Course material

1. Answer: Introduction A tank level control system is a device
Answer:
Introduction
A tank level control system is a device that maintains the volume of fluid in storage tanks.
The main purpose of these systems is to control the speed at which the fluid pump supplies
fluid to the tank in order for it to reach the correct level inside [1]. The job of the tank level
system is to maintain a constant fluid level in the tank. In industrial operations, tank level
control mechanisms are commonly employed.
Open And Closed Loop Systems
An open loop system is the most basic control system in which the system does not have the
potential to correct any errors that may arise from external disturbances. A closed loop
system on the other hand has a feedback path between the output and the reference or
setpoint [2]. This allows the system to self-regulate in the case of negative feedback. A
closed loop negative feedback system can reject external disturbance and correct errors.
Feedback control's success is due to the fact that it makes everything faster, more precise,
and less sensitive to disruptions [3]. Because of its simplicity, open loop control is only
recommended in systems where the outputs and inputs are known and there is no
disturbance [4]. There is a significant downside to systems with feedback control, which is
the possibility of the system being unstable. To avoid this, the suitable controller should be
selected. The most widely used controller is the PID controller which allows both the
system’s transient and steady state response to be controlled [5]. It consists of three control
actions namely proportional control, integral and derivative control. Proportional control
can reduce the steady state error. However, it can also increase the overshoot. Integral
control allows the steady state error to be completely eliminated. However, it may increase
the system’s overshoot and the number of oscillations which could drive the system into
instability [6]. The major effect of derivative control is to reduce the overshoot making the
system more stable.
Objective
The objective of this exercise is to investigate the open and closed loop dynamics of a single

2. tank fluid rig with the aim to:
Establish open and closed loop transfer functions and block diagrams
make observations of open and closed loop response
Open Loop Modeling
Also,
The overall open loop transfer function then becomes,
Figure 1: Open loop block diagram
Theoretical transfer function
Therefore,
Closed loop modeling
Therefore,
Given that,
Overshoot,
Results
Open Loop Response

3. Figure 2: The open loop Response
Closed Loop Response
Tests 1,2 and 3
Figure 3: Closed loop response for test 1,2,3
Tests 4, 5 and 6
Figure 4: Closed loop response for test 4,5,6
Discussion
The system’s open loop response is shown in figure 2 with a step input of . The response
shows the variation of the water level and the flow rate. The response shows that the open
loop system exhibits a large steady state error as neither nor approaches the reference
voltage of . The large steady state error can be attributed to the fact that the system does not
have any feedback mechanism to correct this error.
This problem can be addressed by introducing a negative feedback path between the output
and the reference signal in conjunction with a controller. This yields a closed loop negative
feedback system capable of correcting errors in the flow rate and the tank level. In this
exercise the effects of the control actions of a PID controller was investigated. In test 1, a
proportional controller was investigated by setting and to zero. In this case, exhibits a
large overshoot over the setpoint but eventually settles to a value smaller than the
reference. Similarly is much smaller compared to the reference, hence proportional control
used individually cannot eliminate the system error.
In test 2, a controller is investigated with , and . The response in this case is identical to the
first test. In test 3, the proportional gain was increased to with and set to zero. In this case,
the steady state error in both and reduced due to the increased gain. The introduction of
the integral gain in test 4 greatly changes the response. In this case, the steady state error is
almost eliminated completely. However, it can be observed that the response has multiple
overshoots hence it becomes more oscillatory. Increasing the integral gain further in test 5
increases the amplitudes of the overshoots but reduces the steady state error further. Test 6
investigates the effects of the 3 control actions with , and . In this case, it can be observed
that the steady state error was completely eliminated while the number as well as the
amplitudes of the oscillations was very small.

4. Conclusion
The results obtained from this experiment clearly demonstrate the effects of closed loop
control on a system’s response. Generally, the open loop system has poor transient and
steady state response, with a large steady state error. Introducing closed loop control
greatly improves the response. With the appropriate selection of the PID control
parameters, the steady state error can be eliminated and the settling time and rise time
tuned as desired.
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