10999


FACTA UNIVERSITATIS  
Series: Mechanical Engineering  

https://doi.org/10.22190/FUME221205014Z 

© 2020 by University of Niš, Serbia | Creative Commons License: CC BY-NC-ND 

Original scientific paper 

EFFECTS OF MONITORING SIGNAL HYSTERESIS ON SPEED 

REGULATION FOR THE AERO-DERIVATIVE GAS TURBINE 

Zhibin Zhao1, 2, Wenjie Zhou1, Peijun Liu2, Zhirui Liu2 

1School of Energy and Power Engineering, Jiangsu University, Zhenjiang, China 
2Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing, China 

Abstract: Sensor aging and sensor failure are the common phenomena due to the high 

temperature and pressure environment for gas turbines, which can lead to hysteresis of 

monitoring signals. In this paper, a kind of aero-derivative gas turbine is taken as the 

research object. The hysteresis effects of single monitoring signal and coupling of 

multiple monitoring signals on speed control are mainly studied, and the analysis is 

carried out from the perspective of adjustment time, overshoot, fuel quantity and fuel 

quantity regulation output. The analysis results show that the pressure signal hysteresis 

will lead to speed suspension. The speed signal hysteresis will change the speed 

regulation into a multi-step mode. When the monitoring signal hysteresis is coupled, the 

effect of pressure signal hysteresis is greater than that of speed signal hysteresis. The 

results of this paper can provide a reference for the optimal design of speed control of 

aero-derivative gas turbine. 

Key Words: Aero-derivative gas turbine, Pressure signal hysteresis, Speed signal 

hysteresis, Hysteresis coupling, Multi-step mode 

1. INTRODUCTION 

As the core equipment of the power generation system, the aero-derivative gas turbine 

is an indispensable energy-converting device [1]. The aero-derivative gas turbine is 

developed based on the mature air engine technology. It retains most of the structure of the 

air engine and only adds the power turbine at the end of the gas generator. Therefore, the 

aero-derivative gas turbine inherits most of the advantages of the air engine and has the 

advantages of large power per unit volume, light weight, fast starting, good acceleration 

and high reliability [2, 3], it has become an important energy conversion equipment and 

power plant in the industrial field. At present, the aero-derivative gas turbine has been 

                                                           
Received: December 05, 2022 / Accepted May 05, 2023   

Corresponding author: Wenjie Zhou1, Peijun Liu2 
1 School of Energy and Power Engineering, Jiangsu University, Zhenjiang 212013, China 
2 Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing 100190, China 

E-mail: zhouwenjiezwj@ujs.edu.cn, liupeijun@iet.cn 



Z. ZHAO, W. ZHOU, P. LIU, Z. LIU 2 

widely used in various fields [4, 5], such as distributed energy, pipeline compression, 

marine power, mobile power station, power plant and offshore platform. 

Gas turbine control technology is one of the core technologies in gas turbine, and it is 

also an important guarantee for the economy of gas turbine units. From the perspective of 

development, gas turbine control system has experienced the stages from the mechanical 

hydraulic control, analog electronic control to digital electronic control [6]. With the 

application of low emission combustion control technology, adaptive control technology, 

remote network control technology, intelligent sensors and actuators in the control system 

[7-10], the gas turbine control system is gradually developing towards integrated control, 

network control and active control. 

PID algorithm is the earliest practical control algorithm, it is still the most commonly 

used control law in the control system. With the development of control theory, fuzzy 

control, particle swarm optimization algorithm, genetic algorithm and neural network 

model combined with PID algorithm are widely used in the field of control engineering to 

adapt to more complex controlled objects [11-14]. Less attention has been paid to the 

problems that the PID algorithm iteration results are biased due to the hysteresis of the 

monitoring signal, which causes the control system to send wrong instructions to the 

controlled object, and then leads to the slow adjustment of the control system and the 

deterioration of robustness. 

