Analytical method of PID controller design for parallel cascade control

An analytical method of PID controller design is proposed for parallel cascade control. Firstly, a general structure for parallel cascade control is proposed that takes both setpoint and load disturbance responses into account. Analytical tuning rules for the PID controllers are then derived for the general process model by employing the IMC design procedure. The proposed method offers a simple and effective way to obtain the PID controller rules for parallel cascade control system which takes into account the interaction between primary and secondary control loops. The simulation results illustrate the application of the proposed method and demonstrate its superiority compared to several alternatives.     

An alternative structure for next generation regulatory controllers: Part I: Basic theory for design, development and implementation

Even though employed widely in industrial practice, the popular PID controller has weaknesses that limit its achievable performance, and an intrinsic structure that makes tuning not only more complex than necessary, but also less transparent with respect to the key attributes of the overall controller performance, namely: robustness, set-point tracking, and disturbance rejection. In this paper, we propose an alternative control scheme that combines the simplicity of the PID controller with the versatility of model predictive control (MPC) while avoiding the tuning problems associated with both. The tuning parameters of the proposed control scheme are related directly to the controller performance attributes; they are normalized to lie between 0 and 1; and they arise naturally from the formulation in a manner that makes it possible to tune the controller directly for each performance attribute independently. The result is a controller that can be designed and implemented much more directly and transparently, and one that outperforms the classical PID controller both in set-point tracking and disturbance rejection while using precisely the same process reaction curve information required to tune PID controllers. The design, implementation and performance of the controller are demonstrated via simulation on a nonlinear polymerization process.     

A unified approach to design dead-time compensators for stable andintegrative processes with dead-time

Proposes a unified 2 degrees of freedom robust dead-time compensator, for both stable and integrative plants. Using the performance and robustness as closed loop specifications simple and effective tuning rules are derived for the proposed controller. A comparative analysis with some structures of dead-time compensators that have been proposed in literature is presented. The analysis is made using the two most typical models of processes with delay that are found in the process industry. The comparative analysis shows that for the cases studied the proposed controller gives better or at least the same performance as the others. It is also shown that the tuning of this structure is simple because the tuning parameters have the usual physical meaning. Some simulation and experimental results illustrate the good performance of the controller     

基于衰减频率特性的PID参数优化整定研究

用衰减频率特性法整定PID控制器可使闭环系统获得要求的衰减比,但是求得的整定参数的解是不确定的,因而难以确定最佳整定参数。就此,将基于衰减频率特性的PID控制器整定问题转换成带衰减比约束的控制器参数优化问题,首先用Matlab计算出整定参数的解曲线或解曲面,然后利用Simulink在仿真环境下寻优,获得期望性能下的最佳整定参数。仿真结果表明所提出的整定方法有效,且控制器具有良好的抗干扰能力。     

用直接综合法设计的微分先行鲁棒PID控制器

针对积分时滞系统应用直接综合方法设计了一种微分先行鲁棒PID控制器。这种方法基于比较积分时滞系统与后置超前滞后滤波器的微分先行PID控制器组成的闭环系统的特征方程和期望特征方程。期望特征方程由多个位于同一期望位置的极点组成。所设计的控制器的参数以实现期望鲁棒性的方式获得。通过选择不同的调优参数获取相应的Ms值,进而在参数具有标称性的限定条件下拟合出关于Ms和调优参数的关系曲线。整定规则以解析表达式的形式给出。仿真结果表明该方法在阶跃响应中具有较好的追踪性能和扰动抑制性能以及鲁棒性能,在方波响应中具有很好的跟随性能以及较小的TV值,在给定值频繁变化的系统中响应效果最佳。     

PID auto-tuning using new model reduction method and explicit PID tuning rule for a fractional order plus time delay model

In this paper, a new model reduction method and an explicit PID tuning rule for the purpose of PID auto-tuning on the basis of a fractional order plus time delay model are proposed. The model reduction method directly fits the fractional order plus time delay model to frequency response data by solving a simple single-variable optimization problem. In addition, the optimal tuning parameters of the PID controller are obtained by solving the Integral of the Time weighted Absolute Error (ITAE) minimization problem and then, the proposed PID tuning rule in the form of an explicit formula is developed by fitting the parameters of the formula to the obtained optimal tuning parameters. The proposed tuning method provides almost the same performance as the optimal tuning parameters. Simulation study confirms that the auto-tuning strategy based on the proposed model reduction method and the PID tuning rule can successfully incorporate various types of process dynamics.     

