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This experiment will show the system model type and control it using Matlab’s tools.



In this experiment, we will deal with a fluid control system with a DC motor which will be driving the valve to keep the flow of the fluid under control at two cascaded tanks. The second tank level should be controlled in order to control the system as shown below.






Parameters and Variables: 

The parameters of the electrical circuit and the DC motor are as follows

La= 0.05 Henry                                  armature inductance

Ra= 0.5 Ω                                           armature resistance

Ja= 0.1 N-m-                               armature polar moment of inertia

Jl= 0.05 N-m-                              valve polar moment of inertia

Ba= 0.05 N-m sec                              armature damping coefficient

Bl= 0.05 N-m-sec                               valve damping coefficient

Ke= 0.1 volt-sec                                 back e.m.f constant

Kt= 0.5 N-m/amp                               motor torque constant


The parameters and variables for tank 1

h1= m                                                height of fluid in tank

A1= 0.25                                      area of tank

Qi1= /sec                                     volumetric flow into tank

Qo1= /sec                                     volumetric flow out of tank

P1= 0.1 /sec                                 coefficient relating pump flow to motor position Qi1=P1θm

R1= 0.5 sec/                                 coefficient relating flow out of tank to height of fluid



The parameters and variables for tank 2

H2= m                                               height of fluid in tank

A2= 0.5                                        area of tank

Qi2= /sec                                     volumetric flow into tank

Qo2= /sec                                     volumetric flow out of tank

R2= 0.2 sec/                                 coefficient relating flow out of tank to height of fluid



Dynamic modeling and Development of Transfer functions:


Electrical modeling:



Mechanical modeling:



Where          and


Laplace Transformation:

  • For the Electrical model:




  • For the Mechanical model:



  • Simplify and relate Eq (1) to Eq (2):



From Eq (1)


From Eq (2)                                  (4)


Put Eq (4) in Eq (3)        (5)


From Eq (5)          (6)


From Eq (6)                  (7)


From Eq (7)                      (8)



Tank 1 modeling:






Tank 2 modeling:








Laplace Transformation:


  • For Tank 1:






  • For Tank 2:








  • Simplify and relate Eq (9) to Eq (10):




From Eq (10)                        (11)



Put Eq (11) in Eq (9)          (12)



From Eq (12)                          (13)



From Eq (13)                                  (14)


Now, multiply the relationship between the electrical and mechanical models by the relationship between tank1 and tank2:






After plugging in the values and solving:


Block diagram for the Open Loop system:














Block diagram for the Closed Loop system and the controller:

  1. Proportional P-Controller:



Here we can see the time response of the output with respect to the input in both ways with and without the P-Controller. Controller parameters, Performance, and Robustness is clearly shown in the figure with their values.

The bode phase plot is shown frequency vs. phase (deg) and Magnitude (dB) with and without the P-Controller. In the first case Frequency vs. Magnitude, we can clearly see that the system is getting additional inputs than the system needs without the controller when the frequency is at 0.1 rad/sec and at 1 rad/sec with the P-Controller. The second case phase vs. frequency, we can see that there is a slight delay to make 180 deg phase at 0 dB gain frequency.


The figure shows the system is stable when the gain is from 0 to 33.9. In the other hand, the system is unstable when the gain is from 34 to infinite.



  1. Proportional Integral Derivative PID-controller:




Time response of the output with respect to the input in both cases: with P-controller and PID-Controller along with the controller parameters, performance, and robustness.

The bode phase plot is shown both P-Controller and the PID-Controller frequency response. In the magnitudes vs frequency, we can see the system is getting additional input than it needs when the frequency axes is at 1 rad/s with the P-Controller and when the frequency is at 7 rad/s. In addition, there is a delay shown to make 180 deg at 0 dB gain in the phase vs. frequency


The project was experimentally shown how the open and closed loop system responses when different tests have been implemented on the system; no controller, P-Controller, and PID-Controller. Throughout the experiment, we observed the difference between the P-Controller is being applied on the system and PID controller. We observed that the system will react better when PID-Controller is applied to the system rather than P-Controller. For instance, the settling time when we applied P-Controller to the system was 9.55 sec where the PID controller shows 3.51 sec. In addition, we see less time and lag when we applied PID-Controller in overshoot, rise time, and peak.

System type:

According to the transfer function, it shows that the system is type 1.


In this experiment, we applied different types of controller on a fluid control system that is driven motor in order to control the valve in the cascaded tanks. Between the two types of controller, P Controller and PID Controller, we see a big difference in the second type when we applied it to the control system. We see faster system with better performance when we tested the system experimentally. In summary, PID controller has proved that it will make the system faster and respond better.


Summary of contribution to the project:

All the team members worked and shared their knowledge in order to get this project done on time. Each member worked accordingly to their part of the project.

















  1. Control Theory Project Outline.
  2. The Lecture Note of the course 06-92-321 F16.
  3. DYNAMIC SYSTEMS modeling, simulation, and control by Craig A.Kluever.









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