The hysteresis of monitoring signal mainly comes from two aspects: on the one hand, 

it is caused by sensor failure, on the other hand, it comes from the control system. Gas 

turbines usually operate under complex conditions, such as high temperature, high pressure, 

etc. For monitoring and control, the gas turbine is equipped with many sensors. Due to long 

working hours under adverse conditions, the sensor may output abnormal signals, and then 

the monitoring signal will be delayed [15]. The typical five types of sensor faults are step 

fault, pulse fault, periodic fault, noise fault and drift fault [16-18]. In addition, the gas 

turbine control system is usually composed of measuring elements (sensitive elements), 

electronic controllers and actuators. The problems such as long sampling time, 

communication failure and long response time of actuators may occur during its work, 

which will result in delayed monitoring signal of the gas turbine. 

The research of monitoring signal hysteresis mainly includes the use of fault-tolerant 

control and the establishment of fault diagnosis system. Since fault-tolerant control has the 

ability to reconstruct monitoring signals and can better maintain the stability of the control 

system, Hadroug [19-24] analyzed and discussed the application of fault-tolerant control. 

Fault tolerant control is mainly divided into two types: data-based fault-tolerant control 

and model-based fault-tolerant control. In terms of the current application of fault-tolerant 

control, it is difficult to realize data-based fault-tolerant control in engineering application. 

However, the existing model-based fault-tolerant control will degrade its fault-tolerant 

performance when the object does not match the observer model, and could not adapt to 

the characteristics of gas turbine with variable load. On the other hand, the robustness and 

reliability of the control system can be improved by establishing a fault diagnosis system 

[25]. The researches on fault diagnosis were also been paid more attentions, Rahmoune 

[26, 27] established a fault diagnosis system based on neural network and tested some faults. 

Ogaji [28] established a fault diagnosis system to solve the problem of sensor fault and 

reorganized the fault data into a fault-free form, this reconstructed data could be used to 

accurately perform sensor calculation. Considering that the performance degradation signs 

of the main components of the gas turbine are different at different operating points, 



Effects of Monitoring Signal Hysteresis on Speed Regulation for the Aero-Derivative Gas Turbine 3 

Mohammadi [29] proposed a fuzzy based FDI system with the help of load parameters as 

augmented input, which had robust performance against measurement uncertainty. 

Monitoring signal hysteresis is a common problem in the operation of gas turbine. It 

can reduce the influence of monitoring signal hysteresis on the control system through fault 

tolerant control and fault diagnosis system. However, the influence way and principle of 

monitoring signal hysteresis on the control system are fuzzy. In this paper, an aero-

derivative gas turbine for power generation is taken as the research object. Aiming at the 

problem of monitoring signal hysteresis, a monitoring signal hysteresis model is 

established, which is embedded into the digital simulation model to form a digital 

simulation model with the function of monitoring signal hysteresis. The control 

performance of this type of aero-derivative gas turbine is optimized. The above research 

results can provide an important reference for this type of aero-derivative gas turbine to 

reduce the impact of monitoring signal hysteresis. 

2. ESTABLISHMENT OF DIGITAL SIMULATION SYSTEM 

Using MATLAB/Simulink platform to establish digital simulation model is one of the 

important means of gas turbine research. The digital simulation model established in this 

paper is shown in Fig 1. The establishment process mainly includes four steps: firstly, 

based on the mechanism modeling method, the aero-derivative gas turbine model is 

established; Secondly, based on PID algorithm, the fuel quantity algorithm model is 

established; Thirdly, aiming at the problem of monitoring signal hysteresis, a monitoring 

signal hysteresis model is established; Finally, the three models are combined into a digital 

simulation model with the function of signal hysteresis monitoring. 

 

Fig. 1 Structure diagram of digital simulation model 

2.1 The model of the aero-derivative gas turbine 

The research object of this paper is an aero-derivative gas turbine for power generation. 

Its simplified structure is shown in Fig. 2, mainly including compressor, combustion 

chamber, turbine, power turbine, generator and other components. Gas turbine modeling 

methods are mainly divided into two categories: mechanism modeling and data modeling. 



