Relay Feedback Method Research Articles

Improved sequential autotuning of PI controllers for industrial-scale polymerization (ISP) reactor

Abstract This current work proposes a refined investigation on the improved sequential relay autotuning method to compute the optimal parameters of the decentralized PI controller for Two Input Two Output (TITO) system using relay feedback method. The sustained oscillation occurring in the relay response with the sequential relay autotuning and the simultaneous relay autotuning method is analyzed by taking the higher-order harmonics into consideration and the efficient performance results of the decentralized PI control systems are obtained. These methods have been applied to an Industrial-Scale Polymerization (ISP) reactor transfer function model. In closed-loop studies, comparative analysis of autotuning methods has been carried out using simulation. The effect of measurement noise and robustness are studied in the proposed work. The robustness performance of the system using improved sequential relay autotuning is enhanced by 5–25% for servo operation and 11–40% for regulatory operation. The performance of the systems with the effect of measurement noise using improved sequential relay autotuning is enhanced by 2–24% for servo operation. Comparative analysis has been carried out with the improved sequential relay autotuning and the simultaneous relay autotuning method. It is observed that the proposed method provides improved closed-loop performances and less sum of Integral square error even in presence of robustness and effect of measurement noise.

Mathematical Modeling of Buck Converter with Relay Feedback

This paper proposes the idea of mathematical modeling of the buck converter. The modified approach is achieved through the relay feedback (RF) method and the changes are introduced on the converter output with a soft start. Mathematical modeling of the buck converter is achieved by the state-space model (SSM) and converter’s transfer function (TF) to attain stability. By iteration, the proportional-integral (PI) parameters are tuned by a controller that is incorporated in the RF. The output voltage changes are introduced by maintaining the relay-tuned PI control. The concept requires small tuning times which is obtained at a reduced cost. The effectiveness of buck converter using RF is validated in simulation and hardware.

Shape factor for the relay feedback autotuning

ABSTRACT Relay in the feedback loop produces a stable oscillation whose cyclic steady state response contains process information of ultimate gain and ultimate period. By measuring these process data and Ziegler-Nichols type tuning rules, PID controllers can be designed. Due to its simplicity and performances, this earlier relay feedback method becomes one of the standard methods for autotuning of PID controllers. Later the first-order plus time delay (FOPTD) models are used for the relay feedback method with additional process data such as the process steady-state gain, improving autotuning performances. Like other FOPTD model-based methods, this FOPTD model-based relay feedback method is very popular in the field. However, for some high-order processes, the FOPTD model-based method shows oscillatory closed-loop responses that are not acceptable. For such processes, the critically damped second-order plus time delay (C2PTD) identifiable with the same three process information of steady state gain, ultimate gain and ultimate period can be used. Unfortunately, the C2PTD model-based relay feedback method cannot cover the whole range of processes. One solution is the selective use of FOPTD and C2PTD models. For this purpose of selection, a shape factor that uses the process measurement of average residence time is proposed here.

Methods of weighted moments for the relay feedback autotuning of conservative PI controllers

First order plus time delay (FOPTD) models obtained from the cyclic steady state of the relay feedback oscillations can suffer from poor performances for some processes such as first and second order processes with fast parasitic dynamics. Poor FOPTD models are due to high frequency oscillations that activate parasitic dynamics. Dynamic elements such as hysteresis and integrator added in the feedback loop can reduce the oscillation frequencies but they increase the experimental times. Here, to relieve these problems without increasing the experimental time and computational complexity, relay feedback autotuning methods that apply the method of weighted moments to relay feedback transients are proposed. The proposed methods use the same relay feedback tests as the conventional relay feedback methods and are simple to use computationally, providing conservative PI controllers for all the test batch processes and the above first and second order processes with fast parasitic dynamics.

A Relay Feedback Method for the Tuning of Linear Active Disturbance Rejection Controllers

Active disturbance rejection control (ADRC) is a new control method that estimates the total disturbance by an extended state observer and compensates it by a state feedback law, and good disturbance rejection performance is expected compared to traditional PID control method. However, the parameters of ADRC are hard to tune, even for linear ADRC (LADRC). This paper proposes a new tuning method for second-order LADRC based on relay feedback, which is simple to implement without knowing the information of the controlled plant. Simulation examples show that the proposed method can achieve good performance in disturbance rejection and robust performance. The tuning rule is also tested for the control of a steam condenser. Compared with PID, the proposed method has smaller overshoot and shorter settling time.

Servo System Identification Based on Curve Fitting to Phase-Plane Trajectory

Abstract Many methods have been proposed to identify servo system parameters. However, problems still remain in widely applied offline identification methods, for example, the describing-function-based relay feedback method has the ineradicable approximation error, and acceleration information is indispensable for the least-squares method. In order to identify systems accurately and efficiently with less servo system information, this article proposes a novel method to identify servo system parameters through curve fitting to the phase-plane trajectory under the help of one optimization method. Specifically, the phase-plane trajectory expression of the single-degree-of-freedom system is derived; the process on how to convert the servo system identification problem to a curve-fitting optimization problem is described in detail; and the guidelines of the initial parameter setting are introduced. Simulations and experiments are carried out to verify the efficiency of the proposed method. Finally, a feed-forward control based on the identified parameters is designed to further validate the identification accuracy.