A simple design method for interval type-2 fuzzy pid controllers

In this study, a design method for single Input interval type-2 fuzzy PID controller has been developed. The most important feature of the proposed type-2 fuzzy controller is its simple structure consisting of a single input variable. The presented simple structure gives an opportunity to the designer to form the type-2 fuzzy controller output in closed form formulation for the first time in literature. This formulation cannot be achieved with present type-2 fuzzy PID controller structures which have employed the Karnik-Mendel type reduction. The closed form solution is derived in terms of the tuning parameters which are chosen as the heights of lower membership functions of the antecedent interval type-2 fuzzy sets. Elaborations are done on the derived closed form output and a simple strategy is presented for a single input type-2 fuzzy PID controller design. The presented interval type-2 fuzzy controller structure still keeps the most preferred features of the PID controller such as simplicity and easy design. We will illustrate how the extra degrees of freedom provided by the antecedent interval type-2 fuzzy sets can be used to enhance the control performance on linear and nonlinear benchmark systems by simulations. Moreover, the type-2 fuzzy controller structure has been implemented on experimental pH neutralization. The simulation and experimental results will illustrate that the proposed type-2 fuzzy controller produces superior control performance and can handle nonlinear dynamics, parameter uncertainties, noise and disturbances better in comparison with the standard PID controllers. Hence, the results and analyses of this study will give the control engineers an opportunity to draw a bridge and connect the type-2 fuzzy logic and control theory.     

Optimal-tuning PID controller design in the frequency domain with application to a rotary hydraulic system

In this paper a new PID controller design scheme that uses optimisation in the frequency domain is proposed for industrial process control. An optimal-tuning PID controller is designed to satisfy a set of frequency-domain performance requirements: gain margin, phase margin, crossover frequency and steady-state error. Using an estimated process frequency response, the method can provide optimal PID parameters even in cases where the process dynamics are time variant. This scheme is demonstrated through its application to a rotary hydraulic system and its performance is compared with six alternative PID tuning rules.     

PID参数整定法的仿真

PID调节器的控制品质,主要取决于调节器的参数整定.计算量大是用理论计算方法整定PID调节器参数要解决的难题之一.针对PID调节器参数整定过程中计算复杂、计算量大的问题,提出了一种基于Matlab的调节器参数衰减频率特性整定法.该方法以Matlab为工具,将理论计算与仿真分析结合起来,根据控制要求计算并绘制出控制器整定参数关系曲线,对计算结果进行仿真,分析整定参数在解平面上变化时闭环系统的响应,从而确定出最佳的调节器整定参数.结果表明,对于不同的被控对象参数或不同的整定要求,该方法都能方便地求得最佳的调节器整定参数,使得采用理论计算法整定调节器参数具有了工程实用价值.     

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进行分析,得到二阶LADRC与PID控制器具有较强的联系,且LADRC比PID有着更好的控制性能.提出一种通过现有PID参数直接得到LADRC参数初始值的方法,以达到更好的控制性能,并基于一阶惯性加时延模型,得到将现有PID整定方法转化为二阶线性自抗扰控制参数整定方法.最后通过基准系统仿真表明所提出方法的有效性.     

New methodology for analytical and optimal design of fuzzy PIDcontrollers

Describes a methodology for the systematic design of fuzzy PID controllers based on theoretical fuzzy analysis and, genetic-based optimization. An important feature of the proposed controller is its simple structure. It uses a one-input fuzzy inference with three rules and at most six tuning parameters. A closed-form solution for the control action is defined in terms of the nonlinear tuning parameters. The nonlinear proportional gain is explicitly derived in the error domain. A conservative design strategy is proposed for realizing a guaranteed-PID-performance (GPP) fuzzy controller. This strategy suggests that a fuzzy PID controller should be able to produce a linear function from its nonlinearity tuning of the system. The proposed PID system is able to produce a close approximation of a linear function for approximating the GPP system. This GPP system, incorporated with a genetic solver for the optimization, will provide the performance no worse than the corresponding linear controller with respect to the specific performance criteria. Two indexes, linearity approximation index (LAI) and nonlinearity variation index (NVI), are suggested for evaluating the nonlinear design of fuzzy controllers. The proposed control system has been applied to several first-order, second-order, and fifth-order processes. Simulation results show that the proposed fuzzy PID controller produces superior control performance to the conventional PID controllers, particularly in handling nonlinearities due to time delay and saturation     

模糊PID控制器及在DCS系统中的应用

本文提出了一种基于模糊规则的PID控制器的设计方法。这种方法首先通过建立模糊规则和进行模糊推理来确定PID控制器的Kp,Ki,Kd等参数,而后由PID控制规律控制广义对象。实验结果表明,本文所设计的模糊PID控制系统比常规PID控制系统具有更优良的控制品质。     

Tuning and robustness analysis of event-based PID controllers under different event-generation strategies

In this article, we propose practical rules for tuning event-based PID controllers with two sampling strategies: symmetric send-on-delta (SSOD) and regular quantification (RQ). We present a detailed analysis about the effect of the derivative term of the controller when using SSOD or RQ and some guide lines are given to select the derivative filter coefficient. The two sampling strategies are compared, showing that, even when both of them lead to similar controlled output response, systems with RQ have better robustness properties than those with SSOD. The study is based on the describing function and the results are applicable to process with dynamic responses of different types: with time delays, non-minimum phase, under-damped response, etc. The rules presented here are given in terms of phase and gain margins that are measures of robustness used in the design of continuous PID controllers. This allows the application of conventional PID tuning methods to the case of event-based PID. The tuning rules are very simple and can be used for tuning PID, PI, PD and other controller structures.     