Z. ZHAO, W. ZHOU, P. LIU, Z. LIU 4 

In the modeling process of aero-derivative gas turbine, due to the lack of measurement data 

such as high-temperature component measurement points and air side flow measurement 

points, the data modeling method is limited. However, the mechanism modeling method 

mainly depends on the physical mechanism of gas turbine components. Therefore, based 

on the mechanism modeling method, this paper establishes the model of aero-derivative 

gas turbine. 

 

Fig. 2 Structural diagram of aero-derivative gas turbine 

2.2 The model of fuel quantity algorithm 

Fuel quantity is the most important control variable to change the operating state of gas 

turbine. By changing fuel quantity, the gas turbine can be controlled to complete 

acceleration or deceleration. The fuel quantity algorithm model mainly includes fuel 

quantity control algorithm and fuel quantity optimization link, which is used to receive the 

monitoring signal provided by the gas turbine model, calculate the fuel quantity, and feed 

back the fuel quantity to the gas turbine model. 

2.2.1 Fuel quantity control algorithm 

Due to the simple structure, good stability and reliable operation of the PID control 

algorithm, the PID control algorithm is used to construct the fuel control algorithm. The 

logic of the fuel algorithm consists of nine regulations, one being the primary one and the 

other eight being the limiting one, as shown in Table 1. It can be divided into speed control, 

safety limit control and fuel control according to its functions. 

Based on the aforementioned fuel quantity algorithm logic, the fuel quantity PID 

control logic is designed. The control equation of each PID controller is shown in Eq. (1). 

Different from the traditional integral link, the variable integral gain coefficient is used in 

this paper, and the fuel increment in recent operation cycles is mainly used as the 

adjustment term to prevent excessive overshoot. 

 𝑊𝑓𝑥 = 𝐾𝑝 𝛥 − ∫ 𝐾𝐼
(𝜏−𝑡)𝜏

0
𝑊𝑓 (𝑡 − 1)𝑑𝑡     (𝑡 = 1,2,3, . . . , 𝜏) (1) 



Effects of Monitoring Signal Hysteresis on Speed Regulation for the Aero-Derivative Gas Turbine 5 

where Wfx is the fuel quantity difference, x is the different control variables substituted, KP 

is the proportional gain coefficient, KI is the integral gain coefficient, ∆ is the deviation 

between the limit condition value or the target value of the control variable and the current 

state value, Wf is the fuel increment fed back after priority selection and τ is the number of 

control logic operations that have been run. 

Table 1 Composition of fuel quantity algorithm logic 

Number Fuel quantity control sub circuit Abbreviation Type 

1 Gas generator speed regulation PID_GG Main 

2 Gas generator maximum speed limit regulation PID_GGH Limit 

3 Gas generator acceleration limit adjustment PID_NCA Limit 

4 Gas generator outlet temperature limit regulation PID_T5 Limit 

5 Compressor outlet pressure limit regulation PID_P3 Limit 

6 Compressor outlet temperature limit regulation PID_T3 Limit 

7 Maximum deceleration rate limit regulation PID_NCD Limit 

8 Minimum fuel limit regulation PID_WMIN Limit 

9 Maximum fuel limit regulation PID_WMAX Limit 

2.2.2 Fuel quantity optimization logic 

Since the MIN-MAX selector has multiple input items and only one output is executed, 

which can effectively limit the fuel quantity within the safe range, the fuel quantity 

optimization logic is designed by using the MIN-MAX selector. The designed fuel quantity 

optimization logic is shown in Fig. 3. It contains 9 input items and is selected in three steps, 

and finally outputs the fuel quantity that meets various restriction conditions. 

 

Fig. 3 Logical structure of fuel quantity optimization 

The fuel priority selection logic is designed as a three-level priority with the following 

main functions: 

a. The first priority uses the minimum selector selection to ensure that the fuel 
increment obtained does not exceed the safety limit. 

b. Second priority uses maximum selector selection to ensure fuel increment is greater 
than PID_ WMIN to avoid lean oil extinguishing. 

c. The third priority uses the minimum selector to ensure that the final output fuel 
increment is less than the PID_ WMAX to prevent the gas turbine from rising too fast. 



