorithm incorporates a multi-rate Extended Kalman Filter (EKF) to handle state variable and parameter estimation. A fundamental model is developed for the styrene polymerization CSTR, and control of polymer properties such as number average molecular weight (NAMW) and polydispersity is considered. These properties characterize the final polymer distribution and are strong indicators of the polymer qualities of interest. Production rate control is also demonstrated. Temperature measurements are available frequently while laboratory measurements of concentration and molecular weight distribution are available infrequently with substantial time delays between sampling and analysis. Observability analysis of the augmented system provides guidelines for the design of the augmented disturbance model for use in estimation using the multi-rate EKF. The observability analysis links measurement sets and corresponding observable disturbance models, and shows that measurements of moments of the polymer distribution are essential for good estimation and control. The CSTR is operated at an open-loop unstable steady state. Control simulations are performed under conditions of plant-model structural mismatch and in the presence of parameter uncertainty and disturbances, and the proposed multi-rate NMPC algorithm is shown to provide superior performance compared to linear multi-rate and nonlinear single-rate MPC algorithms. The major contributions of this work are the development of the multi-rate estimator and the measurement design study based on the observability analysis.     

鲁棒自适应前馈控制器及其在间歇式余热锅炉给水系统中的应用

本文提出了基于降阶模型的自适应前馈控制器.当被控对象是开环不稳定或是非最小相 位系统,当存在未建模动态时,当受到有界干扰和可测干扰作用时该控制器不仅可以使自适 应控制系统稳定运行,而且实现对可测干扰的补偿.本文将该控制器应用于本溪第二炼钢厂 间歇式余热锅炉给水系统获得满意效果.     

Robustness of unmodified stochastic adaptive control algorithms

Originally, adaptive control theory was developed for the ideal system models, i.e., linear system models under the assumption that relative degree and upper bounds on the order of the systems are known. In the early 1980s, adaptive control algorithms designed for such ideal system models were strongly attacked by many researchers due to “lack of robustness” in the presence of unmodeled dynamics and external disturbances. The purpose of the present paper is to relax existing constant pressure on the adaptive control algorithms originally designed for the ideal system models. It is shown that such adaptive control algorithms are globally stable and robust with respect to unmodeled dynamics and external disturbances without any modifications, such as iσ-modification, ϵ₁-modification, relative dead-zone, projection of the parameter estimates, etc. Global stability of the unmodified algorithms is established by requiring the reference signal to be persistently exciting     

基于扰动补偿的无微分模型参考自适应控制系统设计

针对一类含有参数不确定性和未知非线性扰动的系统,本文提出一种基于扰动补偿的无微分模型参考自适应控制方法,实现系统输出对参考模型输出信号的高精度跟踪.首先,利用被控对象模型信息设计扰动估计器,对系统非线性扰动进行在线估计;其次,基于非线性扰动估计值设计参考模型和无微分参数更新律,构建无微分模型参考自适应控制器,建立基于扰动补偿和状态反馈的自适应控制律,以消除参数不确定性和非线性扰动对系统输出的影响,保证系统输出对参考模型输出的准确跟踪;然后,给出闭环系统误差信号收敛条件和控制器参数整定方法;最后,通过数值仿真验证所提方法的有效性和优越性.     

Unified treatment of internal model principle based adaptive control algorithms

A number of adaptive control algorithms are summarized here for the control of unknown linear discrete time plants with unknown deterministic disturbances. Adaptive implementation of the internal model principle is used for asymptotical cancellation of the deterministic disturbances. The use of the certainty equivalence principle for implementation of these algorithms can be shown to result in a certain type of unmodelled dynamics error for each of these algorithms. A unified analysis of these algorithms is given under a common framework of unmodelled dynamics. With suitable modification of the parameter estimation algorithm, the global convergence and stability of these algorithms are established without the requirement of the persistency of excitation condition. Some simulation results are provided for support of the analysis.     

A globally stable APCS in the presence of bounded noises and disturbances

This paper presents a globally stable adaptive predictive control system (APCS) for discrete linear processes with pure time delays in the presence of bounded measurement and process noise plus unmeasured disturbances. The main contribution is the proof of stability in the context of discrete adaptive control schemes. This proof is based on the minimization of the a posteriori estimation error and the convergence of the estimated parameters.