Applying a Relay Feedback Test for Autotuning the Electrohydraulic Controller of a Strength Testbed

This paper describes the problem of automation of parameter selection of an electrohy-draulic drive for a single-channel testbed for the strength load of aviation elements. It is proposed to tune the proportional-integral controller parameters of the testbed on the basis of the results of the tests based on relay feedback and time-scale separation method. The results obtained allow for autotuning the strength testbed controller parameters and increasing the accuracy of the strength load cyclograms, which eventually accelerates the strength tests. The results of applying this method on the experimental testbed are given.

Improved Relay Feedback Method Under Noisy and Disturbance Environments

This paper presents a new relay feedback method to guarantee the accuracy of the enhanced relay feedback method. The new method uses the integrals of a process input and output to tune Proportional-Integral-Derivative (PID) controllers automatically even if the process input and output are contaminated by measurement noises and disturbances. This feedback method uses a new disturbance estimator and a new noise magnitude estimator to remove the effects of noises and disturbances on estimates of frequency response data. Simulation and application to a real system to control liquid level demonstrate that the proposed methods provide fairly accurate ultimate data of the process and that the PID controller tuned by the proposed method achieves control faster and with less overshoot than the conventional auto-tuning strategy based on the conventional relay feedback method.

Data‐driven direct automatic tuning scheme for fixed‐structure digital controllers of hybrid systems

In this study, a novel data-driven direct automatic tuning scheme is proposed for the general form of fixed-structure digital controllers of hybrid systems. The controller is directly auto-tuned while it interacts with the real plant; no modelling or plant identification procedure is involved. The auto-tuning problem is formulated as a controller parameter optimisation problem, which is solved using a quasi-Newton method. A new method for calculating the gradient of the objective function from closed-loop experiment data is proposed to reduce the sensitivity to the initial values of the parameters. Domain knowledge of controller design based on pole placement and internal model principle is introduced as a priori information to further improve the performance of the auto-tuning. Numerical simulations are conducted to demonstrate the effectiveness of the proposed scheme and performances of different objective functions are evaluated. The performance of the proposed scheme is compared with the standard relay feedback and iterative feedback tuning methods. Reliable controllers can be obtained automatically by using the proposed scheme; the only remaining task of the control engineer is to estimate the order of the plant by counting the number of independent energy storage elements.

English

English

Identification of DC–DC buck converter dynamics using relay feedback method with experimental validation

Accurate dynamics of power converters are necessary to achieve good control performance. In this study, the dynamical model of the DC-DC buck converter is identified by the relay feedback method. The relay is connected in the closed loop to produce a limit cycle output. The important information of the oscillatory output is used for the identification. The relay is approximated using dual-input describing function (DIDF) in the mathematical modelling. DIDF can handle symmetric and asymmetric limit cycle outputs. The converter is modelled as a second-order plus dead-time system. Using the gain and phase angle criteria, analytical expressions are derived to estimate the dynamics. The converter dynamics obtained from the proposed method are compared with that estimated using the state-space averaging method. The model is also identified from the real-time experiment. To check the efficacy of the identified model, a model validation test is performed.

Identification and control of process using the Modified asymmetrical Relay Feedback method

In this work a single asymmetric relay Feedback method was used in order to identify the parameters of the Different processes, unlike the traditional approach a relay feedback method along with the sinusoidal excitation was employed to generate sustained oscillations with a single asymmetrical relay, for effectiveness of the present method it was compared with other existing methods in the literature. The identified parameters from the Relay feedback test were used to design the Simple PID controller for Different processes.

A New Method for PID Tuning Including Plants Without Ultimate Frequency

The classical relay feedback method for tuning proportional-integral-derivative (PID) controllers cannot be applied to plants whose Nyquist diagrams do not cross the negative real axis; these are customarily tuned based on the reaction curve experiment. In this brief, we propose a tuning method based on a modified relay feedback experiment. In this experiment, a transfer function of constant phase in an arbitrarily large range of frequencies is inserted in the loop. The proposed methodology thus unifies the Ziegler-Nichols-like tuning methods, by allowing PID tuning based on relay feedback for a class of plants without ultimate frequency.

Airfoil Bearing이 장착된 초고속 BLDC 모터 제어

The BLDC motor is used widely in industry due to its controllability and freedom from maintenance because there is no mechanical brush in the BLDC motor. Furthermore, it is suitable for high-speed applications, such as compressors and air blowers. For instance, for a compressor with a small impeller due to miniaturizing, the BLDC motor has to rotate at a very high speed to maintain the compression ratio of the compressor. Typically, to reach an ultra-high speed, airfoil bearings must be used in place of ball bearings because of their friction. Unfortunately, the characteristics of airfoil bearings change drastically depending on the revolution speed. In this paper, a BLDC motor with airfoil bearings is controlled with a PID controller. To analyze and determine the PID coefficients, the relay-feedback method is used. Additionally, for adaptive control, a fuzzy logic controller is used. Furthermore, the auto-tuning and self-tuning techniques are combined to control the BLDC motor. The proposed method is able to control the airfoil-bearing BLDC motor efficiently.