Z. ZHAO, W. ZHOU, P. LIU, Z. LIU 6 

2.3 Hysteresis model of monitoring signal 

In order to achieve the effect of monitoring signal transmitting real data periodically, a 

monitoring signal lag model is established based on the monitoring signal lag principle 

described in Eq. (2.a) and Eq. (2.b) Establishment of a hysteresis model by adding a zero-

order retention module after the monitoring signal output module of the gas turbine model 

and providing a rate conversion module to ensure consistent sampling time. The sampling 

time of the zero-order hold module is hysteresis time, which can be set to 0.1s, 0.2s, etc. as 

needed. 

 𝑛𝑇 ≤ 𝑡 ≤ (𝑛 + 1)𝑇    𝑛 = 0,1,2,3 … (2.a) 

 𝑢(𝑡) = 𝑢(𝑛𝑇)          𝑛 = 0,1,2,3. .. (2.b) 

where T is the hysteresis time, t is the sampling time, u(T) is the signal value at the current 

sampling time and u(nT) is the signal value at the last sampling time. 

3. EXPERIMENTAL SCHEME AND MODEL VERIFICATION 

3.1 Experimental scheme 

The monitoring signal hysteresis mainly comes from two aspects: sensor fault and 

control system fault. Although either cause has little impact on the speed control, the 

impact after the superposition of the two cannot be ignored. In order to explore the 

influence of single monitoring signal hysteresis on speed control, the experimental scheme 

is designed with pressure signal and speed signal as variables. In addition, the experimental 

scheme is designed by coupling speed signal and pressure signal and combining the 

analysis results of single signal hysteresis. 

3.1.1 Experimental scheme of pressure signal 

The proportional gain coefficient (KP) in the fuel quantity algorithm is selected through 

the difference table, and the pressure signal is the input of the difference table. As the main 

influence factor of KP, the pressure signal will lead to deviation in the selection of KP once 

the hysteresis phenomenon occurs. Therefore, it is necessary to study the influence of the 

pressure signal hysteresis on the speed control. In order to obtain the influence law of 

pressure signal hysteresis on speed control, the selected pressure signal hysteresis time T_P 

as shown in Table 2, there are 10 experimental schemes. 

Table 2 Pressure hysteresis time (T_P) 

Plan 1 2 3 4 5 6 7 8 9 10 

T_P(s) 0.1 0.7 1.4 3.5 7 14 21 28 35 50 

3.1.2 Experimental scheme of speed signal 

The start-up stage of a gas turbine is usually judged by the gas generator speed. Once 

the speed signal is delayed, it will inevitably affect the judgment of the gas turbine start-up 

process. Therefore, it is necessary to study the effect of speed signal hysteresis on speed 



Effects of Monitoring Signal Hysteresis on Speed Regulation for the Aero-Derivative Gas Turbine 7 

control. In order to obtain the law of the influence of speed signal hysteresis on speed 

control, the selected speed hysteresis time T_S shown in Table 3, there are seven 

experimental schemes. 

Table 3 Temperature hysteresis time (T_S) 

Plan 1 2 3 4 5 6 7 

T_S(s) 0.1 0.2 0.3 0.4 0.5 1 3 

3.1.3 Experimental scheme of coupling pressure signal and speed signal 

As the gas turbine usually works in the environment of high temperature and high 

pressure, it is very easy to have problems such as sensor performance degradation and 

sensitivity deterioration. Therefore, it is necessary to consider the influence of various 

monitoring signal hysteresis, couple the pressure signal and speed signal, and design the 

coupling scheme according to the influence law of single signal hysteresis. The designed 

coupling scheme is shown in Table 4, including 9 coupling schemes. 

