Academic Journal of Science and Technology 
ISSN: 2771-3032 | Vol. 8, No. 2, 2023 

 

18 

Simulation	Design	of	Level	Cascade	Control	System	for	
Double‐capacity	Water	Tanks	
Yanping Li 

Department of Information Engineering, Ordos Institute of Technology, Ordos 017000, China 

 

Abstract: As a typical representative of process control, double-capacity water tank level control is a common automation 
control system used to control the level of two tanks to achieve level stabilisation and control, which is widely used in various 
fields of industrial production. Liquid level control is the key to the performance of the whole control system due to the existence 
of hysteresis and other problems in the control. Serial control of the sub-loop has a rapid control role, it can effectively overcome 
the impact of the disturbance into the sub-loop, improve the dynamic characteristics of the object, so in order to achieve better 
control performance, this design uses serial control to achieve the level of double-capacity water tank fixed value control. 
Double-capacity water tank level series control system to the tank level as the controlled quantity, first of all, the characteristics 
of the tank, the establishment of its mathematical modelling, and then the use of MATLAB on the simulation of the tank as well 
as PID parameter adjustment, and finally through the response curve to analyze the control performance of the system. The 
simulation results show that the double-capacity water tank level series control performance is good, the system can achieve the 
level of static-free regulation, and anti-interference ability is strong, with good dynamic and steady state performance. 

Keywords: Double-capacity water tank, Cascade control, PID, Simulation. 
 

1. Introduction 
With the continuous development of industrialisation and 

urbanisation, level control systems have become an important 
part of modern production. In the actual production of 
industry, the accuracy and control effect of liquid level control 
directly affects the production cost of the factory, economic 
benefits and even the safety factor of the equipment. Double-
capacity tank level cascade control system to achieve stable 
control of two tanks level to meet the production and life 
needs, is a common level control system, widely used in a 
variety of liquid storage and delivery areas. Although there 
have been many researches on liquid level control system, 
there are still some problems in practical application, such as 
low control accuracy, poor stability, slow response time and 
so on[1]. Therefore, in-depth research and optimisation of the 
double-capacity tank level cascade control system is needed 
to improve the performance and stability of the system. This 
paper focuses on the simulation implementation of the 
double-capacity water tank level cascade control system, and 
focuses on the influence of the control algorithm on the 
system control performance. 

2. Modelling 

2.1. Characteristics of the object  
The overall structural block diagram of the second-order 

double-capacity level control object is shown in Figure 1. 
Take the level H2 of the middle water tank as the main 
parameter and the level H1 of the upper water tank as the 
subparameter, the output of the main regulator is the given 
value of the subregulator, the main loop is a fixed-value 
control system, and the sub-loop is a follower control system. 
The change of water inlet Q1 first makes the upper tank level 
H1 change, the inflow of Q1 on the controlled variable H2 
influence process is more indirect and complex, which also 
exposes the weakness of the single-loop control is poor, and 
the control of the series control system is superior to make up 

for these shortcomings, and make the outflow H2 tend to 
stabilise[2-3]. 

 

 
Figure 1. Second-order double-capacitance level control 

object 
 
The purpose of the serial control system is to make the 

system have good dynamic and steady state performance, 
ensure the control quality of the main controlled quantity, and 
realise non-differential regulation. When there is a 
disturbance in the sub-loop, because the time constant of the 
main controlled object is larger than that of the sub-loop, the 
sub-loop has already made a quick response when the main 
controlled quantity is not reflected, which eliminates the 
influence of the disturbance on the main controlled quantity 
in a timely manner. In addition, if the perturbation acts on the 
main controlled object, the existence of the sub-loop greatly 
reduces the time constant of the subcontrolled object, thus 
speeding up the response of the system and improving the 
dynamic performance. 

From the above figure, it can be seen that the object under 
test consists of two tanks connected in series, which is called 
a double-capacity tank. According to the principle of single-
capacity tank characteristic test, it can be seen that the 
mathematical model of double-capacity tank is the product of 



 

19 

two single-capacity tank mathematical model, i.e., the 
mathematical model of double-capacity tank can be described 
by a second-order inertia link[4-5]: 

 

G(s)=G1(s)G2(s)=
)1)(1(11 212

2

1

1







 sTsT

K

sT

k

sT

k
  (1) 

 
Where K = k1k2, is the amplification factor of the double-

capacity tank, and T1 and T2 are the time constants of the two 
tanks, respectively. 

