Design and Robust Performance Evaluation of a Fractional Order PID Controller Applied to a DC Motor

This paper proposes a methodology for the quantitative robustness evaluation of PID controllers employed in a DC motor. The robustness analysis is performed employing a 23 factorial experimental design for a fractional order proportional integral and derivative controller (FOPID), integer order proportional integral and derivative controller (IOPID) and the Skogestad internal model control controller (SIMC). The factors assumed in experiment are the presence of random noise, external disturbances in the system input and variable load. As output variables, the experimental design employs the system step response and the controller action. Practical implementation of FOPID and IOPID controllers uses the MATLAB stateflow toolbox and a NI data acquisition system. Results of the robustness analysis show that the FOPID controller has a better performance and robust stability against the experiment factors.      

A dead-time compensating PID controller structure and robust tuning

In the present paper a dead-time compensating proportional-integral-derivative (DTC–PID) controller with anti-windup action is derived. The proposed controller also can be configured as a PID controller or as a dead-time compensating PI (DTC–PI) controller. For stable, integrating and unstable processes, approximated with the first-order plus dead-time (FOPDT) model, robust tuning procedure is derived for the DTC–PI controller. Optimization of the regulatory performance of the DTC–PID controller is based on the frequency response of higher-order models, under constraints on the robustness and sensitivity to measurement noise. Excellent performance/robustness trade-off is obtained for stable, integrating and unstable processes, including dead-time, as confirmed by simulations and by experimental results obtained on a laboratory thermal process.     

PID controller frequency-domain tuning for stable, integrating and unstable processes, including dead-time

In the present paper a new tuning procedure is proposed for the ideal PID controller in series with the first-order noise filter. It is based on the recently proposed extension of the Ziegler-Nichols frequency-domain dynamics characterization of a process G_p(s). Measured process characteristics are the ultimate frequency and ultimate gain, the angle of the tangent to the Nyquist curve of the process at the ultimate frequency, and G_p(0). For a large class of processes the same tuning formulae can be effectively applied to obtain closed-loop responses with predictable properties. Load disturbance step responses without the undershoot and reference step responses with negligible overshoot are obtained by analyzing a test batch consisting of stable, integrating and unstable processes, including dead-time and oscillatory dynamics. The proposed tuning makes possible to specify the desired sensitivity to the high frequency measurement noise and the desired maximum sensitivity. Comparison with the optimal ideal PID controller in series with the first-order noise filter is presented and discussed. The extension of the proposed method to the PI controller tuning is direct. Comparison with the optimal PI controller is presented and discussed.     

The setpoint overshoot method: A simple and fast closed-loop approach for PID tuning

A simple method has been developed for PID controller tuning of an unidentified process using closed-loop experiments. The proposed method requires one closed-loop step setpoint response experiment using a proportional only controller, and it mainly uses information about the first peak (overshoot) which is very easy to identify. The setpoint experiment is similar to the classical Ziegler–Nichols (1942) experiment, but the controller gain is typically about one half, so the system is not at the stability limit with sustained oscillations. Based on simulations for a range of first-order with delay processes, simple correlations have been derived to give PI controller settings similar to those of the SIMC tuning rules (Skogestad (2003) [6]). The recommended controller gain change is a function of the height of the first peak (overshoot), whereas the controller integral time is mainly a function of the time to reach the peak. The method includes a detuning factor that allows the user to adjust the final closed-loop response time and robustness. The proposed tuning method, originally derived for first-order with delay processes, has been tested on a wide range of other processes typical for process control applications and the results are comparable with the SIMC tunings using the open-loop model.     

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.     

A unified design for feedback-feedforward control system to improve regulatory control performance

The PID controller is widely used in industries because of its simplicity and robustness. A simple approach to improve regulatory control performance is to combine both feedback PID and feedforward controllers. The feedforward controller enables early compensation of a measured disturbance before it can seriously affect the process. The conventionally derived non-ideal feedforward controllers are not often used in practice. The reason is that an ideal feedforward controller based on direct inversion of process model is often not physically realizable. Several non-ideal feedforward control designs have been proposed where some of them involve rather intensive tuning procedure to obtain good disturbance rejection. In this paper, we present a new systematic method for designing a combined feedback-feedforward control system. The proposed design method is easy to use and applicable to stable, unstable and integrating deadtime processes where the ideal feedforward controller is physically not realizable.     

