Improving disturbance rejection of PI controllers by means of the magnitude optimum method

The magnitude optimum (MO) method provides a relatively fast and nonoscillatory closed-loop tracking response for a large class of process models frequently encountered in the process and chemical industries. However, the deficiency of the method is poor disturbance rejection when controlling low-order processes. In this paper, the MO criterion is modified in order to optimize disturbance rejection performance, while the tracking performance has been improved by an integral set-point filtering PI controller structure. The new tuning rules, referred to as the disturbance rejection magnitude optimum (DRMO) method, were applied to several different two-degrees-of-freedom PI controllers. The DRMO method has also been tested on several different representatives of process models. The results of experiments have shown that the proposed tuning method with the integral set-point filtering PI controller is quite efficient in improving disturbance rejection performance, while retaining tracking performance comparable to the original MO method.     

Comparative study of decay ratios of disturbance-rejection magnitude optimum method for PI controllers

One of the key time-domain closed-loop performance requirements is the closed-loop response decay ratio. In this paper, the decay ratios of the disturbance-rejection magnitude optimum (DRMO) tuning method [Vranci? D, Strmcnik S, Kocijan J. Improving disturbance rejection of PI controllers by means of the magnitude optimum method. ISA Trans 2004; 43: 73-84; Vranci? D, Strmcnik S. Achieving optimal disturbance rejection by using the magnitude optimum method. In: Pre-prints of the CSCC'99 conference. 1999. p. 3401-6] are analyzed and compared to decay ratios of two other modern tuning methods, i.e. the Kappa-Tau tuning method (based on time-domain step-response characteristics) [Astr?m KJ, H?gglund T. PID controllers: Theory, design, and tuning. 2nd ed. Instrument Society of America; 1995] and the non-convex optimization tuning method (based on frequency response) [Panagopoulos H, Astr?m KJ, H?gglund T. Design of PI controllers based on non-convex optimization. Automatica 1998; 34: 585-601; Panagopoulos H, Astr?m KJ, H?gglund T. Design of PID controllers based on constrained optimisation. IEE Proc Control Theory Appl 2002; 149 (1): 32-40]. It is shown that the DRMO method results in such a closed-loop response that the decay ratio is within a relatively narrow interval when compared to the other two methods.     

Discrete-time domain two-degree-of-freedom control design for integrating and unstable processes with time delay

A discrete-time domain two-degree-of-freedom (2DOF) design method is proposed for integrating and unstable processes with time delay. Based on a 2DOF control structure recently developed, a controller is analytically designed in terms of the H₂ optimal control performance specification for the set-point tracking, and another controller is derived by proposing the desired closed-loop transfer function for load disturbance rejection. Both controllers can be tuned relatively independent to realize control optimization. Analytical expression of the set-point response is given for quantitatively tuning the single adjustable parameter in the set-point tracking controller. At the meantime, sufficient and necessary conditions for holding robust stability of the closed-loop control system are established for tuning another adjustable parameter in the disturbance rejection controller, along with numerical tuning guidelines. Illustrative examples from the literature are used to demonstrate the effectiveness of the proposed method.     

Design of a new PID controller using predictive functional control optimization for chamber pressure in a coke furnace

An improved proportional-integral-derivative (PID) controller based on predictive functional control (PFC) is proposed and tested on the chamber pressure in an industrial coke furnace. The proposed design is motivated by the fact that PID controllers for industrial processes with time delay may not achieve the desired control performance because of the unavoidable model/plant mismatches, while model predictive control (MPC) is suitable for such situations. In this paper, PID control and PFC algorithm are combined to form a new PID controller that has the basic characteristic of PFC algorithm and at the same time, the simple structure of traditional PID controller. The proposed controller was tested in terms of set-point tracking and disturbance rejection, where the obtained results showed that the proposed controller had the better ensemble performance compared with traditional PID controllers.     

