2DoF Proportional Integral Research Articles

Robust 2DoF PI tuning rules for integrating processes with dead time via frequency response model matching

The integrating characteristics are commonly found in composition control and level control of a distillation column in chemical processes. This paper presents a simple and intuitive robust tuning method of two-degree-of-freedom (2DoF) proportional-integral (PI) controller for integrating processes with dead time. The frequency response model matching approach is utilized with performance and robustness considerations for both regulatory and servo control issues. The regulatory control issue aims at matching the frequency response of the closed-loop system with that of the reference model for disturbance rejection, where the feedback controller parameters are calculated by solving a group of overdetermined algebraic equations subject to a robustness constraint evaluated by the maximum sensitivity. The target of the servo response is to follow a prescribed set-point reference trajectory, with the set-point weighting factor tuned to satisfy a defined tracking performance metric. A curve fitting procedure is utilized to generate analytical tuning rules in terms of the process model parameters and the desired robustness specification. It is shown that, apart from giving more exact achievement of the control system robustness, the tuning rules presented work well for a wider range of process dynamics than the existing methods. Illustrative examples are given to show the effectiveness of the proposed method.

Performance Assessment of an Islanded Hybrid Power System with Different Storage Combinations Using an FPA-Tuned Two-Degree-of-Freedom (2DOF) Controller

During the past few decades, there has been significant growth in the renewable energy market because of increased concern over global warming and the continuous depletion of fossil fuel resources. There is a promising solar thermal technology that utilizes low-temperature heat to generate electricity. The conversion process of thermal energy to electricity is based on the principle of an organic Rankine cycle (ORC). This study investigated a novel islanded hybrid power system consisting of an ORC low temperature solar thermal system, wind (WTG), diesel generation (DEG) set, and combined application of an energy storage system (ESS), such as a battery (BESS), super magnetic energy storage (SMES), and an ultracapacitor (UC) unit. Furthermore, the hybrid system was employed with a single controller (one of proportional-integral (PI), PI with derivative (PID), two-degree-of-freedom (2DOF) PI, and 2DOF PID controllers) with proportionate gains to the DEG, and the ESS, which is another unique aspect of this work. Moreover, a comparative performance assessment of the flower pollination algorithm (FPA) to tune the PI, PID, 2DOF PI, and 2DOF PID controllers was carried out. Finally, the performance of the above hybrid system was compared with different ESS combinations, namely, (i) only BESS, (ii) BESS + UC, and (iii) BESS + SMES. The simulation results indicated that a renewable integrated isolated power system with BESS + SMES provided a better response than the other ESS combinations. In fact, the presence of comparative dynamic responses verified the superiority of an FPA-tuned 2DOF PID compared with other FPA-tuned controllers.

Two Degree of Freedom PID Controller in Time Delay System using Hybrid Controller Model

In the paper, a hybrid method based two-degree of freedom (2-DOF) PID controller is proposed for tuning the time delay system. The hybrid technique is the combination of fuzzy logic controller (FLC) and gravitational search algorithm (GSA). Here, the GSA is utilised for generating the logic rules of FLC. The 2-DOF proportional integral and derivative (PID) controller ensures highly efficient disturbance rejection and reliable performance. Here, tuning of a 2-DOF PID controller with a time delay system design achieves a high performance for a wide range. For the automatic tuning process, the parameters of time delays system is predicted and tuned optimally in the short period of time. The first order time delay system is tuned and the stability parameters such as small overshoot, settling time and rising time has been achieved. From the results, it is noted that, proposed controller provides enhanced results for the reference tracking and disturbance rejection operations. The effectiveness and feasibility of the proposed technique is demonstrated through the MATLAB/Simulink platform and the performance is tested and compared with the existing controller tuning methods such as FLC technique with genetic algorithm (GA) and artificial neural network (ANN) techniques.

Adaptive two-degree-of-freedom PI for speed control of permanent magnet synchronous motor based on fractional order GPC

In this paper, an adaptive two-degree-of-freedom (2Dof) proportional-integral (PI) controller is proposed for the speed control of permanent magnet synchronous motor (PMSM). Firstly, an enhanced just-in-time learning technique consisting of two novel searching engines is presented to identify the model of the speed control system in a real-time manner. Secondly, a general formula is given to predict the future speed reference which is unavailable at the interval of two bus-communication cycles. Thirdly, the fractional order generalized predictive control (FOGPC) is introduced to improve the control performance of the servo drive system. Based on the identified model parameters and predicted speed reference, the optimal control law of FOGPC is derived. Finally, the designed 2Dof PI controller is auto-tuned by matching with the optimal control law. Simulations and real-time experimental results on the servo drive system of PMSM are provided to illustrate the effectiveness of the proposed strategy.

Adaptive speed control based on just-in-time learning technique for permanent magnet synchronous linear motor

In this paper, an adaptive two degrees of freedom (2Dof) PI controller based on a just-in-time learning (JITL) method is proposed for predictive speed control of permanent magnet synchronous linear motor (PMSLM). Firstly, to guarantee the high identification accuracy and high real-time performance simultaneously, an improved JITL method is proposed to estimate the controlled model parameters of speed control system. Then, based on the dynamic controlled model, a simplified generalized predictive control (GPC) supplies a 2Dof proportional integral (PI) controller with suitable control parameters to follow a sinusoid-type speed command in operating conditions. The main motivation of this paper is the extension of the predictive controller to replace traditional PI controller in industrial applications. Finally, the efficacy and usefulness of the proposed controller are verified through the experimental results.

Model-reference robust tuning of 2DoF PI controllers for first- and second-order plus dead-time controlled processes

The aim of this paper is to present a robust tuning method for two-degree-of-freedom (2DoF) proportional integral (PI) controllers. This is based on the use of a model reference optimization procedure with servo and regulatory target closed-loop transfer functions for first- and second-order plus dead-time (FOPDT, SOPDT) controlled process models. The designer is allowed to deal with the performance/robustness trade-off of the closed-loop control system by specifying the desired robustness level by selecting a maximum sensitivity in the range from 1.4 to 2.0. In addition, a smooth servo/regulatory performance combination is obtained by forcing both closed-loop transfer functions to perform as closely as possible to non-oscillatory dynamic targets. A unified set of controller tuning equations is provided for FOPDT and SOPDT models with normalized dead-times from 0.1 to 2.0 that guarantees the achievement of the design robustness level. The robustness of the control system is analyzed as well as the robustness–fragility and performance–fragility of the optimized controllers. Comparative examples show the effectiveness of the proposed tuning method. The exact achievement of the control system robustness target for all the controlled process models considered (first- and second-order) is one of the distinctive characteristics of the proposed model reference robust tuning (MoReRT) method.