Simultaneous closed-loop tuning of cascade controllers based directly on set-point step-response data

This study presents a novel closed-loop tuning method for cascade control systems, in which both primary and secondary controllers are tuned simultaneously by directly using set-point step-response data without resorting to process models. The tuning method can be applied on-line to improve the performance of existing underperforming cascade controllers by retuning controller parameters, using routine operating data. The goal of the proposed design is to obtain the parameters of two proportional-integral-derivative (PID)-type controllers, so that the resulting inner and outer loops behave as similarly as possible to the appropriately specified reference models. The tuning rule and optimization problem related to the proposed design are derived. Based on the rationale behind cascade control, the secondary controller is designed based on disturbance rejection to quickly attenuate disturbances. The primary controller is designed to accurately account for the inner-loop dynamics, without requiring an additional test. In addition, robustness considerations are included in the proposed tuning method, which enable the designer to explicitly address the trade-off between performance and robustness for inner and outer loops independently. Simulation examples show that the proposed method exhibits superior control performance compared with the previous (model-based) tuning methods, confirming the effectiveness of this novel tuning method for cascade control systems.     

NEW TUNING METHOD FOR PID CONTROL OF A PLANT WITH UNDER‐DAMPED RESPONSE

In this paper, a tuning formula is derived for PID control of plants with under‐damped step responses. The under‐damped systems are modeled by second‐order plus dead time transfer functions. To derive the tuning rule, the dominant pole assignment method was applied to design the PID controllers for a variety of plant models. Then, the correlation between the controller parameters and the parameters of the models was found and the tuning formula derived. Several simulation examples are given to demonstrate the effectiveness and robustness of this formula.     

Design of fuzzy PID controllers using modified triangular membership functions

A design method for fuzzy proportional-integral-derivative (PID) controllers is investigated in this study. Based on conventional triangular membership functions used in fuzzy inference systems, the modified triangular membership functions are proposed to improve a system’s performance according to knowledge-based reasonings. The parameters of the considered controllers are tuned by means of genetic algorithms (GAs) using a fitness function associated with the system’s performance indices. The merits of the proposed controllers are illustrated by considering a model of the induction motor control system and a higher-order numerical model.     

过热汽温二级模糊鲁棒自调整PID控制器设计

许多过程控制对象的模型结构及参数常常具有随设备运行状态改变而产生较大幅度 变化的特性，或者具有某些不确定性，文章探讨了采用增益配置型模糊PID控制器的参数自 调整的鲁棒设计问题，提出利用二级模糊推理结合系统特征在线辨识实现PID参数动态调整 的控制器设计方法，实例仿真表明该控制器能较好地适应对象动态模型的大幅度变化，保持 较优的鲁棒调节性能．     

On the stability and controller robustness of some popular PID tuning rules

In this note, we study the stability and controller robustness of some popular proportional-integral-derivative (PID) tuning techniques that are based on first-order models with time delays. Using the characterization of all stabilizing PID controllers derived in a previous paper, each tuning rule is analyzed to first determine if the proportional gain value dictated by that rule, lies inside the range of admissible proportional gains. Then, the integral and derivative gain values are examined to determine conditions under which the tuning rule exhibits robustness with respect to controller parameter perturbations.     

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.      

Performance comparison between PID and dead-time compensating controllers

This paper is intended to answer the question: ‘‘When can a simple dead-time compensator be expected to perform better than a PID?'. The performance criterion used is the integrated absolute error (IAE). It is compared for PI and PID controllers and a simple dead-time compensator (DTC) when a step load disturbance is applied at the plant input. Both stable and integrating processes are considered. For a fair comparison the controllers should provide equal robustness in some sense. Here, as a measure of robustness, the _∞ norm of the sum of the absolute values of the sensitivity function and the complementary sensitivity function is used. Performance of the DTC's is given also as a function of dead-time margin (D_M).     

IMC design for unstable processes with time delays

A modified IMC structure is proposed for unstable processes with time delays. The structure extends the standard IMC structure for stable processes to unstable processes and controllers do not have to be converted to conventional ones for implementation. An advantage of the structure is that setpoint tracking and disturbance rejection can be designed separately. A method is proposed to tune the modified IMC structure with an emphasis on the robustness of the structure. Design for some typical delayed unstable processes shows that the control structure can be tuned easily and achieve good tradeoff between time-domain performance and robustness.     

