Tuning of multi-loop PI controllers based on gain and phase margin specifications

In this paper, a single-iteration strategy is proposed for the design of a multi-loop PI controller to achieve the desired gain and phase margins for two-input and two-output (TITO) processes. To handle loop interactions, a TITO system is converted into two equivalent single loops with uncertainties drawn from interactions. The maximum uncertainty is estimated for the initial controller design in one loop and single-input and single-output (SISO) controller design is applied. This controller is substituted to other equivalent loop for design, and finally, the first loop controller is refined on knowledge of other loop controller. For SISO controller tuning, a new method is presented to determine the achievable gain and phase margins as well as the relevant controller parameters. Examples are given for illustration and comparison.     

PID controller design of TITO system based on ideal decoupler

The proposed method for designing multivariable controller is based on ideal decoupler D(s) and PID controller optimization under constraints on the robustness and sensitivity to measurement noise. The high closed-loop system performance and robustness are obtained using the same controller in all loops. The method is effective despite the values and positions of the right half plane zeros and dead-times in the process transfer function matrix G_p(s). The validity of the proposed multivariable control system design and tuning method is confirmed using a test batch consisting of Two-Input Two-Output (TITO) stable, integrating and unstable processes, and one Three-Input Three-Output (TITO) stable process.     

A DESIGN OF MULTILOOP PID CONTROLLERS WITH A NEURAL‐NET BASED DECOUPLER

In process industries, PID control schemes have been widely used due to their simple structures and easiness of comprehending the physical meanings of control parameters. However, the good control performance cannot be obtained by simply using PID controlschemes, since most processes are considered as nonlinear multivariable systems with mutual interactions. In this paper, a design method of multiloop PID controllers neural‐net based decoupler is proposed for nonlinear multivariable systems with mutual interactions. The proposed method consists of a decoupler given by the sum of a static decoupler and a neural‐net based decoupler, and multi‐loop PID controllers. Finally, the effectiveness of the proposed control scheme is evaluated on the simulation examples.     

LMI optimization approach to robust decentralized controller design

A new approach for design of robust decentralized controllers for continuous linear time‐invariant systems is proposed using linear matrix inequalities (LMIs). The proposed method is based on closed‐loop diagonal dominance. Sufficient conditions for closed‐loop stability and closed‐loop block‐diagonal dominance are obtained. Satisfying the obtained conditions is formulated as an optimization problem with a system of LMI constraints. By adding an extra LMI constraint to the system of LMI constraints in the optimization problem, the robust control is addressed as well. Accordingly, the decentralized robust control problem for a multivariable system is reduced to an optimization problem for a system of LMI constraints to be feasible. An example is given to show the effectiveness of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd.     

一种多变量系统辨识法及其在蒸发过程的应用

为有效分析分子蒸馏系统中的蒸发环节,提出了一种带有延迟环节的多变量系统参数辨识方法。采用将多变量系统辨识转化为多个单变量系统辨识的思想,对辨识问题进行简化,并给出了该思想的依据。依据阶跃激励信号下被辨识过程的响应数据建立关系式组,并应用辛普森（Simpson）积分公式得到了关系式组中未知系数,通过对该关系式组的求解最终获得蒸发系统的传递函数矩阵。仿真及实际过程中的应用表明,采用的辨识方法具有较强的可实践性及良好的辨识效果。     

Robust Controller Design And Pid Tuning For Multivariable Processes

In this paper, a robust controller design method is first formulated to deal with both performance and robust stability specifications for multivariable processes. The optimum problem is then dealt with using a loop‐shaping H_∞ approach, which gives a sub‐optimal solution. Then a PID approximation method is proposed to reduce a high‐order controller. The whole procedure involves selecting several parameters and the computation is simple, so it serves as a PID tuning method for multivariable processes. Examples show that the method is easy to use and the resulting PID settings have good time‐domain performance and robustness.     

An effective direct closed loop identification method for linear multivariable systems with colored noise

Multivariable control systems with colored noise widely exist in the most industrial fields, while the system identification under the closed loop conditions is needed in many cases. In view of the above two situations, it needs to find a convenient and effective method to solve the problem. Firstly, the design of the external input signals ensures the identifiability of closed loop system. Secondly, to make the direct method feasible for closed loop identification, the noise model selected is reasonably flexible and independently parameterized. On this basis, this paper proposes an improved method combining the direct closed loop identification approach with the iterative least squares parameter estimation algorithm, which can be an practical solution to the closed loop identification of multivariable systems with colored noise. The presented algorithm based hierarchical identification principle has a strong anti-jamming capability to effectively deal with colored noise existed in the system. Finally, the illustrative examples are given to demonstrate the effectiveness and accuracy of the proposed algorithm.     

