Modeling and control of Wiener-type processes

We develop a simple relay feedback method to identify Wiener-type nonlinear processes. It separates the identification problem of the nonlinear static function from that of the linear dynamic subsystem to simplify the identification procedure significantly. Owing to the separation, the unmeasurable output of the linear dynamic subsystem can be obtained in a straightforward manner. Then, determining the model structure of the nonlinear static function becomes very simple and the estimates are robust to additive output noises. We can identify the whole activated region of the nonlinear static function as well as the ultimate information of the linear dynamic subsystem from only one relay feedback test. More information on the linear dynamic subsystem can be estimated by well-established linear system identification methods from additional tests. We use a nonlinear control strategy to compensate the nonlinear dynamics of the Wiener process so that the design parameters can be determined by usual tuning rules developed for linear processes and a high control performance can be achievable as in linear processes.     

Fractional order integrator for the relay feedback identification of a process Nyquist point in the third quadrant

A fractional order integrator can be used for the relay feedback identification of a process Nyquist point in the third quadrant, and to implement the fractional order integrator, it is often approximated by integer order systems. Here, instead of the usual rational transfer function approximation of the fractional order integrator in the relay feedback system, a simple analytic method which utilizes the on-off characteristics of relay output is proposed. Simulation results show that the proposed method can find process Nyquist points in the third quadrant without worrying about the approximation errors and ranges of the fraction order integrator.     

Process identification method using relay feedback and backward integrals

We propose a new process identification method that combines the two methods of the relay feedback to activate the process and the backward integrals to estimate the model parameters. Novel deviation variables are introduced to incorporate the case that the initial part of the process is unsteady-state without sacrificing the dynamic information included in the initial part, while the previous approaches assign zero-weighting to the initial parts, resulting in loss of the dynamic information included in the initial part. The final cyclic-steady-state part of the process input and output data is chosen as the reference of the deviation variables. The proposed method can estimate the model parameters analytically by using the backward integrals and the least squares method.     

On-line process identification and PID controller autotuning

We propose a new and simple on-line process identification method for the automatic tuning of the PID controller. It does not require a special type of test signal generators such as relay or P controller only if the signals are persistently exciting. That is, a user can choose arbitrary signal generators such as relay, a P controller, the controller itself, pulse signal and step signal generator because it needs only the measured process output and the controller output. It can incorporate nonlinearities due to actuator saturation or manual mode operation during identification work and shows a good robustness to measurement noises, nonlinearity of the process and disturbances. The proposed autotuner combined with the identification method and tuning rule using a model reduction shows good control properties compared with previous autotuning methods.     

关联大系统的分散辨识方法研究

关联大系统的特点是维数高、内部子过程间相互关联,使得辨识方法的计算量和存储量急剧增加以及它本身的复杂性,以致常规辨识方法难以实现。为了减少大系统辨识的计算量,避免本身所带来的辨识困难,提出了获得其可分稳态模型的强一致性估计的分散辨识方法。该方法仅使用设定点的阶跃信号作输入辨识信号,并且每个子过程的输入输出和稳态模型的辨识都是在相应的局部单元完成的,因而大大减少了对过程的干扰和信息的交换量,该方法简单易懂,仿真结果说明了该辨识方法的有效性和实用性。     

Extremum seeking control using a partial sum of input-output product

Recent extremum seeking control that uses a continuous perturbation and the integral feedback of perturbation- output product is based on a static nonlinear process. The method can be applied to dynamic nonlinear processes for tracking and maintaining the optimal operating points. It has several tuning parameters, such as the integral controller gain and the magnitude and frequency of the continuous perturbation signal. The frequency of the continuous perturbation signal should be low enough to ensure the time-scale separation between the real-time optimization and the process dynamics for the closed-loop stability. However, for some processes, fast perturbations are preferred because they can be attenuated easily in subsequent processes such as buffers and storages. For this, we propose an extremum seeking control method where the partial sum of perturbation-output product is used for a faster squarewave perturbation. Simulations for two processes of parallel competing reactions have been given, and a simple liquid level system to test extremum seeking control methods is suggested.     

