Relay auto-tuning of PID controllers using iterative feedback tuning

In this paper, ideas from iterative feedback tuning (IFT) are incorporated into relay auto-tuning of the proportional-plus-integral-plus-derivative (PID) controller. The PID controller is auto-tuned to give specified phase margin and bandwidth. Good tuning performance according to the specified bandwidth and phase margin can be obtained and the limitation of the standard relay auto-tuning technique using a version of Ziegler-Nichols formula can be eliminated. Furthermore, by using common modelling assumptions for the relay system, some of the required derivatives in the IFT algorithm can be derived analytically. The algorithm was tested in the laboratory on a coupled tank and good tuning result was demonstrated.     

Adaptive hierarchical tuning of fuzzy controllers

Fuzzy controller design includes both linear and non-linear dynamic analysis. The knowledge base parameters associated within the fuzzy rule base influence the non-linear control dynamics while the linear parameters associated within the fuzzy output signal influence the overall control dynamics. For distinct identification of tuning levels, an equivalent linear controller output and a normalized non-linear controller output are defined. A linear proportional-integral-derivative (PID) controller analogy is used for determining the linear tuning parameters. Non-linear tuning is derived from the locally defined control properties in the non-linear fuzzy output. The non-linearity in the fuzzy output is then represented in a graphical form for achieving the necessary non-linear tuning. Three different tuning strategies are evaluated. The first strategy uses a genetic algorithm to simultaneously tune both linear and non-linear parameters. In the second strategy the non-linear parameters are initially selected on the basis of some desired non-linear control characteristics and the linear tuning is then performed using a trial and error approach. In the third method the linear tuning is initially performed off-line using an existing linear PID law and an adaptive non-linear tuning is then performed online in a hierarchical fashion. The control performance of each design is compared against its corresponding linear PID system. The controllers based on the first two design methods show superior performance when they are implemented on the estimated process system. However, in the presence of process uncertainties and external disturbances these controllers fail to perform any better than linear controllers. In the hierarchical control architecture, the non-linear fuzzy control method adapts to process uncertainties and disturbances to produce superior performance.     

Two-level tuning of fuzzy PID controllers

Fuzzy PID tuning requires two stages of tuning; low level tuning followed by high level tuning. At the higher level, a nonlinear tuning is performed to determine the nonlinear characteristics of the fuzzy output. At the lower level, a linear tuning is performed to determine the linear characteristics of the fuzzy output for achieving overall performance of fuzzy control. First, different fuzzy systems are defined and then simplified for two-point control. Non-linearity tuning diagrams are constructed for fuzzy systems in order to perform high level tuning. The linear tuning parameters are deduced from the conventional PID tuning knowledge. Using the tuning diagrams, high level tuning heuristics are developed. Finally, different applications are demonstrated to show the validity of the proposed tuning method.     

Self-organizing genetic algorithm based tuning of PID controllers

This paper proposes a self-organizing genetic algorithm (SOGA) with good global search properties and a high convergence speed. First, we introduce a new dominant selection operator that enhances the action of the dominant individuals, along with a cyclical mutation operator that periodically varies the mutation probability in accordance with evolution generation found in biological evolutionary processes. Next, the SOGA is constructed using the two operators mentioned above. The results of a nonlinear regression analysis demonstrate that the self-organizing genetic algorithm is able to avoid premature convergence with a higher convergence speed, and also indicate that it possesses self-organization properties. Finally, the new algorithm is used to optimize Proportional Integral Derivative (PID) controller parameters. Our simulation results indicate that a suitable set of PID parameters can be calculated by the proposed SOGA.     

On the automatic tuning and adaptation of PID controllers

A simple approach to the automatic tuning of PID process controllers is proposed. Like the relay-based autotuner, its objective is to attain a design-point on the Nyquist diagram. By injecting sinewaves and employing a phase/frequency estimator, closed-loop adaptive tuning is possible and there is exact convergence to the design-point without the approximations of describing-function theory. The variant discussed here achieves a required phase margin and imposes a carefully chosen constraint on the controller parameters, leading to consistent behaviour for a wide variety of generic test-cases. A real-life demonstration on a non-linear flow rig is provided.     

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.     