Performance-based parameter tuning method of model-driven PID control systems

In this paper, performance-based parameter tuning method of model-driven Two-Degree-of-Freedom PID (MD TDOF PID) control system has been proposed to enhance the control performances of a process. Known for its ability of stabilizing the unstable processes, fast tracking to the change of set points and rejecting disturbance, the MD TDOF PID has gained research interest recently. The tuning methods for the reported MD TDOF PID are based on internal model control (IMC) method instead of optimizing the performance indices. In this paper, an Integral of Time Absolute Error (ITAE) zero-position-error optimal tuning and noise effect minimizing method is proposed for tuning two parameters in MD TDOF PID control system to achieve the desired regulating and disturbance rejection performance. The comparison with Two-Degree-of-Freedom control scheme by modified smith predictor (TDOF CS MSP) and the designed MD TDOF PID tuned by the IMC tuning method demonstrates the effectiveness of the proposed tuning method.     

Set point weighted modified Smith predictor for integrating and double integrating processes with time delay

A simple method of designing the controllers for a modified form of Smith predictor is proposed for integrating and double integrating processes with time delay. The modified Smith predictor has two controllers, namely, a set point tracking controller and a load disturbance rejection controller for obtaining good set point tracking and load disturbance rejection, respectively. The set point tracking controller is designed using the classical direct synthesis method based on the process model without considering the time delay. The disturbance rejection controller is considered as a proportional-derivative (PD) controller and is designed using optimal gain and phase margin approaches. Set point weighting is considered for reducing undesirable overshoots and settling times in the modified Smith predictor. Guidelines are provided for selection of the desired closed loop tuning parameter in the direct synthesis method and the set point weighting parameter. The method gives significant load disturbance rejection performances. Illustrative examples are considered to show the performances of the proposed method. A significant improvement in control performance is obtained when compared to recently reported methods.     

Model predictive control for a class of systems with isolated nonlinearity

The paper is concerned with an overall convergent nonlinear model predictive control design for a kind of nonlinear mechatronic drive systems. The proposed nonlinear model predictive control results in the improvement of regulatory capacity for reference tracking and load disturbance rejection. The design of the nonlinear model predictive controller consists of two steps: the first step is to design a linear model predictive controller based on the linear part of the system at each sample instant, then an overall convergent nonlinear part is added to the linear model predictive controller to combine a nonlinear controller using error driven. The structure of the proposed controller is similar to that of classical PI optimal regulator but it also bears a set-point feed forward control loop, thus tracking ability and disturbance rejection are improved. The proposed method is compared with the results from recent literature, where control performance under both model match and mismatch cases are enlightened.     

IMC-PID design based on model matching approach and closed-loop shaping

Motivated by the limitations of the conventional internal model control (IMC), this communication addresses the design of IMC-based PID in terms of the robust performance of the control system. The IMC controller form is obtained by solving an H-infinity problem based on the model matching approach, and the parameters are determined by closed-loop shaping. The shaping of the closed-loop transfer function is considered both for the set-point tracking and for the load disturbance rejection. The design procedure is formulated as a multi-objective optimization problem which is solved by a specific optimization algorithm. A nice feature of this design method is that it permits a clear tradeoff between robustness and performance. Simulation examples show that the proposed method is effective and has a wide applicability.     

Extension of IMC tuning correlations for non-self regulating (integrating) processes

The filter term of a PID with Filter controller reduces the impact of measurement noise on the derivative action of the controller. This impact is quantified by the controller output travel defined as the total movement of the controller output per unit time. Decreasing controller output travel is important to reduce wear in the final control element. Internal Model Control (IMC) tuning correlations are widely published for PI, PID, and PID with Filter controllers for self regulating processes. For non-self regulating (or integrating) processes, IMC tuning correlations are published for PI and PID controllers but not for PID with Filter controllers. The important contribution of this work is that it completes the set of IMC tuning correlations with an extension to the PID with Filter controller for non-self regulating processes. Other published correlations (not based upon the IMC framework) for PID with Filter controllers fix the filter time constant at one-tenth the derivative time regardless of the model of the process. In contrast, the novel IMC correlations presented in this paper calculate a filter time constant based upon the model of the process and the user's choice for the closed-loop time constant. The set point tracking and disturbance rejection performance of the proposed IMC tunings is demonstrated using simulation studies and a bench-scale experimental system. The proposed IMC tunings are shown to perform as well as various PID correlations (with and without a filter term) while requiring considerably less controller action.     