Simultaneous mixed-integer dynamic scheduling of processes and their energy systems

Increasingly volatile electricity prices make simultaneous scheduling optimization desirable for production processes and their energy systems. Simultaneous scheduling needs to account for both process dynamics and binary on/off-decisions in the energy system leading to challenging mixed-integer dynamic optimization problems. We propose an efficient scheduling formulation consisting of three parts: a linear scale-bridging model for the closed-loop process output dynamics, a data-driven model for the process energy demand, and a mixed-integer linear model for the energy system. Process dynamics is discretized by collocation yielding a mixed-integer linear programming (MILP) formulation. We apply the scheduling method to three case studies: a multiproduct reactor, a single-product reactor, and a single-product distillation column, demonstrating the applicability to multiple input multiple output processes. For the first two case studies, we can compare our approach to nonlinear optimization and capture 82% and 95% of the improvement. The MILP formulation achieves optimization runtimes sufficiently fast for real-time scheduling.     

Dynamic gray‐box modeling for on‐line monitoring of polymer extrusion viscosity

Melt viscosity is a key indicator of product quality in polymer extrusion processes. However, real time monitoring and control of viscosity is difficult to achieve. In this article, a novel “soft sensor” approach based on dynamic gray‐box modeling is proposed. The soft sensor involves a nonlinear finite impulse response model with adaptable linear parameters for real‐time prediction of the melt viscosity based on the process inputs; the model output is then used as an input of a model with a simple‐fixed structure to predict the barrel pressure which can be measured online. Finally, the predicted pressure is compared to the measured value and the corresponding error is used as a feedback signal to correct the viscosity estimate. This novel feedback structure enables the online adaptability of the viscosity model in response to modeling errors and disturbances, hence producing a reliable viscosity estimate. The experimental results on different material/die/extruder confirm the effectiveness of the proposed “soft sensor” method based on dynamic gray‐box modeling for real‐time monitoring and control of polymer extrusion processes. POLYM. ENG. SCI., 2012. © 2012 Society of Plastics Engineers     

Arma neuron networks for modeling nonlinear dynamical systems

A new neuronal structure, the ARMA neuron, is proposed here. These new neurons are designed for modeling nonlinear dynamics often encountered in chemical engineering processes. They are an extension of standard neurons which are used for static process modeling. These new neurons contain internal input/output dynamic structure and can model dynamic non-linearities in a flexible manner. A nonlinear output transformation is used here as opposed to a linear version used earlier (Krishnapura and Jutan, 1993). New algorithms for training networks comprised of the new ARMA neurons are developed using the backpropagation approach. The ARMA neurons are used to model both simulated and experimental nonlinear dynamic processes, including an industrial fluidized bed reactor.     

变增益的非线性预测控制算法

采用变增益策略,用输入与稳态输出的映射表示系统的静态非线性,用一个增益为1的ARX模型表示系统的动态模型,代替多数文献中常用的分段线性多模型方法进行非线性系统的预测控制.文中通过对连续搅拌釜反应器(CSTR)的仿真,验证了本算法的有效性.     

Two-degree-of-freedom output feedback controllers for nonlinear processes

In this work, a nonlinear output feedback control algorithm is proposed, in the spirit of model-state feedback control. The structure provides state estimates using a process model, the measured output, and the residual between the model output and the measured output. These estimates will track the process states at a rate determined by a set of tunable parameters. An algebraic transformation of the state estimates is incorporated in the control structure to ensure that the input/output gain of the observer matches the model upon which the static state feedback control law is based. The transformed states are then used in the control law. This leads to a controller of minimal order possessing integral action. The control structure is shown to have the same properties as the standard model-state feedback structure. The resulting algorithm is a two-degree of freedom control law, in the sense that the control action is not a function of the error only, but the output and the set point are processed in different ways. Finally, a simulation example using an exothermic CSTR operating at an open-loop unstable steady state is used to demonstrate the closed-loop performance of the proposed method.     