基于理想Bode传递函数的分数阶PID频域设计方法及其应用

基于理想Bode传递函数,提出一种简便的分数阶PID控制器频域设计方法.采用传递函数模型匹配与辨识方法,将分数阶PID控制器5个参数的复杂设计问题转化为单个参数的一维搜索问题进行求解;结合短记忆法实现分数阶PID控制器数字化.该方法已成功应用于直流电机调速控制系统,能够达到期望的响应性能,具有强鲁棒性.实验结果验证了所提出设计方法的有效性.     

Design and analysis of direct-action CMAC PID controller

This paper is to propose a direct-action (DA) cerebellar model articulation controller (CMAC) proportional-integral-derivative (PID) controller. The proposed controller, termed the DAC-PID controller, can generate four simple types of the nonlinear functions and then determine a control effort from those functions to control the process. In addition, the real-coded genetic algorithm is used to tune the parameters of the DAC-PID controller such that we can optimize those parameters. The performance of the proposed controller is also discussed in the sense of quantitative analysis. Simulation results demonstrate that the DAC-PID controller is superior to the conventional PID controller tuned by Ziegler–Nichols method and, moreover, as better as the optimal PID controller and the optimal fuzzy-PID controller.     

Maximum sensitivity based fractional IMC–PID controller design for non-integer order system with time delay

A simple approach with a small number of tuning parameters is a key goal in fractional order controller design. Recently there have been a number of limited attempts to bring about improvements in these areas. In this paper, a new design method for a fractional order PID controller based on internal model control (IMC) is proposed to handle non-integer order systems with time delay. In order to reduce the number of tuning parameters and mitigate the impact of time delay, the fractional order internal model control scheme is used. Considering the robustness of the control system with respect to process variations and model uncertainty, maximum sensitivity is applied to the tuning of the parameters. The resulting controller has the structure of a fractional order PID which is cascaded with a filter. This is named a fractional IMC–PID controller. Numerical results are given to show the efficiency of the proposed controller.     

模糊PID控制在纳米微动台系统中的应用

针对在纳米级运动控制中,传统PID算法的参数配置在抑制系统运动超调、提高系统定位精度,以及保障系统稳定性等方面存在矛盾的问题,提出了将模糊自适应PID控制器应用于该系统的方案.并基于大量工程整定实验,给出了针对纳米量级控制特点的模糊集设置和模糊整定规则,选取了合理的PID参数论域取值.实验结果表明,所设计的模糊控制器通...     

模糊自适应PID控制的研究及应用仿真

传统PID控制器参数的整定是在获取对象数学模型的基础上,根据某一整定规则来确定的,难以适应复杂多变的控制系统。针对其参数整定不良、性能欠佳,对被控过程的适应性差等缺点采用模糊控制与自适应PID控制结合起来,设计了模糊自适应PID控制器。利用模糊推理方法实现对PID参数的在线自整定,进一步完善PID控制器的性能,提高系统的控制精度。仿真结果表明该模糊自适应PID控制器既具有PID控制器高精度的优点,又具有模糊控制器快速、适应性强的特点,使被控对象具有良好的动、稳态特性,有较好的工程应用前景。     

Simultaneous automatic tuning of cascade control systems from closed-loop step response data

This study presents a novel automatic tuning method for cascade control systems in which both primary and secondary controllers are tuned simultaneously using a single closed-loop step test. The proposed technique identifies the required process information with the help of B-spline series representation for the step responses. The two proportional–integral–derivative (PID) controllers are then tuned using an internal model control (IMC) approach. Considering the rationale of cascade control, the secondary controller is designed for faster disturbance attenuation. Without requiring an additional experiment, the primary controller is designed based on an identified process model that accurately accounts for inner loop dynamics. Finally, this study includes robustness considerations in the controller tuning process, and develops explicit guidelines for the selection of the IMC tuning parameters, completing the automatic tuning procedure for cascade control systems. The proposed method is robust to measurement noise because of the filtering property of the B-splines, and can provide superior control performance for both set-point tracking and disturbance rejection. Simulation examples demonstrate the effectiveness of the proposed automatic tuning method.