一类串联系统的分散闭环辨识与控制器设计

Decentralized closed-loop identification and controller design for a kind of cascade processes composed of several sub-processes are studied. There are only input couplings between adjacent sub-processes. First, the cascade process is divided into several two-input two-output systems and coupling models of adjacent sub-processes are obtained via decentralized identification. TITO sys- tem is decoupled equivalently into four independent single open-loop processes with the same input signal. Then, a distributed model predictive control algorithm is proposed based on the coupling models of adjacent sub-processes.     

Decentralized relay-based multivariable process identification in the frequency domain

In this paper, a modified decentralized relay test is designed for multivariable processes, and then, a new method is proposed to identify the frequency response matrix at multiple points based on the test. In the modified decentralized relay test, only very first periods of oscillating inputs are implemented, so that the unsymmetrical two-sided pulse signals are produced automatically. The two-sided pulse waveform contains enough continuous spectrum over the important frequency range so that the frequency response matrix of interest can be obtained by using Fourier analysis without prior knowledge of the processes. Simulation examples are given to show both effectiveness and practicality of the identification method for a wide range of multivariable processes.     

基于改进混合蛙跳算法的电渣重熔过程多变量PID 控制器设计

根据电渣重熔过程的工艺特点和数学模型,提出了基于改进混合蛙跳算法（ISFLA）的多变量参数自整定PID控制策略.提出一种新的蛙跳规则,用以增强SFLA的局部搜索能力.该规则主要通过模拟青蛙的感知和运动的不确定性来动态随机地调整青蛙的局部搜索空间和步长,以防止SFLA算法过早收敛,提高算法的搜索效率.仿真结果和工业应用实验均表明了所提出控制方法的可行性和有效性.     

DIGITAL PID CONTROLLER DESIGN FOR DELAYED MULTIVARIABLE SYSTEMS

A new methodology is proposed to design digital PID controllers for multivariable systems with time delays. Except for a few parameters that are preliminarily selected, most of the PID parameters are systematically tuned using the developed plant state‐feedback and controller state‐feedforward LQR approach, such that satisfactory performance with guaranteed closed‐loop stability is achieved. In order to deal with the modeling error owing to the delay time rational approximation, an IMC structure is utilized, such that robust stability is achieved, without need for an observer, and with improved online tuning convenience. Using the prediction‐based digital redesign method, the digital implementation is obtained based on the above‐proposed analog controller, such that the resulting mixed‐signal system performance will closely match that of the analog controlled system. An illustrative example is given for comparison with alternative techniques.     

Digital Redesign Of Continuous‐Time Suboptimal Tracker For Two‐Dimensional Systems

In this paper, the digital redesign of a continuous suboptimal tracker for the two‐dimensional (2‐D) systems is proposed. This paper presents a new optimal digital redesign technique of 2‐D systems for finding a dynamic digital control law from the given continuous‐time 2‐D systems by minimizing a quadratic cost function (performance index). We directly convert the original continuous‐time 2‐D quadratic cost function into the discretized form and solve the optimization problem in the discrete‐time domain. The developed optimal digital redesign control law enables the output of the digitally controlled closed‐loop systems to closely match the reference signal for 2‐D systems, and it can be easily implemented using microcomputers. An illustrative example is presented to demonstrate the effectiveness of the proposed procedure.     

Practical application of model identification based on ARX models with transfer functions

A novel model identification methodology for ARX models based on transfer functions has been proposed. The identification approach converts transfer functions to ARX models with no approximation, except zero-order hold. Model parameters of the transfer functions are estimated directly. Model identification for process controls, especially MPCs, is of great importance for achieving the highest performance from them. However, step testing for model identification is a time-consuming task. Model identification techniques are necessary to save time for step tests. Therefore, a closed-loop identification method of multivariable systems is useful and helpful for time-saving. Herein, the proposed method, with control by model predictive controllers, is suited for a closed-loop identification technique and is applied in an industrial chemical plant.     

Decentralized closed-loop parameter identification for multivariable processes from step responses

This paper presents a novel technique for on-line decentralized closed-loop parameter identification of multivariable processes from step responses. Based on simple sequential step tests, the coupled closed-loop n-inputs and n-outputs (n × n) multivariable process is decoupled equivalently into n² independent single open-loop processes with an unit step input signal acting on the n² transfer functions. By using virtual step response signals, the parameters of each element in the transfer function matrix can be directly identified by the well-developed least squares methods. The significance of the proposed method is that it relaxes most restrictions of existing multivariable process identification methods, it is universally applicable to closed-loop identification for cross-coupling multivariable processes. Simulation examples are given to show both effectiveness and practicality of the identification method for a wide range of multivariable processes.     