2.2. Modelling of the object  
In the experiment, a step signal is input to the upper water 

tank to make its level leave the original equilibrium state. 
After a certain adjustment time, the tank level re-entered the 
equilibrium state. Using the curve fitting method of 
MATLAB, the experimentally measured data were fitted, and 
the transfer function of the water tank was calculated through 
the tangent method, resulting in a MATLAB curve fitting 
diagram shown in Figure 2: 

 

 
Figure 2. Fitted curve of the upper tank 

 
In the experiment, the lower tank generates a step signal to 

make its liquid level leave the original equilibrium state. After 
a certain adjustment time, the tank level re-entered the 
equilibrium state. The curve fitting method of MATLAB is 
used to fit the experimentally measured data, and the transfer 
function of the water tank is calculated through the tangent 
method, resulting in a MATLAB curve fitting diagram shown 
in Figure 3: 

Figure 3. Fitted curve of the lower tank 
 
According to the curve using tangent graphing method to 

calculate the upper and lower tank characteristic parameters, 
from the upper and lower tank transfer function to the double-
capacity tank transfer function is:  

 

y=
17.98

083.0

s
×

1s2.244

097.0


                  (2) 

 

2.3. PID control algorithm 
The PID algorithm is one of the most widely used 

algorithms in industrial applications, which can automatically 
correct the control system accurately and quickly in the 
control of closed-loop systems. PID control is a linear 
combination of proportional, integral, and differential 
deviations to form a control quantity, which can be used to 
bring the controlled variable in the control system to the 
desired value or to stabilise it within the desired range[6]. The 
PID control algorithm can be expressed as follows: 

 

]
)(

)(
1

)([)(
0 dt

tde
Tdte

Ti
teKptU

t

        (3) 

The PID control algorithm is representable in the form of a 
transfer function:  

 

)
1

1(
)(

)(
)( Tds

Tis
kp

sE

sU
sG         (4) 

3. Simulation Results 
The series level control system is simulated using Simulink 

tool and the system simulation is shown in Fig 4: 
 

 
Figure 4. Simulation of the serial control system 



 

20 

 
In order to verify the superiority of the series control 

system of the dual-capacity water tank, a single-pole, double-
throw switch is added to the system simulation block diagram, 
which can be used to derive two different control systems, a 
control system with added sub-loop control, i.e., the series 
control system, and a single-loop control system without sub-
loop control, respectively. Double-capacity tank level control 

system using PID control algorithm to achieve constant value 
control of the tank level, PID control parameters using the 
trial and error method for parameter calibration, after repeated 
trial and error, to get the proportional time constant of 250, 
the integral time constant of 2 seconds, the differential time 
constant of 5 seconds, the simulation curve is shown in the 
following figure: 

 

 
Figure 5. Single-loop PID control waveforms 

 

 
Figure 6. Cascade control PID control waveforms 

 
From the above two graphs, it can be seen that under the 

action of the same PID control parameters, the regulation time 
of the series control is about 200s, and the regulation time of 
the single-loop PID control is about 1450s, and the overshoot, 
volatility, and steady-state error of the series control are 
smaller compared with that of the single-loop control, which 

can be seen that the rapidity, stability, and accuracy of the 
series control are better than that of the single-loop control 
system. In order to verify the anti-disturbance capability of 
the serial control, a disturbance signal is added to the control 
loop for simulation, and the system simulation structure is 
shown in Fig. 8: 

 

 
Figure 7. Simulation of a series system with added perturbation 

 
The effect of the perturbation on the waveform is analysed 

in the original unchanged system to compare the effect of the 
perturbation on the control performance of the system, and 
the waveforms of the two control loops are shown below: 

 



 

21 

 
Figure 8. Single-loop PID control waveform with added perturbation 

 

 
Figure 9. Series loop PID control waveform with added perturbation 

 
From the above two graphs, it can be seen that after the 

perturbation is added at 2500 seconds, the system with simple 
loop control takes a longer time to return to the smooth state 
from the perturbation, while the time for the series system is 
very short, and it can be seen that the perturbation has less 
effect on the series system, which proves the superiority of 
the control performance of the series system. 

4. Conclusion 
Through the above simulation results can be obtained, 

compared with the use of conventional single-loop control, 
the use of series-level control to achieve the level of dual-
capacity tank fixed-value control system has a good 
performance in terms of dynamic characteristics, steady-state 
characteristics and anti-interference characteristics, suitable 
for industrial production, can effectively improve the real-
time, accuracy and smoothness of the production process. 

Acknowledgment 
This work is supported by Natural Science Foundation of 

Inner Mongolia (2022MS06014) and Research Program of 
Science and Technology at Universities of Inner Mongolia 

Autonomous Region (NJZY22210). 

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