A generalized relay identification method for time delay and non-minimum phase processes

A generalized relay identification method is proposed in this paper for time delay and non-minimum phase processes. A distinct merit of the proposed method is that the process gain can be uniformly derived from a single run of the relay test, independent of the relay type being unbiased or biased. An analytical relay response expression is derived for assessing the process response under an unbiased or biased relay test. A frequency response algorithm is also derived for estimating the multiple frequency response points of the process. By categorizing cases of the model parameters to be identified, the corresponding identification algorithms are developed using fitting conditions established for the process response at the oscillation frequency. Based on the improved estimation of multiple frequency response points, a recursive least-squares identification algorithm is then proposed for obtaining further enhanced fitting accuracy over a user specified frequency range, e.g., the low frequency range often concerned in practical controller tuning. Illustrative examples from the recent literature are given to demonstrate the effectiveness and merits of the proposed algorithms.     

无模型SISO时滞系统的PID参数稳定域研究

针对无精确模型的单输入单输出(SISO)时滞系统, 利用频率响应数据, 给出确定PID参数稳定域的解析方法. 首先通过继电反馈频域辨识法得到系统的频率响应数据, 然后基于该数据确定控制参数的奇异边界线和非奇异边界线, 并判断边界线的哪一侧具有更少的不稳定极点, 从而给出能使闭环系统稳定的控制参数区域. 该方法避免了模型辨识的复杂计算过程, 为无模型SISO时滞系统的PID控制器设计和调节提供了一条简单有效的途径. 仿真结果验证了方法的有效性.     

Relay feedback auto-tuning of process controllers — a tutorial review

The PID relay auto-tuner of Astrom–Hagglund is one of the simplest and most robust auto-tuning techniques for process controllers and has been successfully applied to industry for more than 15 years. This tuner is based on an approximate estimation of the critical point on the process frequency response from relay oscillations. Many developments have recently been reported to extend its applications. It turns out that more and accurate information on process dynamics can be obtained from the same relay test with the help of new identification techniques, and used to tune PID controllers better. Extensions are also made to tune model-based advanced controllers and multivariable controllers. The present paper reviews these developments and shows the state-of art in relay auto-tuning of process controllers.     

Advanced controller auto-tuning and its application in HVAC systems

In this paper, an advanced PID auto-tuner for both single- and multi-variable processes is described and its application to HVAC systems is presented. The auto-tuner exploits two different process identification methods to suit a wide range of processes. It incorporates two recent PID design rules to achieve high control performances for processes with different dynamic characteristics. Decoupling control is used for multivariable processes. The auto-tuner was implemented on a distributed control system and applied in industry. Experimental results demonstrate the effectiveness and superior performance of the implemented auto-tuner over the manually tuned PID controller and the standard relay auto-tuner.     

Robust closed-loop identification with application to auto-tuning

In this paper, a simple yet robust closed-loop identification method is proposed, and an auto-tuner is then constructed by combination with a new PID tuning rule. The method can accommodate a wide range of tests such as step and relay provided that the test produces steady state responses. Using the FFT, the process frequency response is first calculated from the recorded process input and output time responses to the closed-loop test. Then the process step response is constructed using the inverse FFT. A general second-order plus dead-time model is thus obtained using our newly developed technique on robust identification of process transfer function from step responses. Simulation examples and real time test show its effectiveness.     

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。     

Automatic tuning of decentralized PID controllers for MIMO processes

An automatic tuning algorithm for decentralized PID control in multiple-input multiple-output (MIMO) plants is presented. This algorithm generalizes the authors' recent auto-tuner for two-input two-output systems to any number of inputs and outputs. The algorithm consists of two stages. In the first, the desired critical point, which consists of the critical gains of all the loops and a critical frequency, is identified. The auto-tuner identifies the desired critical point with almost no a priori information about the process. During the identification phase all controllers are replaced by relays, thus generating limit cycles with the same period in all loops. It is shown that each limit cycle corresponds to a single critical point of the process. By varying the relays parameters different points can be determined. The auto-tuner contains a procedure which converges rapidly to the desired critical point while maintaining the amplitudes of the process variables as well as of the manipulated variables within prespecified ranges. In the second stage, the data of the desired critical point is used to tune the PID controllers by the Ziegler-Nichols rules or their modifications. This paper focuses on the first stage. The steady-state process gains, which are required for the appropriate choice of the desired critical point, are determined by the auto-tuner in closed-loop fashion simultaneously with the identification of the critical point. The identification of the process gains is achieved at no extra plant time. Based upon a large number of simulated cases, the proposed auto-tuner seems to be efficient and robust. The paper discusses the underlying principles of the auto-tuner and its properties and capabilities are demonstrated via examples.     

