A new Smith predictor and controller for control of processes with long dead time

Good control of processes with long dead time is often achieved using a Smith predictor configuration. Typically a PI or PID controller is used; however, it is shown in this paper that for some situations improved set point and disturbance responses can be obtained if a PI-PD controller is used. Several methods are possible for selecting the parameters of the PI-PD controller but when the plant transfer function has no zeros, the use of the standard forms provides a simple algebraic approach, and also reveals why difficulties may be encountered if a PID controller is used. Some examples are given to show the value of the approach presented.     

Autotuning of a new PI-PD Smith predictor based on time domain specifications

The paper extends a recent work on a modified PI-PD Smith predictor, which leads to significant improvements in the control of processes with large time constants or an integrator or unstable plant transfer functions plus long dead time for reference inputs and disturbance rejections. Processes with high orders or long time delays are modeled with lower order plant transfer functions with longer time delays. The PI-PD controller is designed so that the delay-free part of the system output will follow the response of a first-order plant or second-order plant, where it is appropriate, assuming a perfect matching between the actual plant and model in both the dynamics and time delay. The provided simple tuning formulas have physically meaningful parameters. Plant model transfer functions and controller settings are identified based on exact analysis from a single relay feedback test using the peak amplitude and frequency of the process output. Examples are given to illustrate the simplicity and superiority of the proposed method compared with 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.     

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.     

Smith predictor based-sliding mode controller for integrating processes with elevated deadtime

An approach to control integrating processes with elevated deadtime using a Smith predictor sliding mode controller is presented. A PID sliding surface and an integrating first-order plus deadtime model have been used to synthesize the controller. Since the performance of existing controllers with a Smith predictor decrease in the presence of modeling errors, this paper presents a simple approach to combining the Smith predictor with the sliding mode concept, which is a proven, simple, and robust procedure. The proposed scheme has a set of tuning equations as a function of the characteristic parameters of the model. For implementation of our proposed approach, computer based industrial controllers that execute PID algorithms can be used. The performance and robustness of the proposed controller are compared with the Matausek-Mici? scheme for linear systems using simulations.     

PID controller tuning for integrating processes

Minimizing the integral squared error (ISE) criterion to get the optimal controller parameters results in a PD controller for integrating processes. The PD controller gives good servo response but fails to reject the load disturbances. In this paper, it is shown that satisfactory closed loop performances for a class of integrating processes are obtained if the ISE criterion is minimized with the constraint that the slope of the Nyquist curve has a specified value at the gain crossover frequency. Guidelines are provided for selecting the gain crossover frequency and the slope of the Nyquist curve. The proposed method is compared with some of the existing methods to control integrating plant transfer functions and in the examples taken it always gave better results for the load disturbance rejection whilst maintaining satisfactory setpoint response. For ease of use, analytical expressions correlating the controller parameters to plant model parameters are also given.     

Computation of stabilizing PI and PID controllers for processes with time delay

In this paper, a new method for the computation of all stabilizing PI controllers for processes with time delay is given. The proposed method is based on plotting the stability boundary locus in the (kp, ki) plane and then computing the stabilizing values of the parameters of a PI controller for a given time delay system. The technique presented does not need to use Pade approximation and does not require sweeping over the parameters and also does not use linear programming to solve a set of inequalities. Thus it offers several important advantages over existing results obtained in this direction. Beyond stabilization, the method is used to compute stabilizing PI controllers which achieve user specified gain and phase margins. The proposed method is also used to design PID controllers for control systems with time delay. The limiting values of a PID controller which stabilize a given system with time delay are obtained in the (kp, ki) plane, (kp, kd) plane, and (ki, kd) plane. Examples are given to show the benefits of the method presented.     

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.     

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.     

Digital redesign of anti-wind-up controller for cascaded analog system

The cascaded conventional anti-wind-up (CAW) design method for integral controller is discussed. Then, the prediction-based digital redesign methodology is utilized to find the new pulse amplitude modulated (PAM) digital controller for effective digital control of the analog plant with input saturation constraint. The desired digital controller is determined from existing or pre-designed CAW analog controller. The proposed method provides a novel methodology for indirect digital design of a continuous-time unity output-feedback system with a cascaded analog controller as in the case of PID controllers for industrial control processes with the presence of actuator saturations. It enables us to implement an existing or pre-designed cascaded CAW analog controller via a digital controller effectively.     