Identification and PID Control for a Class of Delay Fractional-order Systems

In this paper, a new model identification method is developed for a class of delay fractional-order system based on the process step response. Four characteristic functions are defined to characterize the features of the normalized fractionalorder model. Based on the time scaling technology, two identification schemes are proposed for parameters' estimation. The scheme one utilizes three exact points on the step response of the process to calculate model parameters directly. The other scheme employs optimal searching method to adjust the fractional order for the best model identification. The proposed two identification schemes are both applicable to any stable complex process, such as higher-order, under-damped/over-damped, and minimum-phase/nonminimum-phase processes. Furthermore, an optimal PID tuning method is proposed for the delay fractionalorder systems. The requirements on the stability margins and the negative feedback are cast as real part constraints (RPC) and imaginary part constraints (IPC). The constraints are implemented by trigonometric inequalities on the phase variable, and the optimal PID controller is obtained by the minimization of the integral of time absolute error (ITAE) index. Identification and control of a Titanium billet heating process is given for the illustration.      

Online identification of nonlinear multivariable processes using self‐generating RBF neural networks

This paper addresses the problem of online model identification for multivariable processes with nonlinear and time‐varying dynamic characteristics. For this purpose, two online multivariable identification approaches with self‐organizing neural network model structures will be presented. The two adaptive radial basis function (RBF) neural networks are called as the growing and pruning radial basis function (GAP‐RBF) and minimal resource allocation network (MRAN). The resulting identification algorithms start without a predefined model structure and the dynamic model is generated autonomously using the sequential input‐output data pairs in real‐time applications. The extended Kalman filter (EKF) learning algorithm has been extended for both of the adaptive RBF‐based neural network approaches to estimate the free parameters of the identified multivariable model. The unscented Kalman filter (UKF) has been proposed as an alternative learning algorithm to enhance the accuracy and robustness of nonlinear multivariable processes in both the GAP‐RBF and MRAN based approaches. In addition, this paper intends to study comparatively the general applicability of the particle filter (PF)‐based approaches for the case of non‐Gaussian noisy environments. For this purpose, the Unscented Particle Filter (UPF) is employed to be used as alternative to the EKF and UKF for online parameter estimation of self‐generating RBF neural networks. The performance of the proposed online identification approaches is evaluated on a highly nonlinear time‐varying multivariable non‐isothermal continuous stirred tank reactor (CSTR) benchmark problem. Simulation results demonstrate the good performances of all identification approaches, especially the GAP‐RBF approach incorporated with the UKF and UPF learning algorithms. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

A two‐stage searching method for continuous time‐delay systems identification

This paper presents a novel method to estimate the unknown parameters of continuous‐time systems with time delay. In the proposed method, the time delay and plant parameters are estimated separately. To estimate the time delay, a one‐dimensional searching method with variable step size is proposed to improve computational efficiency. The searching method consists of two stages: the coarse stage and the refined searching stage. To analyze the convergence of the searching method, the concept of significant interval is proposed. By defining the significant interval, a sufficient condition for global convergence of the searching method is provided. Based on the two‐stage searching method, a novel identification algorithm is developed in which the simplified refined instrumental variable for continuous‐time models algorithm is used to estimate the plant parameters. Simulation results demonstrate that the proposed identification method can estimate the unknown parameters of continuous‐time system with time delay efficiently. The estimation results under different noisy conditions verify the reliability and robustness of the proposed method. The applicability of the developed identification method is demonstrated by a practical example.     

Decentralized Closed-loop Identification and Controller Design for a Kind of Cascade Systems

Decentralized closed-loop identification and controller design for a kind of cascade pro- cesses composed of several sub-processes are studied.There are only input couplings between adjacent sub-processes.First,the cascade process is divided into several two-input two-output systems and coupling models of adjacent sub-processes are obtained via decentralized identification.TITO sys- tem is decoupled equivalently into four independent single open-loop processes with the same input signal.Then,a distributed model predictive control algorithm is proposed based on the coupling models of adjacent sub-processes.     

一种基于改进双通道继电测试的闭环辨识方法研究

基于双通道继电反馈测试及其改进方案，提出一种提取SISO系统频域信息的闭环辨识测试方法，该方法具有许多有意义的特性，能在很大程度上克服现有辨识测试方法的问题与不足，在充分获取系统频域信息的基础上，引入频域辨识算法得到系统的低阶传递函数模型。对两个典型过程的仿真取得了良好的效果。表明了所提出方法的有效性。