Indirect approach to continuous time system identification of food extruder

A three-stage approach to system identification in the continuous time is presented which is appropriate for day-to-day application by plant engineers in the process industry. The three stages are: data acquisition using relay feedback; non-parametric identification of the system step response; and parametric model fitting of the identified step response. The method is evaluated on a pilot-scale food-cooking extruder.     

基于偏置继电反馈的一种新的频域辨识方法

提出一种新的基于偏置继电反馈的频域辨识算法,能够对包括迟延在内的SISO系统的传递函数参数进行在线辨识。首先利用偏置继电反馈辨识过程的频率响应,一次继电测试可以辨识过程Nyquist曲线上的多点。接着利用最小二乘法估计过程传递函数参数的初值,最后应用非线性共轭梯度法准确的辨识传递函数参数。该方法辨识精度高,同时可以有效避免大多继电反馈辨识方法测试时间过长及只能辨识固定的低阶模型的缺点。仿真结果验证了算法的有效性与准确性。     

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.      

Improved critical point estimation using a preload relay

In this paper, we present a technique to automatically estimate the critical point of a process frequency response. The method yields significantly and consistently improved accuracy over the relay feedback method, pioneered by Astrom and co-workers, at no significant incremental costs in terms of implementation resources and application complexities. The proposed technique improves the accuracy of the conventional approach by boosting the fundamental frequency in the forced oscillations, using a preload relay which comprises a normal relay with a parallel gain. In addition, we will show empirically the other benefits of the proposed method in terms of assessment performance based on an improved estimate, applicability to other classes of processes when the conventional relay method fails, a shorter time duration to attain stationary oscillations, and possible application to extract other points of the process frequency response. The effectiveness of the proposed technique is verified by simulation results, and also demonstrated via real-time experimental results in the critical point estimation of a coupled-tanks system.     

Relay feedback methods combining sub-relays to reduce harmonics

The relay feedback method is considered to be one of the easiest identification methods available for obtaining the ultimate information of the process. It has been widely used in industry to automatically tune the PID controller. Many applications of the method have been developed. In this research, a new framework has been proposed to reduce the harmonics of the relay feedback signal. It linearly combined several sub-relay signals, which had different frequencies and gains and resulted in a significant reduction of harmonic terms. Improved versions of several previous relay feedback methods have been successfully developed on the basis of the proposed framework.     

A nonparametric approach to design robust controllers for uncertain systems: Application to an air flow heating system

This paper presents an approach to design robust fixed structure controllers for uncertain systems using a finite set of measurements in the frequency domain. In traditional control system design, usually, based on measurements, a model of the plant, which is only an approximation of the physical system, is first built, and then control approaches are used to design a controller based on the identified model. Errors associated with the identification process as well as the inevitable uncertainties associated with plant parameter variations, external disturbances, measurement noise, etc. are expected to all contribute to the degradation of the performance of such a scheme. In this paper, we propose a nonparametric method that uses frequency-domain data to directly design a robust controller, for a class of uncertainties, without the need for model identification. The proposed technique, which is based on interval analysis, allows us to take into account the plant uncertainties during the controller synthesis itself. The technique relies on computing the controller parameters for which the set of all possible frequency responses of the closed-loop system are included in the envelope of a desired frequency response. Such an inclusion problem can be solved using interval techniques. The main advantages of the proposed approach are: (1) the control design does not require any mathematical model, (2) the controller is robust with respect to plant uncertainties, and (3) the controller structure can be chosen a priori, which allows us to select low-order controllers. To illustrate the proposed method and demonstrate its efficacy, an application to an air flow heating system is presented.     

Auto-tuning of phase lead/lag compensators

In the tuning of phase lead/lag compensators, knowledge of specific points on the frequency response of the plant are required. Such points are specified by their frequency, gain and phase and are not readily available without an accurate model of the plant. Yet such information is important for any auto-tuning procedure to succeed. In this paper, relays with hysterisis are tuned to determine points on the frequency response of a plant with a user-specified gain, g₀ or phase, φ₀. On-line algorithms are developed to tune the operating point of the relay feedback system so that the resulting oscillations correspond to the frequency response of the plant with either gain, g₀ or phase, φ₀. Tuning involves setting either the amplitude of the relay or its hysterisis width. Improvement over the simple application of the describing function is also shown. The results are applied to the auto-tuning of phase lead and lag compensators. Simulations are presented to illustrate the auto-tuning procedures.     

