The effects of the FOPI controller and time delay on stability region of the fuel cell microgrid

2020 ◽  
Vol 45 (60) ◽  
pp. 35064-35072 ◽  
Author(s):  
Mahmut Temel Özdemir
Keyword(s):  
Fuel Cell ◽  
Time Delay ◽  
Stability Region ◽  
Fopi Controller

Uncertain Gain and Time-Delay Control of 300-kW SOFC-GT

2021 ◽  
Author(s):  
Tooran Emami ◽  
David Tucker ◽  
John Watkins
Keyword(s):  
Fuel Cell ◽  
Time Delay ◽  
Pid Controller ◽  
Transfer Functions ◽  
Cell Mass ◽  
Electric Load ◽  
Cold Air ◽  
Internal Gain ◽  
Air Valve ◽  
Turbine Speed

Abstract This paper presents a Proportional Integral Derivative (PID) controller design with the presence of an uncertain internal gain and additional time delay in the forward path of a 300 kW Solid Oxide Fuel Cell-Gas Turbine (SOFC-GT). The outputs of the system are turbine speed and the fuel cell mass flow rate. A fixed set of proportional controller coefficients are determined to graphically develop an area of selection for the integral and derivative coefficients of the PID controller. The inputs to the power plant are the electric load and cold air valve. The decentralized controllers are applied to four sub-systems as a Single Input Single Output (SISO). The PID controller coefficients are selected from a singular matrix solution that stabilizes the system and satisfies the internal gain and time delay uncertainties. Two sub-systems are the transfer functions of the turbine speed over the electric load and the cold air valve. The other two sub-systems are the transfer functions of the fuel cell mass flow rate over the electric load and the cold air bypass valve. Multiple options for selecting PID controller coefficients are beneficial to the SOFC-GT plant due to the wide range of operations and internal uncertainty interactions. The specific internal time delay and gain margins increase the reliability and robustness of the SOFC-GT with multiple uncertain parameters.

An Efficient Approach for Stability Analysis and Parameter Tuning in Delayed Feedback Control of a Flying Robot Carrying a Suspended Load

2019 ◽  
Vol 141 (8) ◽  
Author(s):  
Wei Dong ◽  
Ye Ding ◽  
Luo Yang ◽  
Xinjun Sheng ◽  
Xiangyang Zhu
Keyword(s):  
Time Delay ◽  
Feedback Control ◽  
Spectral Radius ◽  
Stability Region ◽  
Parameter Tuning ◽  
Suspended Load ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
The Stability ◽  
Flying Robot

This paper presents an accurate and computationally efficient time-domain design method for the stability region determination and optimal parameter tuning of delayed feedback control of a flying robot carrying a suspended load. This work first utilizes a first-order time-delay (FOTD) equation to describe the performance of the flying robot, and the suspended load is treated as a flying pendulum. Thereafter, a typical delayed feedback controller is implemented, and the state-space equation of the whole system is derived and described as a periodic time-delay system. On this basis, the differential quadrature method is adopted to estimate the time-derivative of the state vector at concerned sampling grid point. In such a case, the transition matrix between adjacent time-delay duration can be obtained explicitly. The stability region of the feedback system is thereby within the unit circle of spectral radius of this transition matrix, and the minimum spectral radius within the unit circle guarantees fast tracking error decay. The proposed approach is also further illustrated to be able to be applied to some more sophisticated delayed feedback system, such as the input shaping with feedback control. To enhance the efficiency and robustness of parameter optimization, the derivatives of the spectral radius regarding the parameters are also presented explicitly. Finally, extensive numeric simulations and experiments are conducted to verify the effectiveness of the proposed method, and the results show that the proposed strategy efficiently estimates the optimal control parameters as well as the stability region. On this basis, the suspended load can effectively track the pre-assigned trajectory without large oscillations.

scholarly journals Design of PI controller for Liquid Level System using Siemens Distributed Control System

2019 ◽  
Vol 8 (3) ◽  
pp. 2783-2789
Keyword(s):  
Time Delay ◽  
Stability Region ◽  
Dead Time ◽  
Pi Controller ◽  
Liquid Level ◽  
Order System ◽  
System Response ◽  
Level System ◽  
Geometric Center ◽  
The Stability