一种新的积分过程PID控制器整定方法

针对积分过程，提出了一种简单、实用的PID控制器。该方法首先通过PD控制器对积分过程建立内部反馈控制回路，将内部闭环系统近似为二阶加纯滞后模型；然后，根据有效的模型，基于鲁棒性能指标设计外部反馈回路的PID控制器；最后，简化控制系统的结构，采用设定值加权PID控制器控制积分过程。仿真结果表明了设定值加权PID控制器的有效性和可行性。     

Tuning PI controllers for stable processes with specifications on gain and phase margins

In industrial practice, controller designs are performed based on an approximate model of the actual process. It is essential to design a control system which will exhibit a robust performance because the physical systems can vary with operating conditions and time. Gain and phase margins are well known parameters for evaluating the robustness of a control system. This paper presents a tuning algorithm to design and tune PI controllers for stable processes with a small dead time while meeting specified gain and phase margins. Simulation examples are given to demonstrate that the proposed design method can result, in a closed-loop system, in better performances than existing design methods which are also based on user-specified gain and phase margins.     

An effective frequency domain approach to tuning non-PID controllers for high performance

In this paper, a new tuning method is proposed for the design of non-PID controllers for complex processes to achieve high performance. Compared with the existing PID tuning methods, the proposed non-PID controller design method can yield better performance for a wide range of complex processes. A suitable objective transfer function for the closed-loop system is chosen according to process characteristics. The corresponding ideal controller is derived. Model reduction is applied to fit the ideal controller into a much simpler and realizable form. Stability analysis is given and simulation examples are provided to demonstrate the effectiveness of the proposed method.     

Design and robust tuning of control scheme based on the PD controller plus Disturbance Observer and low-order integrating first-order plus dead-time model

This paper presents an effective design and robust tuning method for the control structure based on a series PD controller and a simple Disturbance Observer. All elements of the proposed controller are directly obtained from the low-order Integrating First-Order Plus Dead-Time (IFOPDT) model, used to approximate essential dynamic characteristics of lag-dominant stable, integrating and unstable plants. The structure of the proposed controller is an effective, easy to implement and tune, extension of the series PID controller. For the same robustness, a better disturbance rejection response is obtained by the proposed controller than that of the PID, by adjusting only two parameters with a clear meaning. A comparison with well-tuned PIDs, done by simulations, and the experimental results, obtained on a real thermal power plant, confirm that high performance and robustness are obtained, for dynamic characteristics common to industrial processes.     

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.     

Centralized PI control for high dimensional multivariable systems based on equivalent transfer function

This article presents a new scheme to design full matrix controller for high dimensional multivariable processes based on equivalent transfer function (ETF). Differing from existing ETF method, the proposed ETF is derived directly by exploiting the relationship between the equivalent closed-loop transfer function and the inverse of open-loop transfer function. Based on the obtained ETF, the full matrix controller is designed utilizing the existing PI tuning rules. The new proposed ETF model can more accurately represent the original processes. Furthermore, the full matrix centralized controller design method proposed in this paper is applicable to high dimensional multivariable systems with satisfactory performance. Comparison with other multivariable controllers shows that the designed ETF based controller is superior with respect to design-complexity and obtained performance.     

A frequency response model matching method for PID controller design for processes with dead-time

In this paper, a PID controller design method for the integrating processes based on frequency response matching is presented. Two approaches are proposed for the controller design. In the first approach, a double feedback loop configuration is considered where the inner loop is designed with a stabilizing gain. In the outer loop, the parameters of the PID controller are obtained by frequency response matching between the closed-loop system with the PID controller and a reference model with desired specifications. In the second approach, the design is directly carried out considering a desired load-disturbance rejection model of the system. In both the approaches, two low frequency points are considered for matching the frequency response, which yield linear algebraic equations, solution of which gives the controller parameters. Several examples are taken from the literature to demonstrate the effectiveness and to compare with some well known design methods.