Iterative tuning of modified uncertainty and disturbance estimator for time-delay processes: A data-driven approach

Uncertainty and disturbance widely exist in the process industry, which may deteriorate control performance if not well handled. The uncertainty and disturbance estimator (UDE) emerges as a promising solution by treating the external disturbances and internal uncertainties simultaneously as a lumped term. To overcome its limitation caused by time delay, a modified UDE (MUDE) has been proposed recently. However, its parameter tuning relies heavily on trial-and-error, thus being time-consuming in balancing the robustness and performance. To this end, this paper aims to develop an automatic tuning procedure for the MUDE-based control system. The quantitative relationship between system performance and the scaled parameters is empirically built. Iterative Feedback Tuning (IFT) is utilized to approximate the nominal model towards actual process. Through the empirical formula and optimized model, an automatic design procedure is proposed after taking into account the system robustness and output performance simultaneously. Simulation results show the superiority of the closed-loop performance over the original MUDE controllers. The experimental results validate the feasibility of the method proposed in this paper, depicting a promising prospect in the practical application.     

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.     

Modified Smith predictor design for periodic disturbance rejection

In this paper, a modified Smith predictor control scheme is proposed for periodic disturbance rejection in both stable and unstable processes with time delay. Without affecting the superior setpoint response of Smith predictor control, the regulation performance under periodic disturbance can be enhanced significantly by the proposed design. Meanwhile, the asymptotical rejection for non-periodic disturbance will also be improved. Internal stability is investigated for a closed-loop control system. The effectiveness of the proposed scheme will be demonstrated by simulations as well as a test on an experimental thermal system.     

Robust controller synthesis for high order unstable processes with time delay using mirror mapping technique

In this note, a general scheme is proposed for the high order unstable delay process with one or more positive poles, using the mirror mapping technique. The Nyquist criteria is employed to establish a systematic methodology to tune the parameter. The stabilizing parameter region could guarantee the prespecified robustness specification. In the scheme, a control law is designed based on the all-pole Padé approximated model. The unstable process was first mapped into a minimum-phase system, and the actual control is obtained by the closed-loop gain shaping algorithm (CGSA). The advantages are that one has a concise design procedure and can achieve good performance such as disturbance rejection and robustness. Finally, three highly cited examples are used to illustrate the effectiveness 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.     

Optimized robust control for industrial unstable process via the mirror-mapping method

In this work, a novel optimized robust control algorithm, based on the mirror-mapping method, is proposed for a class of industrial unstable process with time delay. The optimizing criterion is to minimize the sensitivity function to enhance its robustness. The controllers are designed based on the Padé approximated mirror-mapping process with a stable form, other than the original unstable system. The developed algorithm could release the internal stability constraints to the unstable plant. By using the graphical stability criterion, a systematic methodology is derived to obtain the exact stabilizing region, where the sole design parameter is related to the stability degree of the closed-loop system. The proposed algorithm is with characteristics of concise and efficient design. Three experiments has been employed to illustrate that the control effects can achieve the satisfied performance in aspects of disturbance rejection and robustness.     

Analytical design of modified Smith predictor in a two-degrees-of-freedom control scheme for second order unstable processes with time delay

A modified form of Smith predictor is designed for controlling unstable second order plus time delay (USOPTD) processes, with/without a zero. USOPTD process transfer functions arise in modeling of many chemical and biological systems, such as isothermal continuous stirred tank reactors (CSTR) carrying out autocatalytic reactions, crystallizers and non-isothermal CSTRs. The modified Smith predictor scheme requires the design of three controllers. Synthesis method is used for the design of the three controllers, and analytical formulas are given for these controllers. The method has two tuning parameters, and guidelines are provided for selecting the tuning parameters. Robust disturbance rejection performances are achieved. Different examples are considered, and simulation studies are given, to show the effectiveness of the proposed method. A significant improvement is obtained, when compared with recently reported methods.     

Robust image signal-to-noise ratio estimation using mixed Lagrange time delay estimation autoregressive model

A new technique based on the statistical autoregressive (AR) model has recently been developed as a solution to signal-to-noise (SNR) estimation in scanning electron microscope (SEM) images. In the present study, we propose to cascade the Lagrange time delay (LTD) estimator with the AR model. We call this technique the mixed Lagrange time delay estimation autoregressive (MLTDEAR) model. In a few test cases involving different images, this model is found to present an optimum solution for SNR estimation problems under different noise environments. In addition, it requires only a small filter order and has no noticeable estimation bias. The performance of the proposed estimator is compared with three existing methods: simple method, first-order linear interpolator, and AR-based estimator over several images. The efficiency of the MLTDEAR estimator, being more robust with noise, is significantly greater than that of the other three 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.     

Analytical design of an industrial two-term controller for optimal regulatory control of open-loop unstable processes under operational constraints

This paper proposes a novel optimization-based approach for the design of an industrial two-term proportional-integral (PI) controller for the optimal regulatory control of unstable processes subjected to three common operational constraints related to the process variable, manipulated variable and its rate of change. To derive analytical design relations, the constrained optimal control problem in the time domain was transformed into an unconstrained optimization problem in a new parameter space via an effective parameterization. The resulting optimal PI controller has been verified to yield optimal performance and stability of an open-loop unstable first-order process under operational constraints. The proposed analytical design method explicitly takes into account the operational constraints in the controller design stage and also provides useful insights into the optimal controller design. Practical procedures for designing optimal PI parameters and a feasible constraint set exclusive of complex optimization steps are also proposed. The proposed controller was compared with several other PI controllers to illustrate its performance. The robustness of the proposed controller against plant-model mismatch has also been investigated.     