The PI controller design for a liquid level system using the weighted geometric center method is discussed. Every real-time process have dead time. This dead time leads to the generation of oscillation in the system response. The oscillation generated due to dead time introduces instability in system performance. This paper presents a tuning method based on calculating a geometric center in the stability region for a higher order system. In this, the stability region calculated by plotting (Kp , Ki )-plane based on boundary locus stability technique. Further centre point computed in the stability locus by a geometric center method. This center point will provide Kp , Ki value for tuning the PI controller. The First Order Plus Dead Time (FOPDT) process considered to elaborate the method for computing the tuning parameters. A nonlinear time-delay system and a plant having time-delay response are controlled in simulation. The performance of the newly obtained PI controller based on weighted geometric center method is compared with the existing results to show the usefulness of the control scheme. Moreover, disturbance rejection ability of the newly obtained PI controller based on weighted geometric center method is demonstrated by applying disturbances. In addition, the designed controller implemented using Siemens DCS PCS7 V8.1 platform.

scholarly journals Generic Noninteger Order Controller for Time-Delay Systems

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Sami Hafsi ◽  
Sadem Ghrab ◽  
Kaouther Laabidi
Keyword(s):  
Time Delay ◽  
Stability Region ◽  
Delay Systems ◽  
Pid Controllers ◽  
Time Delay Systems ◽  
First Order ◽  
Industrial Utilization ◽  
Complete Set ◽  
Order Representation ◽  
Fractional Controller

This paper focuses on the problem of fractional controller P I stabilization for a first-order time-delay systems. For this reason, we utilize the Hermite–Biehler and Pontryagin theorems to compute the complete set of the stabilizing P I λ parameters. The widespread industrial utilization of PID controllers and the potentiality of their noninteger order representation justify a timely interest in P I λ tuning techniques. Step responses are calculated through K p , K i , l a m b d a parameters inside and outside stability region to prove the method efficiency.

Lyapunov–Krasovskii based FPID controller for LFC in a time-delayed micro-grid system with fuel cell power units

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Kamel Sabahi ◽  
Amin Hajizadeh ◽  
Mehdi Tavan
Keyword(s):  
Fuel Cell ◽  
Time Delay ◽  
Frequency Control ◽  
Implementation Process ◽  
Load Frequency Control ◽  
Content Type ◽  
Nonlinear Input ◽  
Micro Grid ◽  
Mathematical Analyses ◽  
The Stability

Purpose In this paper, a novel Lyapunov–Krasovskii stable fuzzy proportional-integral-derivative (PID) (FPID) controller is introduced for load frequency control of a time-delayed micro-grid (MG) system that benefits from a fuel cell unit, wind turbine generator and plug-in electric vehicles. Design/methodology/approach Using the Lyapunov–Krasovskii theorem, the adaptation laws for the consequent parameters and output scaling factors of the FPID controller are developed in such a way that an upper limit (the maximum permissible value) for time delay is introduced for the stability of the closed-loop MG system. In this way, there is a stable FPID controller, the adaptive parameters of which are bounded. In the obtained adaptation laws and the way of stability analyses, there is no need to approximate the nonlinear model of the controlled system, which makes the implementation process of the proposed adaptive FPID controller much simpler. Findings It has been shown that for a different amount of time delay and intermittent resources/loads, the proposed adaptive FPID controller is able to enforce the frequency deviations to zero with better performance and a less amount of energy. In the proposed FPID controller, the increase in the amount of time delay leads to a small increase in the amount of overshoot/undershoot and settling time values, which indicate that the proposed controller is robust to the time delay changes. Originality/value Although the designed FPID controllers in the literature are very efficient in being applied to the uncertain and nonlinear systems, they suffer from stability problems. In this paper, the stability of the FPID controller has been examined in applying to the frequency control of a nonlinear input-delayed MG system. Based on the Lyapunov–Krasovskii theorem and using rigorous mathematical analyses, the stability conditions and the adaptation laws for the parameters of the FPID controller have been obtained in the presence of input delay and nonlinearities of the MG system.

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