Table 4 Hysteresis time coupling scheme of monitoring signal 

Plan 1 2 3 4 5 6 7 8 9 

T_P(s) 0.1 0.1 0.1 14 14 14 35 35 35 

T_S(s) 0.1 0.5 1 0.1 0.5 1 0.1 0.5 1 

3.2 Model validation 

In order to verify the function of the hysteresis model of the monitoring signal, the 

hysteresis time of a single monitoring signal is calculated as a variable and compared with 

the parameters without hysteresis. The comparison results are shown in Fig. 4. 

 

Fig. 4 Monitoring signal hysteresis curve: (a) Speed hysteresis, (b) Pressure hysteresis 

From Fig. 4, it can be seen that the speed hysteresis curve is similar to the normal 

operation curve, and the hysteresis phenomenon is obvious. The pressure hysteresis will 

result in a smaller pressure output value, and the difference between the pressure hysteresis 

curve and the normal operating curve is a necessary phenomenon. Therefore, the 



Z. ZHAO, W. ZHOU, P. LIU, Z. LIU 8 

established monitoring signal hysteresis model has a good ability to reproduce the 

phenomenon of monitoring signal hysteresis. 

4. EFFECT OF SINGLE MONITORING SIGNAL HYSTERESIS 

4.1 Performance index 

4.1.1 Adjustment time 

Adjustment time is the shortest time that a controlled variable changes from a previous 

stable state to a new stable state when the control system is affected by external 

disturbances. In fact, the shortest time required for a control variable to enter a new steady-

state value of ± 5% is called the adjustment time of the control system. The adjustment 

time is calculated as shown in Eq. (3): 

 𝑇𝑆 = 𝑇2 − 𝑇1 (3) 

where TS is the adjustment time, T2 is the time when the controlled variable reaches a new 

balance state, and T1 is the time when the controlled variable begins to adjust. 

4.1.2 Overshoot 

The ratio of the maximum deviation of the adjustment parameter to the steady state 

value is called overshoot during the adjustment of the control system, and the maximum 

deviation refers to the deviation between the maximum value of the adjustment parameter 

and the steady state value. In this paper, for a clearer comparison and analysis, the 

maximum deviation of the adjustment parameters is defined as overshoot, and the 

overshoot is solved by Eq. (4):  

 𝜎 = 𝐺𝐺𝑀𝐴𝑋 − 𝐺𝐺𝑆𝑆𝑉  (4) 

where σ is overshoot, GGMAX is the maximum output value of the adjusted parameter, GGSSV 

is the steady-state value of the adjusted parameter. 

4.2 Effect of pressure signal hysteresis 

In order to obtain the changing trend of gas generator speed when the pressure signal 

is hysteresis, the calculation is carried out according to the 10 pressure signal hysteresis 

schemes described in Table 2, and the calculation results are shown in Fig. 5. 

It can be got from Fig. 5 that when the pressure signal hysteresis exists, the gas 

generator speed mainly presents four phenomena: 

a. The gas generator speed has obvious overshoot (the target speed is 6800rpm), and 
the overshoot gradually disappears with the increase of T_P. 

b. When the T_P exceeds 3.5 seconds, the speed of the gas generator remains at 4600 
rpm, which is called the speed suspension phenomenon. 

c. When the T_P exceeds 35 seconds, the speed decreases. In the actual operation 
process, this phenomenon will trigger the downtime process. 

d. When the T_P exceeds 50 seconds, the speed of the gas generator cannot reach the 
speed demand value. 



Effects of Monitoring Signal Hysteresis on Speed Regulation for the Aero-Derivative Gas Turbine 9 

 

Fig. 5 Contour chart of gas generator speed when pressure signal is hysteresis 

In order to further determine the influence of pressure signal hysteresis, the influence 

degree of pressure signal hysteresis on speed control is analyzed by taking performance 

parameters such as overshoot and adjustment time as evaluation criteria. The adjustment 

time and the solution of the overshoot follow Eq. (3) and Eq. (4) and the results are shown 

in Fig. 6. 