Modified active disturbance rejection control for time-delay systems

Industrial processes are typically nonlinear, time-varying and uncertain, to which active disturbance rejection control (ADRC) has been shown to be an effective solution. The control design becomes even more challenging in the presence of time delay. In this paper, a novel modification of ADRC is proposed so that good disturbance rejection is achieved while maintaining system stability. The proposed design is shown to be more effective than the standard ADRC design for time-delay systems and is also a unified solution for stable, critical stable and unstable systems with time delay. Simulation and test results show the effectiveness and practicality of the proposed design. Linear matrix inequality (LMI) based stability analysis is provided as well.     

A new design method for PI–PD control of unstable processes with dead time

PID controllers are still widely practiced in the industrial systems. In the literature, many publications can be found considering PID controller design for unstable processes. However, owing to the structural limitations of PID controllers, generally, good closed loop performance cannot be achieved with a PID for controlling unstable processes and usually a step response with a high overshoot and oscillation is obtained. On the other hand, PI–PD controllers are proved to give very satisfactory closed loop performances for unstable processes. The paper presents a simple design method to tune parameters of a PI–PD controller for the control of the unstable processes with time delay. The proposed method is based on plotting the stability boundary locus, which is a locus dependent on the parameters of the controller and frequency, in the parameter plane. The method uses a new concept named centroid of the convex stability region. Simulation examples and an experimental application are given to illustrate the superiority of the proposed method over some existing ones.     

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.     

A ratio control scheme decoupling disturbance response from set-point response

In this paper a novel ratio control scheme is proposed for stable and unstable processes with time delay. The proposed ratio control system consists of two control loops with two-degrees-of-freedom control structure, which decouples the set-point response of each loop from its disturbance response. Two ratio controllers separately for the set-point and load disturbance changes are introduced between the two control loops, in order to achieve improved ratio control performance during the transients caused by the set-point and disturbance changes and to decouple the set-point response of the whole ratio control system from its disturbance response. For easy understanding and tuning, all the controllers in the ratio control system are designed analytically. As a result, the set-point and load disturbance responses of the ratio control system can be independently and conveniently tuned by a single control parameter. In addition, the proposed ratio control scheme can provide quantitative performance estimation. Simulation examples are included to illustrate the effectiveness of the proposed method.     

基于阶跃响应的反向响应过程的预测函数控制

通过分析被控过程产生反向响应的内在机理,基于过程阶跃响应系数利用预测函数控制算法实现反向响应过程的控制。将系统控制结构归结为内模控制结构,并在此基础上给出控制系统的鲁棒稳定性证明。该方法的优点是所得控制器结构简单、参数易于调节,且所给方法也适用于其他非最小相位系统的控制。实验结果证实该方法有很强的抗干扰能力和较好鲁棒性。     

Performance of a mixed Lagrange time delay estimation autoregressive (MLTDEAR) model for single-image signal- to-noise ratio estimation in scanning electron microscopy

A novel technique based on the statistical autoregressive (AR) model has recently been developed as a solution to estimate the signal-to-noise ratio (SNR) in scanning electron microscope (SEM) images. In another research study, the authors also developed an algorithm by cascading the AR model with the Lagrange time delay (LTD) estimator. This technique is named the mixed Lagrange time delay estimation autoregressive (MLTDEAR) model. In this paper, the fundamental performance limits for the problem of single-image SNR estimation as derived from the Cramer–Rao inequality is presented. We compared the experimental performances of several existing methods – the simple method, the first-order linear interpolator, the AR-based estimator as well as the MLTDEAR method – with respect to this performance bound. In a few test cases involving different images, the efficiency of the MLTDEAR single-image estimation technique proved to be significantly better than that of the other three methods. Study of the effect of different SEM setting conditions that affect the autocorrelation function curve is also discussed.     

Heating-up control with delay-free output prediction for industrial jacketed reactors based on step response identification

To improve the heating-up control performance for industrial jacketed reactors typically involved with long input delay, a predictor-based two-degree-of-freedom (2DOF) control scheme is proposed for the heating-up process operation, based on model identification from a practical step response test. By performing a simple step test (i.e., turning on the electrical heater with certain power (e.g., 50% or 100% of the heating power) to observe the heating-up temperature response), a transfer function identification method is developed to establish an integrating type process model with time delay for describing fundamental dynamics of the heating-up response. Based on the identified model, a predictor-based 2DOF control structure is established, where the delay-free output prediction is obtained by constructing two filters. The 2DOF controllers are analytically derived by proposing the desired transfer functions for the set-point tracking and load disturbance rejection, respectively. There is a single adjustable parameter in each controller (or filter), which may be monotonically tuned to obtain the desired control (or prediction) performance. Illustrative examples from the existing references and a practical application to a 4-liter jacketed reactor for pharmaceutical crystallization are given to demonstrate the effectiveness and advantage of the proposed identification and control methods in comparison with the existing methods.