Limit cycle-based exact estimation of FOPDT process parameters under input/output disturbances: a state-space approach

ABSTRACTA set of novel explicit expressions for the identification of stable, unstable and integrating first-order plus dead time process dynamics is presented. In the absence of sensor noise/static load disturbances, an autonomous relay control system with an asymmetrical relay induces a smooth limit cycle at the process output. Dynamic model parameters are estimated using the set of proposed expressions which depend on the parameters of limit cycle output and its derivatives. However, in practice, the process output is generally corrupted by the measurement noise, thereby rendering an erroneous identification of process dynamics. Furthermore, static load disturbance during an identification test also induces an asymmetrical limit cycle output resulting in inaccurate measurements. Hence, a fast Fourier transform technique and biased relay feedback methods are implemented to obviate the problem of asymmetries and chattering in the limit cycle output yielding the original limit cycle and its subsequent derivatives. The proposed method has been validated, considering five typical examples from literature. An extensive comparison study with existing approaches based on Nyquist plots demonstrate the efficacy of the method presented.

Experimental Study of Position Controller for an Electro-Mechanical Throttle Actuator for Automotive Applications

This paper introduces an electro-mechanical throttle actuator and presents its real time position controllers using a proportional-derivative-plus-conditional-integrator (PDPCI) controller. The throttle actuator is built using a linear actuation DC motor which is directly connected to the engine throttle using a metal cable. The throttle actuator system is remotely placed inside the control room for carrying out engine performance tests safely. A PC-based ratio controller system is implemented using Matlab/Simulink® software and a NI PCI-6259 data acquisition system card. Two sets of initial PID parameters, opening and closing, are determined experimentally using combination of relay feedback method and Ziegler Nicholl formula. The performance of the throttle actuator controller is assessed in terms of percent overshoot, settling time and steady state error.

Experimental study of an electro-mechanical CVT ratio controller

This paper introduces an electro-mechanical, dual acting pulley, continuously variable transmission (EMDAPCVT) and presents its real time ratio controller using a proportional-derivative-plus-conditional-integral (PDPCI) controller. The ratio controller system is developed based on primary (input) and secondary (output) pulley position controllers. Each position controller has two PID parameters, releasing and clamping, which are determined experimentally using a relay feedback method. A PC-based ratio controller system is implemented using Matlab/Simulink® software and a Keithley DAS-1602 data acquisition system card. The experimental results show that the PDPCI controller system can control the CVT ratio adequately.

Frequency parameterization of H∞ PID controllers via relay feedback: A graphical approach

Abstract This paper focuses on a graphical approach to determine the region of proportional-integral-derivative (PID) controllers in the parameter space for which the closed-loop system is internally stable and the H ∞ optimization criteria are satisfied for a class of single-input single-output arbitrary order plant with or without dead time. Unlike conventional methods which the analytical models, such as transfer functions and state space models, are needed, the design information of the proposed approach is only the frequency response data, which are directly calculated from a single relay test for stable plants, or extracted from the closed-loop system frequency response data by dividing out the known stabilizing compensator for unstable plants using relay feedback methods. It is shown that the problem to be solved can be translated into simultaneous stabilization of the closed-loop characteristic function and a family of characteristic functions. Based on the technique of D-decomposition, the analytical boundaries of root invariant regions are derived and the admissible H ∞ region in the parameter space is the intersection of the admissible sets, and it can be drawn and identified immediately, not to be computed mathematically. A practical algorithm of determining the H ∞ region is proposed and two examples are used to illustrate the proposed method.

Third quadrant Nyquist point for the relay feedback autotuning of PI controllers

The original relay feedback autotuning method of Astrom and Hagglund [1] is based on the Nyquist point at the phase angle of −π (the critical frequency). Recently, Friman and Waller [8] showed that the critical frequency is too high to tune PI controllers and proposed an autotuning method that finds a Nyquist point at the third quadrant through the two-channel relay. Here, the method to find Nyquist points in the third quadrant is revisited and adaptive relay feedback method which can be applied to noisy processes is proposed. It is shown that the bandwidths of PI control systems and the first-order plus time delay model identifications support the Nyquist point at the third quadrant. Nyquist points at the third quadrant can be obtained by introducing a filter and hysteresis to the relay feedback loop. However, the filter time constant and the size of hysteresis should be adjusted iteratively because their phase shifts are dependent on the resulting relay oscillation frequency. Simulations show that this adaptive relay feedback method finds a given Nyquist point at the third quadrant accurately under noisy environments and provides excellent PI control systems.

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