On control design and tuning for first order plus time delay plants with significant uncertainties

Time-delay characteristics of various industrial processes may degrade the stability and dynamic performance of the control systems. Aiming at the problems of the existing methods in dealing with the time delay plant, a modified fractional-order proportional–integral–derivative (FOPID) controller for the first-order plus time-delay (FOPTD) system is developed. Assisted by a modified active disturbance rejection control (ADRC) scheme with increased observer bandwidth, the proposed FOPID controller inherently obtains good robustness to time-delay uncertainties and external disturbances. In addition, taking advantage of the fractional-order operator, the proposed controller can provide larger stability margin over the proportional–integral–derivative (PID) controller. By suitably establishing the relation between ADRC and FOPID controller parameters, the proposed controller can be analytically tuned based on the common design indices. A practical tuning guideline is developed according to frequency-domain characteristic analysis, making the proposed controller more acceptable to industrial application. The performance of the ADRC-based FOPID controller is tested by the control simulation of some typical FOPTD systems and a diesel engine speed regulation system. The efficiency of the ADRC-based FOPID controller is demonstrated by the comparisons with some existing controllers.

In this paper, we examine a design method for a modified Smith predictor for a class of non-minimum-phase time-delay plants. The modified Smith predictor is well known as an effective time-delay compensator for a plant with large time delays. Several papers on the modified Smith predictor have been published. However, the parametrization of all stabilizing modified Smith predictors has not been obtained. The purpose of this paper is to propose the parametrization of all stabilizing modified Smith predictors for a class of non-minimum-phase time-delay plants and present a design method of modified Smith predictors. At first, the definition of modified Smith predictor is given. Next, we propose the parametrization of all stabilizing modified Smith predictors for a class of non-minimum-phase system which is not necessarily stable. The control characteristics of the control system using the parametrization of all stabilizing modified Smith predictors are also given. The obtained parametrization of all stabilizing modified Smith predictor has a free-parameter which is used to specify control specification. Next, in order to specify input-output characteristics, we present a design method of modified Smith predictor using the fusion of obtained parametrization of all stabilizing modified Smith predictors and the model matching methods. Finally, a numerical example for unstable plant is illustrated to show the effectiveness of the proposed method.

The modified Smith predictor is well known as an effective time-delay compensator for a plant with large time delays, and several papers on the modified Smith predictor have been published. The parametrization of all stabilizing modified Smith predictors for minimum-phase time-delay plants is obtained by Yamada and Matsushima. In addition, Yamada et al. expanded the result by Yamada and Matsushima and proposed the parametrization of all stabilizing modified Smith predictors for non-minimum-phase time delay plants. However, no paper examines the parametrization of all stabilizing 2-degree-of-freedom modified Smith predictors that can specify the input-output characteristic and the feedback characteristic separately. From the practical point of view, it is desirable that the input-output characteristic and the feedback characteristic are specified separately. In this paper, we propose the parametrization of all stabilizing 2-degree-of-freedom modified Smith predictors for time-delay plants that can specify the input-output characteristic and the feedback characteristic separately.

In this paper, a straightforward and practical Indirect-internal model control (I-IMC) PID controller with an Extended state observer (ESO) is exhibited for the first order plus time delay plants (FOPTD) agitated by the uncertainties and disturbances. Firstly, the I-IMC PID controller design for FOPTD plants separately, then a linear extended state observer is integrated with I-IMC PID controller for active disturbance rejection control (ADRC) and estimates the state of time delay, where linear ESO greatly reduced the distance between the control plant and the conceptual model. So it is a easy and efficient control method for analysis and implementation, such that the identified model's accuracy has been compared with other existing methods in the presence of model uncertainties. The proposed method simulated in MATLAB/Simulink to verify the result with existing methods, that shows faster response and better accuracy for time delay plant with external disturbance.

The modified Smith predictor is well known as an effective time-delay compensator fora plant with large time-delays, and several papers on the modified Smith predictor have been published.Recently, the parameterization of all stabilizing modified Smith predictors for time-delay plantswas obtained by Yamada et al. But, their method cannot specify the input-output characteristic andthe feedback characteristic separately. From the practical point of view, it is desirable that the inputoutputcharacteristic and the feedback characteristic are specified separately. In this paper, we proposethe parameterization of all stabilizing two-degree-of-freedom modified Smith predictors for multipleinput/multiple-output time-delay plants.

To tackle systems with both uncertainties and time delays, several modified active disturbance rejection control (ADRC) methods, including delayed designed ADRC (DD-ADRC), polynomial based predictive ADRC (PP-ADRC), Smith predictor based ADRC (SP-ADRC) and predictor observer based ADRC (PO-ADRC), have been proposed in the past years. This paper is aimed at rigorously investigating the performance of these modified ADRCs, such that the improvements of each method can be demonstrated. The capability to tackle time delay, the necessity of stable open loop and the performance of rejecting uncertainties for these methods are fully studied and compared. It is proven that large time delay cannot be tolerated for the stability of the closed-loop systems based on DD-ADRC and PP-ADRC. Moreover, stable open loop is shown to be necessary for stabilizing the closed-loop systems based on SP-ADRC. Furthermore, the performance of rejecting the “total disturbance” at low frequency for these modified ADRCs is evaluated and quantitatively discussed. Finally, the simulations of a boiler turbine system illustrate the theoretical results.