As shown in Fig. 6, on the one hand, with the increase of T_P, the speed adjustment 

time gradually increases, and finally tends to 60 seconds, which fails to reach the target 

speed of 6800 rpm. On the other hand, with the increase of T_P, the speed overshoot 

decreases gradually, and eventually tends to -800rpm, which means that the speed fails to 

reach the expected target. Therefore, the pressure signal hysteresis will cause higher 

adjustment time for gas generator speed, and even make the speed cannot reach the target 

speed. 

 

Fig. 6 Performance parameters for pressure signal hysteresis: (a) Adjustment time, (b) 

Overshoot 

Since the fuel quantity is the main variable to control the speed, and the fuel quantity 

is selected by the nine types fuel quantity regulation output through the fuel quantity 

optimization logic, in order to further analyze the reasons for the above phenomena, the 

selected data are shown in Fig. 7 and Fig. 8. 



Z. ZHAO, W. ZHOU, P. LIU, Z. LIU 10 

 

Fig. 7 Fuel quantity curve with pressure signal hysteresis: (a) T_P=0.1s, (b) T_P=3.5s, 

(c) T_P=35s, (d) T_P=50s 

Since the fuel quantity is the main variable to control the speed, and the fuel quantity 

is selected by the nine types fuel quantity regulation output through the fuel quantity 

optimization logic, in order to further analyze the reasons for the above phenomena, the 

selected data are shown in Fig. 7 and Fig. 8. 

As shown in Fig. 7, fuel quantity and T_P is inversely proportional, and there is a step 

supply phenomenon. The main manifestation is that when T_P is small, the fuel quantity 

curve fluctuates sharply. When T_P is large, the fuel quantity curve gradually flattens and 

presents a step supply phenomenon, which ultimately results in a slow increase in gas 

turbine speed. 

As shown in Fig. 8, with the increase of T_P, PID_GG and PID_WMAX show different 

degrees of hysteresis phenomenon, and PID_P3 is always larger than PID_GG and 

PID_WMAX, which has no effect on the results of fuel optimization. Further analysis of 

PID_GG and PID_WMAX reveals that the main reasons for this phenomenon are: 

a. The proportional gain factor (KP_GG) of the PID_GG is determined by the outlet 
pressure of the compressor. The principle is that the pressure at the outlet of the compressor 

is used as the input of the two-dimensional difference table, KP_GG is selected, and 

PID_GG is calculated. Once the outlet pressure of the compressor is hysteresis, the selected 

value of KP_GG cannot meet the speed adjustment requirements, and the speed of the gas 

generator rises slowly. 

b. Compressor outlet pressure is directly involved in the calculation of PID_WMAX. 



Effects of Monitoring Signal Hysteresis on Speed Regulation for the Aero-Derivative Gas Turbine 11 

When the pressure at the outlet of the compressor is lagged, the calculated value of 

PID_WMAX is smaller, which results in a smaller result of fuel quantity optimal selection, 

insufficient fuel supply, and the gas generator speed is difficult to reach the target value. 

 

Fig. 8 Fuel quantity regulation output curve with pressure signal hysteresis: (a) T_P=0.1s, 

(b) T_P=3.5s, (c) T_P=35s, (d) T_P=50s 

4.3 Effect of speed signal hysteresis 

In order to obtain the changing trend of gas generator speed when the speed signal is 

hysteresis, the calculation is carried out according to the 7 speed signal hysteresis schemes 

described in Table 3. The calculation results are shown in Fig. 9. 

In order to further determine the influence of speed signal hysteresis, the influence of 

speed signal hysteresis on speed control is analyzed by taking performance parameters such 

as overshoot and adjustment time as evaluation criteria. The corresponding adjustment time 

and overshoot, which are settled according to Eq. (3) and Eq. (4), are shown in Fig. 10. 

It can be seen from Fig. 10 that when the speed signal is hysteresis, the gas generator 

speed mainly exhibits two phenomena: 



Z. ZHAO, W. ZHOU, P. LIU, Z. LIU 12 

a. With the increase of T_S, the gas generator speed gradually tends to steep and the 
peak gradually increases. 

b. With the increase of T_S, the gas generator speed curve shows a stepped upward 
trend in varying degrees. When T_S is 3 seconds, the gas generator speed curve cannot 

reach a steady state, and fluctuates repeatedly in the range of 6000 rpm to 7800 rpm. 