Optimization of PID controller with higher-order noise filter

The proposed PID controller optimization is based on the frequency response of a process G_p(s) and maximization of the proportional gain, under constraints on the desired sensitivity to measurement noise, desired maximum sensitivity and desired maximum complementary sensitivity. The set-point and load disturbance step responses with negligible overshoot are obtained for stable processes, processes with oscillatory dynamics, integrating and unstable processes. Simulations, with a band-limited white noise added to the controlled variable, and experimental results, on a laboratory thermal plant with noisy measurements, are used to demonstrate the effectiveness of the proposed PID optimization method.     

Revisiting the Magnitude Optimum criterion for robust tuning of PID type-I control loops

The revision of the conventional Magnitude Optimum design criterion for tuning the PID type controller's parameters reveals three fundamental drawbacks. These drawbacks restrict the PID controller's optimal tuning in terms of robustness and disturbance rejection at the output of the controlled process. Specifically (1) the conventional PID tuning via the Magnitude Optimum criterion restricts the controller's zeros to be tuned only with real values, (2) for determining the PID controller's zeros, exact pole-zero cancellation has to be achieved between the process's poles and the controller's zeros and (3) the conventional design procedure via the Magnitude Optimum criterion has been tested only to a limited class of simple process models. To overcome the aforementioned drawbacks a revised PID type control law is proposed in this work. For the development of the control law a general transfer function of the process model is employed in the frequency domain. The final control law consists of analytical expressions that involve all modelled process parameters. The resulting control law can be applied directly to any linear Single Input Single Output stable process regardless of its complexity. For evaluating the proposed theory, an extensive simulation test batch between the conventional and the revised PID tuning is performed for various benchmark processes. Throughout this evaluation, the validity of several literature comments related to the Magnitude Optimum criterion is discussed. Finally, it is shown that the performance of the proposed control law compared to the conventional PID design procedure achieves satisfactory results both in the time and the frequency domain, in terms of robustness and disturbance rejection.     

IMC based Robust PID design: Tuning guidelines and automatic tuning

This communication addresses the problem of tuning a PID controller for step response. The tuning is based upon a First Order Plus Time Delay (FOPTD) model and aims to achieve a step response specification while taking into account robustness considerations. The industrial ISA-PID formulation is chosen. A tuning rule is derived first where the four parameters of the ISA-PID are determined by means of two new parameters: one parameter is related to the desired closed-loop time constant and the other one to the robustness level. On a second step, these two parameters are set to a fixed value in order to get a simple and automatic rule that directly gives the controller parameters in terms of the process model parameters. The proposed automatic tuning rule is compared with other known tunings.     

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.     

一类工业过程的PID控制器整定方法

PID调节器具有结构简单、适应性强、不依赖于被控对象的精确模型、鲁棒性较强等优点。控制器的性能直接关系到生产过程的平稳高效运行以及产品的最终质量。针对一类可用带有纯时间延迟的一阶对象来近似描述的工业过程,本文通过对工业过程现场采集的数据,利用Levenberg-Marquardt最小二乘拟合法辨识出被控对象的数学模型,进而根据典型PID控制器的参数整定方法求出PID控制器的参数。通过对一个典型工业对象的仿真研究,结果表明所提出的方法简单有效。     

A robust self-tuning scheme for PI- and PD-type fuzzy controllers

Proposes a simple but robust model independent self-tuning scheme for fuzzy logic controllers (FLCs). Here, the output scaling factor (SF) is adjusted online by fuzzy rules according to the current trend of the controlled process. The rule-base for tuning the output SF is defined on error (e) and change of error (Δe) of the controlled variable using the most natural and unbiased membership functions (MFs). The proposed self-tuning technique is applied to both PI- and PD-type FLCs to conduct simulation analysis for a wide range of different linear and nonlinear second-order processes including a marginally stable system where even the well known Ziegler-Nichols tuned conventional PI or PID controllers fail to provide an acceptable performance due to excessively large overshoot. Performances of the proposed self-tuning FLCs are compared with those of their corresponding conventional FLCs in terms of several performance measures such as peak overshoot, settling time, rise time, integral absolute error and integral-of-time-multiplied absolute error, in addition to the responses due to step set-point change and load disturbance and, in each case, the proposed scheme shows a remarkably improved performance over its conventional counterpart