Fuzzy logic based set-point weight tuning of PID controllers

A methodology, based on fuzzy logic, for the tuning of proportional-integral-derivative (PID) controllers is presented. A fuzzy inference system is adopted to determine the value of the weight that multiplies the set-point for the proportional action, based on the current output error and its time derivative. In this way, both the overshoot and the rise time in set-point following can be reduced. The values of the proportional gain and the integral and derivative time constant are determined according to the well-known Ziegler-Nichols formula so that a good load disturbance attenuation is also assured. The methodology is shown to be effective for a large range of processes and is valuable for industrial settings since it is intuitive, it requires only a small extra computational effort, and it is robust with regard to parameter variations. The tuning of the parameters of the fuzzy module can be easily done by hand or by means of an autotuning procedure based on genetic algorithms     

Evaluation and simple tuning of PID controllers with high-frequency robustness

An extensive study of robust and optimal tuning of PID controllers for stable non-oscillating plants is presented. It is built on a set of well defined criteria related to output performance, stability margins and control activity. Different interesting properties of the closed loop systems are observed. A set of simple tuning rules is based on these observations. These rules are compared to a couple of well established tuning methods and are shown to give well competitive results, especially when simplicity, low control activity and high-frequency robustness are emphasized. Derivative action is shown to improve performance significantly compared to PI control, with equal stability margin and a moderate increase of control activity, for most plants, including those with significant time delay.     

一种PID参数整定的粒子群优化算法

提出了一种PID控制器参数整定的粒子群优化算法。该方法首先通过定义一个包含系统超调量、上升时间和稳态误差指标项的适应度函数,并根据系统的实际控制要求对各指标项适当加权。之后由带收缩因子的粒子群算法对PID进行多目标寻优,从而实现PID控制器的自动参数整定。仿真结果表明,该方法优化得到PID控制器的综合性能优于常规方法得到的PID控制器。     

Relay feedback tuning of robust PID controllers with iso-damping property.

A new tuning method for proportional-integral-derivative (PID) controller design is proposed for a class of unknown, stable, and minimum phase plants. We are able to design a PID controller to ensure that the phase Bode plot is flat, i.e., the phase derivative w.r.t. the frequency is zero, at a given frequency called the "tangent frequency" so that the closed-loop system is robust to gain variations and the step responses exhibit an iso-damping property. At the "tangent frequency," the Nyquist curve tangentially touches the sensitivity circle. Several relay feedback tests are used to identify the plant gain and phase at the tangent frequency in an iterative way. The identified plant gain and phase at the desired tangent frequency are used to estimate the derivatives of amplitude and phase of the plant with respect to frequency at the same frequency point by Bode's integral relationship. Then, these derivatives are used to design a PID controller for slope adjustment of the Nyquist plot to achieve the robustness of the system to gain variations. No plant model is assumed during the PID controller design. Only several relay tests are needed. Simulation examples illustrate the effectiveness and the simplicity of the proposed method for robust PID controller design with an iso-damping property.     

Optimizing fuzzy neural networks for tuning PID controllers using an orthogonal simulated annealing algorithm OSA

In this paper, we formulate an optimization problem of establishing a fuzzy neural network model (FNNM) for efficiently tuning proportional-integral-derivative (PID) controllers of various test plants with under-damped responses using a large number P of training plants such that the mean tracking error J of the obtained P control systems is minimized. The FNNM consists of four fuzzy neural networks (FNNs) where each FNN models one of controller parameters (K, T/sub i/, T/sub d/, and b) of PID controllers. An existing indirect, two-stage approach used a dominant pole assignment method with P=198 to find the corresponding PID controllers. Consequently, an adaptive neuro-fuzzy inference system (ANFIS) is used to independently train the four individual FNNs using input the selected 176 of the 198 PID controllers that 22 controllers with parameters having large variation are abandoned. The innovation of the proposed approach is to directly and simultaneously optimize the four FNNs by using a novel orthogonal simulated annealing algorithm (OSA). High performance of the OSA-based approach arises from that OSA can effectively optimize lots of parameters of the FNNM to minimize J. It is shown that the OSA-based FNNM with P=176 can improve the ANFIS-based FNNM in averagely decreasing 13.08% error J and 88.07% tracking error of the 22 test plants by refining the solution of the ANFIS-based method. Furthermore, the OSA-based FNNMs using P=198 and 396 from an extensive tuning domain have similar good performance with that using P=176 in terms of J.     

基于PID参数整定的线性自抗扰控制参数整定

线性自抗扰控制(linear active disturbance rejection control,LADRC)是不依赖于被控对象的数学模型,在工业过程中具有极大的应用前景,LADRC参数整定是其在工业过程中能否应用的重要环节.鉴于实际工业控制中大都采用PID控制器,通过对二阶LADRC结构与其状态观测器的传递函数...     

