Tuning PID Controllers for Optimal Performance

This assignment requires students to explain how they would tune a PID controller used to control the oil flow rate in an oil refinery. It also asks them to consider the tuning process for a Lasik eye surgery laser beam system, where the goal is to fix the eye rather than burn the cheek. Additionally, students are expected to evaluate and modify values in Butterworth filters based on raw data.

Mechatronic System Design

1) Explain how you would tune a PID controller used to control the oil flow rate in an
oil refinery. (Hint: It does not matter much what the system is, the conceptual
tuning process is the same/similar.)
Answer:
Generally, the controlling process of a PID controller is adjustable with the help of tuning
the settings of the controller. Tuning refers to a process, where the optimal gains are set
for, P, I along with D, so that the control system can receive a response which is ideal.
Generally, the plant control systems are automated. However, control performance
changes along with the passage of time. Thus, it is required tuning. Control system’s
tuning ensures in improvising the plant’s overall performance. The PID controllers help
in controlling the flow rate, pressure, temperature and level of the oil. In the plant, oil
refining controllers comprise of several control loops, for keeping the product’s quality at
a required value and for enforcing safe working operations, in the plant. “Guess and
check” method and the other method named as Ziegler Nichols method, are some of the
common methods used for tuning.
In guess and check method, ‘I’ and ‘D’ are sets as zero. Then, ‘P’ (proportional
gain) will be increased till the loop starts to oscillate. Here, adjustments are required to
balance the stability, by setting the required fast response. It is required to set P and I
with a required fast control system, that has least steady state error. Further, the
derivative term will be maximized, till the loop is reasonably fast and increases its
sensitiveness to noise. The Ziegler-Nichols method works exactly like the “Trial and
error method”. Even in this method, I and D will be set as zero then P will be increased
till the loop begins to oscillate. Later, as the oscillation commences, the information of
critical gain and oscillation periods are collected, which helps to adjust P, I and D.
On the other hand, prior to tuning it is necessary to independently linearize every
single valve, using controller. The valve’s normal operating range must be considered, in
case if the maximum gain is two to three times more when compared to the minimum
gain, then it is best to opt linearizing characteristic of flow.
Thus, I would use one of the above mentioned methods for tuning the oil, to
ensure controlling the oil flow rate, in the oil refinery.
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2) You implemented a PID controller for a Lasik eye surgery laser beam system. The
laser responds well, with minimal oscillations; however, it burns the cheek rather
than fixes the eye. What gain(s) should be adjusted in the PID controller? Should
the gain(s) be increased or decreased? Explain your reasoning.
Answer:
Lasik eye surgery is operated on a delicate part i.e., eye. Even a slightest mishandling or
neglect can harm the eyesight of the patient. PID settings are used as a help in correcting
the curvature of patient's eye, with laser. Thus, stability is essential before optimizing the
behaviour of the system. PID is the major element that ensures to help optimization of the
productivity. According to Najim (9), in Lasik eye surgery PID tuning benefits with
finding the limit cycle and other points for system's frequency responses.
The relative system works based on set point and process variable’s difference.
This difference is called, “Error term”. If, proportional gain gets increased, it increases
the control system’s response speed, which makes the process variable to oscillate due to
large Proportional gain. However, increasing Controller Gain (Kc) leads to highly
increasing the oscillations, which makes the system unstable and could make it difficult
to control. The reason is, because the proportional gain is the ratio of output response for
the error signal, where if 10 is the magnitude of error term, then 5 as proportional gain
produces a 50 as its proportional response.
Therefore, the proportional gain and Controller Gain must be adjusted in the PID
controller. The gain should be decreased. The determination of PID gains is established
using a gain table, depending on different operating conditions. However, the optimal
gain can differ based on time, because of deterioration features.
3) How might you evaluate and modify your values in butter-Worth filters (i.e. if you
have the raw data how can you tell if you have the right parameters).
Answer:
The butter-worth filters contains a property of extremely flat frequency response
and the pass band hardly contains any ripples. It has monotonically changing magnitude
function. In the stop band, the filter often moves to zero. The response slowly slides
towards linear side, where it has negative infinity on the logarithmic Bode plot.
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According to (Schreven et al. 5), the evaluation of Butterworth using the raw data,
will be determined based on denoised signals. The pass band must have a linear phase
response. It should have high order stopband specifications. Then, four threshold rules
help in analyzing the efficiency of noise removal. Effectively, the cut-off frequency for
butter-worth must be between 4 to 8 Hz, which is mostly utilized in filtering movement
data. Next, the dynamic precision and the cut-off frequency both must be optimal, with
optimal accuracy. The non-linear transformations results in distorted noise and provides
systematic error. Even, the weight factors also help in determining the correctness of the
parameters.
All the above factors help to determine that the present raw data has right
parameters. Further, helping in evaluating and modifying the values in butter-Worth
filters.
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References
Najim, Kaddour. Control Of Continuous Linear Systems. John Wiley & Sons, 2010.
Schreven, Sander et al. "Optimising Filtering Parameters For A 3D Motion Analysis
System". Journal Of Electromyography And Kinesiology, vol 25, no. 5, 2015, pp. 808-
814. Elsevier BV, doi:10.1016/j.jelekin.2015.06.004.
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