Performance assessment of PID and IMC tuning methods for a mixing process with time delay

A flow process with time delay has been considered for modeling and control. A dilute solution of sodium chloride is used as tracer and an online conductivity measurement unit as sensor and recorder. The objective of the current study is to design control algorithms and present corresponding robust control analysis for the process. The control methodologies considered are (i) conventional PID control and (ii) internal model control (IMC). The control structures are comparatively analyzed using standard robustness measures for stability and performance. Of the two control algorithms, conventional PID and IMC, IMC exhibits faster settling time, no overshoot, better set-point tracking and disturbance rejection, and good robust performance than the PID control scheme.     

模糊规则调整微分作用的PID控制方法

PID控制器广泛应用于工业过程控制中 ,但对于非线性、时变不确定性的系统 ,常规 PID控制器难以获得满意效果。随着模糊控制理论的不断发展 ,利用其非线性特征 ,将其与 PID控制相结合 ,能有效改善 PID控制效果。设定值权系数的模糊逻辑整定 PID控制器 (FSW)方法在固定设定值权系数的基础上 ,用模糊推理方式计算“动态”的权系数 ,取得了一定的效果 ,但是仍存在一些问题。针对阶跃响应的上升及调整时间长、第一次超调后的反向振幅较大的缺点 ,采用模糊逻辑规则调整微分作用的改进方法 ,可以弥补上述不足。对一些典型对象进行仿真 ,结果表明该方法明显优于 Z- N方法 ,固定设定值权系数 b方法和 FSW方法     

二自由度PID调节器的内模整定方法

本文针对典型的工业过程控制对象，提出了一种二自由度PID调节器的设计方法，所设计的调节器仅有两个可调参数，而且被调参数与系统的性能直接相关，可以使系统同时具有良好的目标值跟随特性和干扰抑制特性，仿真研究结果表明了它的有效性。     

Design of PID controllers in double feedback loops for SISO systems with set-point filters

A PID controller is widely used to control industrial processes that are mostly open loop stable or unstable. Selection of proper feedback structure and controller tuning helps to improve the performance of the loop. In this paper a double-feedback loop/method is used to achieve stability and better performance of the process. The internal feedback is used for stabilizing the process and the outer loop is used for good setpoint tracking. An internal model controller (IMC) based PID method is used for tuning the outer loop controller. Autotuning based on relay feedback or the Ziegler-Nichols method can be used for tuning an inner loop controller. A tuning parameter (λ) that is used to tune IMC-PID is used as a time constant of a setpoint filter that is used for reducing the peak overshoot. The method has been tested successfully on many low order processes.     

Enhanced IMC design of load disturbance rejection for integrating and unstable processes with slow dynamics

In view of the deficiencies in existing internal model control (IMC)-based methods for load disturbance rejection for integrating and unstable processes with slow dynamics, a modified IMC-based controller design is proposed to deal with step- or ramp-type load disturbance that is often encountered in engineering practices. By classifying the ways through which such load disturbance enters into the process, analytical controller formulae are correspondingly developed, based on a two-degree-of-freedom (2DOF) control structure that allows for separate optimization of load disturbance rejection from setpoint tracking. An obvious merit is that there is only a single adjustable parameter in the proposed controller, which in essence corresponds to the time constant of the closed-loop transfer function for load disturbance rejection, and can be monotonically tuned to meet a good trade-off between disturbance rejection performance and closed-loop robust stability. At the same time, robust tuning constraints are given to accommodate process uncertainties in practice. Illustrative examples from the recent literature are used to show effectiveness and merits of the proposed method for different cases of load disturbance.     

Modified Smith predictor based cascade control of unstable time delay processes

An improved cascade control structure with a modified Smith predictor is proposed for controlling open-loop unstable time delay processes. The proposed structure has three controllers of which one is meant for servo response and the other two are for regulatory responses. An analytical design method is derived for the two disturbance rejection controllers by proposing the desired closed-loop complementary sensitivity functions. These two closed-loop controllers are considered in the form of proportional-integral-derivative (PID) controller cascaded with a second order lead/lag filter. The direct synthesis method is used to design the setpoint tracking controller. By virtue of the enhanced structure, the proposed control scheme decouples the servo response from the regulatory response in case of nominal systems i.e., the setpoint tracking controller and the disturbance rejection controller can be tuned independently. Internal stability of the proposed cascade structure is analyzed. Kharitonov's theorem is used for the robustness analysis. The disturbance rejection capability of the proposed scheme is superior as compared to existing methods. Examples are also included to illustrate the simplicity and usefulness of the proposed method.     