Globally stable control systems for processes with input multiplicities

A nonlinear process with input multiplicity has two or more input values for a given output at the steady state, and the process steady state gain changes its sign as the operating point changes. A control system with integral action will be unstable when both signs of the process gain and the controller integral gain are different, and its stability region will be limited to the boundary where the process steady state gain is zero. Unlike processes with output multiplicities, feedback controllers cannot be used to correct the sign changes of process gain. To remove such stability limitation, a simple control system with parallel compensator is proposed. The parallel compensator can be easily designed based on the process steady state gain information and tuned in the field. Using the two time scale method, the stability of proposed control systems for processes with input multiplicities can be checked.     

AUTOMATIC TUNING OF SYSTEMS WITH ONE OR TWO UNSTABLE POLES

Stabilizability and identification of systems with one or two unstable poles is addressed. Two limit points of conditional stability are characterized using closed-loop dynamics with a relay and a novel nonlinear element. An algorithm is developed to analyze information from the resultant stable limit cycles in the process input and output. An easily tuned cascade PID control structure is then proposed to stabilize the system and achieve desirable performance. The proposed autotuning technique is tested with good results on a wide variety of unstable systems.     

Dynamic output feedback covariance control of stochastic dissipative partial differential equations

In this work, we develop a method for dynamic output feedback covariance control of the state covariance of linear dissipative stochastic partial differential equations (PDEs) using spatially distributed control actuation and sensing with noise. Such stochastic PDEs arise naturally in the modeling of surface height profile evolution in thin film growth and sputtering processes. We begin with the formulation of the stochastic PDE into a system of infinite stochastic ordinary differential equations (ODEs) by using modal decomposition. A finite-dimensional approximation is then obtained to capture the dominant mode contribution to the surface roughness profile (i.e., the covariance of the surface height profile). Subsequently, a state feedback controller and a Kalman-Bucy filter are designed on the basis of the finite-dimensional approximation. The dynamic output feedback covariance controller is subsequently obtained by combining the state feedback controller and the state estimator. The steady-state expected surface covariance under the dynamic output feedback controller is then estimated on the basis of the closed-loop finite-dimensional system. An analysis is performed to obtain a theoretical estimate of the expected surface covariance of the closed-loop infinite-dimensional system. Applications of the linear dynamic output feedback controller to both the linearized and the nonlinear stochastic Kuramoto-Sivashinsky equations (KSEs) are presented. Finally, nonlinear state feedback controller and nonlinear output feedback controller designs are also presented and applied to the nonlinear stochastic KSE.     

A self-tuning control method for Wiener nonlinear systems and its application to process control problems

Many chemical processes can be modeled as Wiener models, which consist of a linear dynamic subsystem follow-ed by a static nonlinear block. In this paper, an effective discrete-time adaptive control method is proposed for Wiener nonlinear systems with uncertainties. The parameterization model is derived based on the inverse of the nonlinear function block. The adaptive control method is motivated by self-tuning control and is derived from a modified Clarke criterion function, which considers both tracking properties and control efforts. The un-certain parameters are updated by a recursive least squares algorithm and the control law exhibits an explicit form. The closed-loop system stability properties are discussed. To demonstrate the effectiveness of the obtained results, two groups of simulation examples including an application to composition control in a continuously stirred tank reactor (CSTR) system are studied.     

An Efficient Measure for Quantification of Nonlinearity in Chemical Engineering Processes Based on I/O Steady-State Loci

Nonlinearity is virtually ubiquitous in chemical engineering plants, and assessing the degree of nonlinearity involved in a process is of special interest for process control purposes. In this paper, we introduce a simple nonlinearity measure to quantify the extent of nonlinearity in a dynamic system based on its normalized steady-state input/output loci. Our nonlinearity measure obviates the limitations of previous metrics in terms of computational effort and correct identification of highly nonlinear relationships. The measure is satisfactorily applicable to various I/O relationships—from truly linear to sinusoidal, for instance. In order to illustrate the efficiency of the proposed measure, four numerical examples concerning a double-effect evaporator, a jacketed continuously stirred tank reactor (CSTR) with an irreversible reaction, a CSTR involving van de Vusse reactions, and the Henson–Seborg–Pottmann CSTR are presented.     