 

Fig. 9 Gas generator speed curve with speed signal hysteresis 

 

Fig. 10 Performance parameters for speed signal hysteresis: (a) Adjustment time, (b) 

Overshoot 

On the one hand, the adjustment time is inversely proportional to T_S, on the other hand, 

with the increase of T_S, the overshoot increases gradually. When T_S is 3 seconds, the 

overshoot and adjustment time are difficult to calculate due to the sharp fluctuation of 

speed, so the adjustment time is the maximum of the expected adjustment time. 

Using the same analysis method as pressure signal hysteresis, the influence mechanism 

of speed signal hysteresis is analyzed. The selected data are shown in Fig. 11 and Fig. 12. 

From Fig. 11, it can be seen that with the increase of T_S, the amount of fuel increases 



Effects of Monitoring Signal Hysteresis on Speed Regulation for the Aero-Derivative Gas Turbine 13 

gradually, the degree of chaos decreases, and the cycle regulation mode tends. From Figure 

12, with the increase of T_S, the step phenomenon becomes obvious, the step number 

decreases, and the chaos degree of fuel optimization results decreases. 

The main reason for the above phenomenon is that when there is a velocity signal 

hysteresis, the speed adjustment is equivalent to the multiple step adjustment mode. The 

number of steps is inversely proportional to T_S, the period of steps is positively 

proportional to T_S. 

a. When T_S is small, the number of steps is large and the step cycle is short. In order 
to meet the requirements of speed adjustment, fuel adjustment changes frequently, resulting 

in sharp fluctuations in fuel quantity. 

b. With the increase of T_S, the number of steps decreases and the period of steps 
increases. At this time, the speed adjustment is closer to the target, and the fluctuation of 

fuel quantity and fuel quantity regulation is reduced. 

c. When T_S is 3 seconds, the number of steps is the smallest and the step cycle is the 
longest. As shown in Figure 9, during the fourth step cycle, it is always considered that the 

speed does not reach the target value, the fuel quantity and fuel quantity adjustment 

continue to increase and exceed the demand value. During the fifth step cycle and sixth 

step cycle, the rotation speed starts to revert, and the fuel and fuel adjustments continue to 

decrease and fall below the demand value. Rotation speed adjustment shows cyclic 

regulation, which is manifested by repeated fluctuations of rotation speed in the range of 

6000rpm to 7800rpm. 

 

Fig. 11 Fuel quantity curve with speed signal hysteresis: (a) T_S=0.1s, (b) T_S=0.3s, (c) 

T_S=0.5s, (d) T_S=3s 



Z. ZHAO, W. ZHOU, P. LIU, Z. LIU 14 

 

Fig. 12 Output curve of fuel quantity regulation in case of speed signal hysteresis: (a) 

T_S=0.1s, (b) T_S=0.3s, (c) T_S=0.5s, (d) T_S=3s 

5. INFLUENCE OF HYSTERESIS COUPLING OF MONITORING SIGNAL 

In order to obtain the speed control performance of multiple monitoring signals with 

hysteresis coupling, a coupling scheme is designed according to the influence rule of single 

monitoring signal hysteresis, which is used to calculate the gas generator speed as shown 

in Table 4. Deep analysis is made from the angle of control performance parameters, fuel 

quantity and fuel quantity adjustment. The calculation results of the gas generator speed 

are shown in Fig. 13. The main variation rules of the speed are as follows: 

a. When T_P is constant, the gas generator speed curve tends to steep with the 
increase of T_S, and the more obvious peaks occur when T_P is 0.1 seconds. 

b. When T_S is constant, the gas generator speed curve tends to be flat with the 
increase of T_P, and secondary regulation occurs when T_S is 35 seconds. 