Disturbance-rejection-based tuning of proportional–integral–derivative controllers by exploiting closed-loop plant data

A systematic data-based design method for tuning proportional–integral–derivative (PID) controllers for disturbance attenuation is proposed. In this method, a set of closed-loop plant data are directly exploited without using a process model. PID controller parameters for a control system that behaves as closely as possible to the reference model for disturbance rejection are derived. Two algorithms are developed to calculate the PID parameters. One algorithm determines the optimal time delay in the reference model by solving an optimization problem, whereas the other algorithm avoids the nonlinear optimization by using a simple approximation for the time delay term, enabling derivation of analytical PID tuning formulas. Because plant data integrals are used in the regression equations for calculating PID parameters, the two proposed algorithms are robust against measurement noises. Moreover, the controller tuning involves an adjustable design parameter that enables the user to achieve a trade-off between performance and robustness. Because of its closed-loop tuning capability, the proposed method can be applied online to improve (retune) existing underperforming controllers for stable, integrating, and unstable plants. Simulation examples covering a wide variety of process dynamics, including two examples related to reactor systems, are presented to demonstrate the effectiveness of the proposed tuning method.     

Tuning of linear active disturbance rejection controller with robustness specification

Active disturbance rejection control (ADRC) treats all the model uncertainties and all the external disturbances as a generalized disturbance. It uses an extended state observer (ESO) to estimate the generalized disturbance in real time, and compensate it using a state-feedback control law, thus can achieve good disturbance rejection performance. For linear ADRC (LADRC), the parameters can be tuned via the bandwidths of the ESO and the feedback control, thus an LADRC can be regarded as a fixed-structured controller with several parameters to tune, just like a PID controller. To help tuning the parameters of LADRC, a tuning rule is proposed in this paper, with the aim to minimize the load disturbance attenuation performance in the integral of time square error sense, under the constraint of a specified robustness measure for the first-order processes with deadtime. The tuning rule is tested for a variety of benchmark systems and the gravity drained tanks case, and the performances are compared with the well-known PID tuning methods.     

Particle Swarm Optimization Technique Based Design of Pi Controller for a Real-Time Non-Linear Process

Abstract

The increasing complexity of modern control systems has emphasized the idea of applying new approaches in order to solve design problems for different control engineering applications. Proportional-Integral-Derivative (PID) control schemes have been widely used in most of process control systems represented by chemical processes for a long time. However, a very important problem is how to determine or tune the PID parameters, because these parameters have a great influence on the stability and the performance of the control system. Computational intelligence (CI), which has caught the eyes of researchers due to its simplicity, low computational cost, and good performance, makes it a possible choice for tuning of PID controllers, to increase their performance. This paper discusses, in detail, the Particle Swarm Optimization (PSO) algorithm, a CI technique, and its implementation in PID tuning for a controller of a real time process. Compared to other conventional PID tuning methods, the result shows that better performance can be achieved with the proposed method. The ability of the designed controller, in terms of tracking set point, is also compared and simulation results are shown.     

An improved auto-tuning scheme for PI controllers

Ziegler-Nichols tuned PI and PID controllers are usually found to provide poor performances for high-order and nonlinear systems. In this study, an improved auto-tuning scheme is presented for Ziegler-Nichols tuned PI controllers (ZNPICs). With a view to improving the transient response, the proportional and integral gains of the proposed controller are continuously modified based on the current process trend. The proposed controller is tested for a number of high-order linear and nonlinear dead-time processes under both set-point change and load disturbance. It exhibits significantly improved performance compared to ZNPIC, and Refined Ziegler-Nichols tuned PI controller (RZNPIC). Robustness of the proposed scheme is established by varying the controller parameters as well as the dead-time of the process under control.