In this paper, a simple method for finding the stability region of feedback control system with One Non-Integer Plus Time Delay (NIOPTD-I) plant and fractional order Proportional Integral Derivative (FOPID) controller is presented. Analytical expressions for finding the asymptotic stability regions in (X, Y, Z) space are derived using D-partition method. Stability regions are obtained for various fractional orders of P\(I^{\lambda }D{^\mu }\) controller in the range of (0, 2). Fractional order parameters are chosen such that larger stability region in positive direction than integer order parameters is obtained. Controller tuning parameters are chosen from the obtained stability region. The use of proposed FOPID controller for the NIOPTD-I plant increases the stability region and also the degree of freedom increases from three to five in comparison to FOPI controller. Knowledge of these stability regions makes design of controller easier. Effectiveness of the proposed method is illustrated with examples, which shows better control performance.

This paper presents a preliminary analysis of the energy spent making control of first order plus time delay (FOPTD) plants, using a fractional proportional integral (FOPI) controller. Using three representative FOPTD plants and adjusting the FOPI parameters, the control energy is analyzed using simulation studies. The results are compared to that obtained using a classical proportional integral (PI) controller using the same tuning rule, under ideal conditions and also in the presence of non linearity in the sensor path, showing that the energy used for control can be reduced when using the FOPI controller, compared to the case using the PI controller. This suggests that using FOPI could be more efficient than using integer order controllers, from an an energy use viewpoint, justifying a follow up of this research.

Fractional order proportional derivative control for time delay plant of the second order: The frequency frame

Proportion integral-type active disturbance rejection generalized predictive control for distillation process based on grey wolf optimization parameter tuning

A Simple Algorithm of Adaptive Control for Systems with Time Delay

Large time constant and time delay are common challenges in industrial processes, often leading to increased overshoot, prolonged settling times, larger steady‐state errors, and potential instability. This paper proposes a novel control strategy that combines linear active disturbance rejection control (LADRC) with internal model control (IMC) in a dual‐loop feedback structure (IMC‐ADRC) to address the challenges in systems with large time constants and time delay uncertainties. The inner loop, utilizing IMC, directly compensates for time delay, improving tracking performance. Meanwhile, the outer loop, using LADRC, estimates and suppresses both internal and external disturbances, reducing errors from disturbances and model uncertainties. Simulation results demonstrate that the integrated IMC‐ADRC approach significantly enhances system response accuracy, system response speed, and disturbance rejection compared to LADRC and IMC, as well as the delayed designed ADRC (DD‐ADRC) and Smith predictor‐based ADRC (SP‐ADRC). Notably, IMC‐ADRC retains these advantages even in systems with low model accuracy. This approach provides a robust and adaptable solution for systems with large time constants and time delays, thereby providing valuable perspectives for the field of industrial process control.

To improve the performance of the Active Disturbance Rejection Control (ADRC) in systems which have large time delay, reduce online computation for Proportional Integral-type Generalized Predictive Control (PI-GPC) method, the Proportional Integral-type Active Disturbance Rejection Generalized Predictive Control (PI-ADRGPC) based on Controlled Auto Regression and Moving Average (CARMA) model is designed. The frequency domain analysis method is used to analyse the stability of the PI-ADRGPC based on CARMA model. By using the open-loop transfer function of the PI-GPC discrete form, the influence of parameter changes on the PI-ADRGPC performance is analysed. The performance of the PI-ADRGPC and ADRC algorithm is compared through the application in a second-order time delay system and distillation column system. The research results show that compared with the ADRC algorithm, the PI-ADRGPC method has a shorter rise time and better performance.

The performance of existing dead time compensation controllers for both non-integrating and integrating plants with large time delays is improved by an online estimation scheme. The estimation scheme uses a backpropagation-type update law for estimating simultaneously the plant time delay and static gain. Fuzzy logic is used to tune the estimator performance. Simulation results are provided to illustrate the scheme's performance.

A calculation method of Hankel singular values is discussed for input and unilateral time delay systems. For input time delay systems, whose channels involve different value of time delays independently, the Hankel singular values are obtained based on a matrix Lyapunov equation. By introducing auxiliary systems for the unilateral time delay system, it is shown that the singular values are characterized based on the preliminary results for input time delay systems. When Hankel singular values and vectors are derived for input and unilateral time delay systems, the calculation method of balanced reduction is constructed. We investigate balanced reduction with numerical examples.