Enhanced frequency response estimator to guarantee pre-specified phase angle and static disturbance rejection with all harmonics removed

We propose a new frequency response estimation method in order to guarantee a pre-specified phase angle of the estimated model under static disturbance circumstances with rejecting harmonics completely. The proposed method uses one cycle of the conventional relay feedback signal followed by a sinusoidal signal. The sinusoidal signal in a cyclic steady state has no harmonics, resulting in exact frequency response estimates. Also, it guarantees the pre-specified phase angle and removes the effects of static disturbances by adjusting the reference value of the sinusoidal signal.     

Relay feedback identification for processes under drift and noisy environments

Relay feedback identification methods are widely used to find the process ultimate information and tune proportional‐integral‐derivative controllers. The conventional relay feedback method has several disadvantages, which include poor estimates of the process ultimate information for low‐order processes, chattering of relay for noisy environments, and asymmetric relay responses for constant biases or slow drifts in the process outputs. Methods to mitigate each of the above disadvantages are available. However, a systematic method to treat all of them has not been studied yet. Here, simple relay feedback methods that resolve these problems by introducing band‐pass filters in the feedback loop are proposed. The high‐pass filter part in band‐pass filter removes a constant bias or low frequency drift, and the low‐pass filter part removes high frequency noise and high‐order harmonic terms in the relay feedback oscillation, resulting better estimates of the process ultimate information. Because filters used for the proposed methods are able to reject constant biases, the process steady state gains can be estimated without disturbing the relay feedback oscillations and first order plus time delay (FOPTD) models can be obtained by combining the process steady state gains with the relay oscillation information. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

A SIMPLE METHOD FOR TUNING CASCADE CONTROL SYSTEMS

A simple method for tuning controllers in a cascade system is presented, In this method, all the relations that facilitate the tuning procedures are well prepared in terms of figures or simple equations. Using these figures and equations, the controller tuning for different configurations of cascade systems becomes easy and straightforward when process models are available. On the other hand, when process models are not available, a simple method that uses one single run of step input experiment to develop such models is proposed. Based on these developments in the controller tuning and process models, an autotuning system that uses relay feedback is presented. Unlike the existing autotuning systems, this proposed system conducts identification and controller tuning in a decoupled manner. As a result, no excessive trial- and-error efforts for modeling and tuning are required. Simulation results show the potential usage of such a method, It is interested to see that the resulting systems have almost compatible responses to those systems which have been designed optimally in one way or another as reported in the literature. It is not, however, the purpose of this article to emphasize on obtaining superior performance to all other existing methods, but to emphasize on its effectiveness and simplicity for application.     

Selection of control configurations for economic model predictive control systems

Economic model predictive control (EMPC) is a feedback control method that dictates a potentially dynamic (time‐varying) operating policy to optimize the process economics. The objective function used in the EMPC system may be a general nonlinear function that describes the process/system economics. As this function is not derived on the sole basis of classical control considerations (stabilization, tracking, and optimal control action calculation) but rather on the basis of economics, selecting the appropriate control configuration, and quantifying the influence of a given input on an economic cost is an important task for the proper design and computational efficiency of an EMPC scheme. Owing to these considerations, an input selection methodology for EMPC is proposed which utilizes the relative degree and the sensitivity of the economic cost with respect to an input to identify and select stabilizing manipulated inputs with the most dynamic and steady‐state influence on the economic cost function to be assigned to EMPC. Other considerations for input selection for EMPC are also discussed and integrated into a proposed input selection methodology for EMPC. The control configuration selection method for EMPC is demonstrated using a chemical process example. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3230–3242, 2014