SISO approaches for linear programming based methods for tuning decentralized PID controllers

Two tuning techniques are proposed to design decentralized PID controllers for weakly coupled and general MIMO systems, respectively. Each SISO loop is designed separately, and the controller parameters are obtained as a solution of a linear programming optimization problem with constraints on the process stability margins. Despite the SISO approach, loop interactions are accounted for either by Gershgorin bands (non-iterative method) or an equivalent open-loop process (iterative method). The tuning results and performance from both methods are illustrated in four simulations of linear processes, and a laboratory-scale application in a Peltier process. Four applications contemplate closed-loop performance comparisons between the proposed techniques and techniques from the literature. One application illustrates the feasibility of the proposed iterative method, based on EOPs, in tuning decentralized PIDs for a 5 × 5 system. Moreover, an analysis of the effect of model uncertainty in the phase and gain margins of the closed-loop process is performed.     

A tuning strategy for multivariable PI and PID controllers using differential evolution combined with chaotic Zaslavskii map

A technique for tuning of decoupled proportional-integral (PI) and proportional-integral-derivative (PID) multivariable controllers based on a chaotic differential evolution (DE) approach is presented in this paper. Due to the simple concept, easy implementation and quick convergence, nowadays DE has gained much attention and wide application in solving continuous non-linear optimization problems. However, the performance of DE greatly depends on its control parameters and it often suffers from being trapped in local optimum. The application of chaotic sequences based on chaotic Zaslavskii map instead of random sequences in DE is a powerful strategy to diversify the population and improve the DE’s performance in preventing premature convergence to local optima. The optimized PD and PID controllers shows good closed-loop responses in control of the binary Wood–Berry distillation column, a multivariable process with strong interactions between input and output pairs. Some comparison results of PD and PID tuning using chaotic DE, classical DE and genetic algorithm are presented and discussed.     

Integral criteria for optimal tuning of PI/PID controllers for integrating processes

Tuning formulas for PI/PID controllers for integrating processes are presented in this paper. The controller parameters are obtained by minimizing various integral performance index. Bacterial Foraging strategy, a new entrant to the family of evolutionary algorithms is used for minimization to avoid the local minima in the optimization procedure. A setpoint filter is used to reduce the large overshoot, and a significant improvement in control performance is obtained when compared to recently reported methods. Simulation results for an assumed perturbation in the plant delay are also given to illustrate the robustness of the proposed controller design method. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Online tuning of fuzzy PID controllers via rule weighing based on normalized acceleration

In this study, an on-line tuning method is proposed for fuzzy PID controllers via rule weighing. The rule weighing mechanism is a fuzzy rule base with two inputs namely; “error” and “normalized acceleration”. Here, the normalized acceleration provides relative information on the fastness or slowness of the system response. In deriving the fuzzy rules of the weighing mechanism, the transient phase of the unit step response of the closed loop system is to be analyzed. For this purpose, this response is assumed to be divided into certain regions, depending on the number of membership functions defined for the error input of the fuzzy logic controller. Then, the relative importance or influence of the fired fuzzy rules is determined for each region of the transient phase of the unit step response of the closed loop system. The output of the fuzzy rule weighing mechanism is charged as the tuning variable of the rule weights; and, in this manner, an on-line self-tuning rule weight assignment is accomplished. The effectiveness of the proposed on-line weight adjustment method is demonstrated on linear and non-linear systems by simulations. Moreover, a real time application of this new method is accomplished on a pH neutralization process.     

The dilemma of PID tuning

A lot of automatic feedback control and learning tasks carried out on many dynamical systems still fundamentally rely on a form of proportional–integral–derivative (PID) control law. The PID law is often viewed as a simplistic computational control algorithm. However just like all non-convex optimization problems, tuning the PID algorithm for accurate and stable closed-loop control becomes a NP-Hard Problem. This leads to a dilemma, for both users and designers, most especially in practise. It is then no wonder that tuning software is a big business in the industrial automation sector. In this review, we present and classify PID tuning methods till date into three general areas. Finally, we then present a proposal to minimize the dilemma of complexity and cost that has become associated with tuning the three main parameters of the PID control law. Hopefully, continuous attempts at the minimization of this dilemma can lead to both a money-savings investment and a significant improvement in the field of PID control design.