Effects of Monitoring Signal Hysteresis on Speed Regulation for the Aero-Derivative Gas Turbine 15 

 

Fig. 13 Monitor the gas generator speed when the signal is hysteresis coupling 

 

Fig. 14 Speed performance when monitoring signal hysteresis coupling: (a) Adjustment 

time, (b) Overshoot 

The adjustment time and overshoot are calculated and analyzed by Eq. (3) and Eq. (4). 

The calculation results of adjustment time and overshoot are shown in Fig. 14. As shown 

in Fig. 14, on the one hand, the adjusting time is mainly affected by T_P, and the adjusting 

time is proportional to T_P, the adjusting time decreases slightly when T_S increases. On 

the other hand, pressure signal hysteresis has a great effect on overshoot, and the overshoot 

is inversely proportional to T_P, the overshoot increases slightly with T_S increases. 



Z. ZHAO, W. ZHOU, P. LIU, Z. LIU 16 

 

Fig. 15 Fuel quantity curve under hysteresis coupling of monitoring signal: (a) Plan 4, (b) 

Plan 5, (c) Plan 6 

In order to further analyze the mechanism of the effect of the hysteresis coupling of the 

monitoring signal on the speed control, a discussion is made from the angle of fuel quantity 

and fuel quantity regulation, which is shown in Fig. 15 and Fig. 16. As shown in Fig. 15, 

the fuel quantity curves of the three coupling schemes have the same trend with only 

different oscillations. Both T_P and T_S in plan 4 are smaller, resulting in smaller 

proportional gain factor, more steps and shorter step cycle, and sharp fluctuation of fuel 

quantity curve. As T_P increases, the fluctuation of the fuel quantity curve decreases. 

Therefore, the influence on the speed adjustment is the overlap of pressure hysteresis and 

speed hysteresis after the monitoring signal hysteresis coupling. 

The main reasons for the above changes are as follows: firstly, the coupling of pressure 

signal hysteresis and speed signal hysteresis will not only affect the selection of 

proportional gain coefficient and the calculation value of maximum fuel quantity in the 

output of fuel quantity regulation, but also change the speed regulation into a multi-step 

regulation mode. Secondly, the pressure signal is one of the main parameters in the fuel 

quantity algorithm. Compared with the speed signal, the pressure signal has a more direct 

influence on the fuel quantity control. Thirdly, the speed signal hysteresis only affects the 

speed adjustment mode, making the speed more tend to the multi-step adjustment mode, 

and the impact on the fuel quantity control is indirect. 



Effects of Monitoring Signal Hysteresis on Speed Regulation for the Aero-Derivative Gas Turbine 17 

 

Fig. 16 Output curve of fuel quantity regulation under hysteresis coupling of monitoring 

signal: (a) plan 4, (b) Plan 5, (c) Plan 6 

6. CONCLUSION 

This paper takes an aero-derivative gas turbine for power generation as the research 

object and carries out two aspects of research. On one hand, the influence of pressure signal 

hysteresis and speed signal hysteresis on speed control is studied. On the other hand, the 

influence of monitoring signal hysteresis coupling on the speed control is also considered. 

The main conclusions are as follows: 

1．Hysteresis of pressure signal will affect the selection of proportional gain 
coefficient and the calculation of maximum fuel quantity limit value, resulting in deviation 

of fuel quantity supply, speed suspension of gas turbine and even trip failure. 

2．The speed signal hysteresis changes the speed control into a multi-step regulation 
mode, which results in frequent changes and confusion of fuel supply, serious overshoot 

of gas generator speed and even speed oscillation. 

3．The effects of pressure signal hysteresis and speed signal hysteresis will be 



Z. ZHAO, W. ZHOU, P. LIU, Z. LIU 18 

combined when the coupling monitoring signal hysteresis is considered, and pressure 

signal hysteresis is the main influencing factor, resulting in very complex speed adjustment 

and a longer time for gas generator speed adjustment. 

Acknowledgement: This work was supported by the Project funded by China Postdoctoral 

Science Foundation (Grant No. 2018M642177) and the Zhejiang Postdoctoral Preferential 

Foundation (Grant No. zj2018009). 

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