A new tuning method for two-degree-of-freedom internal model control under parametric uncertainty

The purpose of controller tuning is to determine the parameters of controller in order to ensure the time response of close-loop control system at the desired performance. Proportional Integral Derivative (PID) controller has been used in the industry since 1940’s for this purpose. However, the PID controller can not completely compensate for the complexity of industrial processes and desired high product quality due to interactions, nonlinearities, and time delay of the process variables. Internal model control (IMC) has been developed to overcome the deficiencies of the PID. Unfortunately, IMC yields very good performance for set point tracking, but gives sluggish response for disturbance rejection problem. The present study has developed a controller for disturbance rejection based on feedback / feedforward IMC structure. The controller is then called as feedback 2DOF-IMC. A new tuning method has been proposed for the controller. The proposed tuning method consists of three steps: Firstly, determine the worst case of the model uncertainty. Secondly, specify the parameter of set point controller using maximum peak (Mp) criteria. And thirdly, obtain the parameter of the disturbance rejection controller using gain margin (GM) criteria. The proposed method is called Mp-GM tuning method. The effectiveness of the proposed feedback 2DOF-IMC and Mp-GM tuning method has evaluated and compared with standard 2DOF-IMC using IMCTUNE and Kaya 2DOF-IMC using Mp-GM tuning as bench mark. The evaluation and comparison are investigated through simulation and implementation on a number of first order plus dead time (FOPDT) and higher order processes. The FOPDT process tested include processes with controllability ratio in the range 0.7 to 2.5. The higher processes include second order with underdamped and third order with nonminimum phase processes. Although the two of higher order process are considered difficult processes, the proposed feedback 2DOF-IMC and Mp-GM tuning method were able to obtain the optimal controller even under process uncertainties. The proposed feedback 2DOF-IMC and the proposed Mp-GM tuning are also successfully implemented in real-time on a laboratory scale air heater pilot plant. The process model is divided into two regions. The time responses show that the proposed feedback 2DOF-IMC and the proposed Mp- GM tuning gave faster set point tracking and disturbance rejection responses than 1DOF-IMC and standard 2DOF-IMC in both regions

Maximum Peak-Gain Margin 2DOF-IMC Tuning for a 2DOF-PID Filter Set Point Controller Under Parametric Uncertainty

The specification of controller setting for a standard controller typically requires a trade-off between set point tracking and disturbance rejection. For this reason two simple strategies can be used to adjust the set point and disturbance responses independently. These strategies are referred to as controllers with two degree of freedom. Unfortunately, the tuning parameters in the case of model uncertainty at two degree of freedom structure controller is difficult to obtain. Juwari et al (2013) has introduced maximum peak-gain margin (Mp-GM) tuning method to obtain setting parameter of two degree of freedom structure controller based on model uncertainty. This tuning method are able to obtain the good controller parameter even under processes uncertainties on standard two degree of freedom (was abbreviated as 2DOF) IMC. This research will be conducted on development maximum peak-gain margin tuning method for a two degree of freedom PID filter set point structure controller. The simulation results show that the maximum peak gain margin tuning method can give a good target set point tracking, disturbance rejection and robustness in system a 2DOF-PID filter set point controller

Analytical design of a generalised predictor-based control scheme for low-order integrating and unstable systems with long time delay

In this study, the problem of controlling integrating and unstable systems with long time delay is analysed in the discrete-time domain for digital implementation. Based on a generalised predictor-based control structure, where the plant time delay can be taken out of the control loop for the nominal plant, an analytical controller design is proposed in terms of the delay-free part of the nominal plant model. Correspondingly, further improved control performance is obtained compared with recently developed predictor-based control methods relying on numerical computation for controller parameterisation. The load disturbance rejection controller is derived by proposing the desired closed-loop transfer function, and another one for set-point tracking is designed in terms of the H-2 optimal control performance specification. Both controllers can be tuned relatively independently in a monotonic manner, with a single adjustable parameter in each controller. By establishing the sufficient and necessary condition for holding robust stability of the closed-loop control system, tuning constraints are derived together with numerical tuning guidelines for the disturbance rejection controller. Illustrative examples taken from the literature along with temperature control tests for a crystallisation reactor are used to demonstrate the effectiveness and merit of the proposed method.This work was supported in part by the National Thousand Talents Program of China, NSF China Grants 61473054, the Fundamental Research Funds for the Central Universities of China, and the Grants TIN2014-56158-C4-4-P and PROMETEOII/2013/004 from the Spanish and Valencian Governments.Chen, Y.; Liu, T.; García Gil, PJ.; Albertos Pérez, P. (2016). Analytical design of a generalised predictor-based control scheme for low-order integrating and unstable systems with long time delay. IET Control Theory and Applications. 10(8):884-893. https://doi.org/10.1049/iet-cta.2015.0670S88489310

A comprehensive review of modified Internal Model Control (IMC) structures and their filters for unstable processes

This paper reviews the evolution of Internal Model Control (IMC) techniques developed so far for unstable processes. The IMC strategy has shown significant results over the past two decades, including recent inclusions of fractional-order approaches. After a comprehensive study of various methods, the critical tuning methods and structural changes are clearly accumulated with their significance and limitation concerning controlling unstable time-delay systems. The comparisons with main structural changes and filter designs are also included in the numerical study and in discussion. Finally, the key research gaps and future motivations are indicated in the IMC approaches, considering available methods in the literature

Fractional - order tilt integral derivative controller design using IMC scheme for unstable time - delay processes

The paper proposes a modified IMC-based Smith predictor (SP) control method for unstable time-delay processes. A novel design method to tune the parameters of a fractional-order tilt integral derivative controller has been developed using fractional-order IMC filter and process model parameters. The tuning parameters of the fractional-order filter are calculated from the new robustness index and desired performance constraint. The expected performance constraint satisfies good setpoint tracking and optimal control signal. The significant feature of the presented method is that the fractional IMC-SP structure provides a better outcome without adding much computational complexity. For a given robustness index, the optimal controller, which minimizes the performance constraint, the combination of control effort and integral time squared error, helps calculate the two tuning parameters. The benefit does verify under parameters’ uncertainties, external load disturbances and noise. The comparative study with various numerical examples from recently reported methods shows better overall servo and regulatory performances

A unified approach for proportional-integral-derivative controller design for time delay processes

Abstract−An analytical design method for PI/PID controller tuning is proposed for several types of processes with time delay. A single tuning formula gives enhanced disturbance rejection performance. The design method is based on the IMC approach, which has a single tuning parameter to adjust the performance and robustness of the controller. A simple tuning formula gives consistently better performance as compared to several well-known methods at the same degree of robustness for stable and integrating process. The performance of the unstable process has been compared with other recently published methods which also show significant improvement in the proposed method. Furthermore, the robustness of the controller is investigated by inserting a perturbation uncertainty in all parameters simultaneously, again showing comparable results with other methods. An analysis has been performed for the uncertainty margin in the different process parameters for the robust controller design. It gives the guidelines of the M s setting for the PI controller design based on the process parameters uncertainty. For the selection of the closed-loop time constant, (τ c ), a guideline is provided over a broad range of θ/τ ratios on the basis of the peak of maximum uncertainty (M s ). A comparison of the IAE has been conducted for the wide range of θ/τ ratio for the first order time delay process. The proposed method shows minimum IAE in compared to SIMC, while Lee et al. shows poor disturbance rejection in the lag dominant process. In the simulation study, the controllers were tuned to have the same degree of robustness by measuring the M s , to obtain a reasonable comparison