Automated Maximum Sensitivity And Phase Margin Specification Attainment In Pi Control

The prevailing industrial and academic autotune paradigm uses the relay experiment to find the ultimate data of an unknown system, followed by the use of this data in PI (D) tuning rules. This paper firstly reviews a novel method of obtaining desired frequency response data‐points of an unknown system which is more accurate and flexible than the relay experiment. The paper then demonstrates how this new identification module can be used in closed loop to automate PI controller tuning to achieve classical robustness specifications. The new algorithm is given along with details of MATLAB/SIMULINK simulation results. The non‐parametric identification method developed by the authors and used in this work is termed the Phase Locked Loop method (PLL). The classical robustness specification to be achieved by the PI controller is a pair of desired maximum sensitivity and phase margin specifications. Conclusions and future research directions close the paper.     

Self-tuning control with additional feedback signals

Conventional self-tuning controllers utilise only the controlled output for feedback. In this paper a new minimum prediction error self-tuning controller which utilises additional system outputs for feedback is developed. The advantages of such an approach are assessed. The application of the new self tuner to power system stabilisation is considered. Simulation studies demonstrate an improvement in the dynamic performance of a synchronous generator equipped with the new self tuner instead of the conventional self-tuning stabiliser.     

火电厂主气温系统的继电反馈多模型控制

针对火电厂变负荷机组主汽温系统时变和非线性的特点,提出了基于继电反馈的多模型控制算法;首先利用继电反馈的方法,对若干典型工况点建立的固定模型设计子控制器;在运行过程中,利用多模型控制根据系统工况的变化选择相应的控制器以保证系统的控制性能,仿真结果表明应用该方法建立的控制系统具有良好的控制品质和较强的自适应能力。     

一种新的电力系统频率实时测量方法

提出了一种基于波形拟合技术和泰勒级数展开的实时频率测量方法,并针对电压信号中谐波分量对测频精度的影响,设计了数字带通滤波器,对实时采集电压信号进行数字滤波处理以减小谐波成分,进而提高了测频精度.仿真试验表明算法实现简单、准确,对谐波有较好的抑制能力,适合于电力系统继电保护和测量的要求.     

一种鲁棒逆基控制器的设计方法

针对多变量病态过程的控制问题,提出一种鲁棒逆基控制器的设计方法。该方法把频域响应近似法(Frequency Response Approximation,FRA)和高级鲁棒控制方法相结合,采用频域响应近似法设计一个低阶逆基控制器来近似,通过高级鲁棒控制方法获得的高阶鲁棒控制器。得到的控制器结构简单,容易实现,并且具有良好的鲁棒控制性能。通过对一个在过程控制领域被广泛研究的病态精馏塔模型进行设计与仿真,验证了该方法在病态过程控制问题中的有效性。     

A model-free design of reduced-order controllers and application to a DC servomotor

This paper presents a new model-free technique to design fixed-structure controllers for linear unknown systems. In the current control design approaches, measured data are used to first identify a model of the plant, then a controller is designed based on the identified model. Due to errors associated with the identification process, degradation in the controller performance is expected. Hence, we use the measured data to directly design the controller without the need for model identification. Our objective here is to design measurement-based controllers for stable and unstable systems, even when the closed-loop architecture is unknown. This proposed method can be very useful for many industrial applications. The proposed control methodology is a reference model design approach which aims at finding suitable parameter values of a fixed-order controller so that the closed-loop frequency response matches a desired frequency response. This reference model design problem is formulated as a nonlinear programming problem using the concept of bounded error, which can then be solved to find suitable values of the controller parameters. In addition to the well-known advantages of data-based control methods, the main features of our proposed approach are: (1) the error is guaranteed to be bounded, (2) it enables us to avoid issues related to the use of minimization methods, (3) it can be applied to stable and unstable plants and does not require any knowledge about the closed-loop architecture, and (4) the controller structure can be selected a priori, which means that low-order controllers can be designed. The proposed technique is experimentally validated through a real position control problem of a DC servomotor, where the results demonstrate the efficacy of the proposed method.