Optimizing PID Temperature Control: Settling Time, Deviation, and Delay Analysis, Exercises of Linear Control Systems

The optimization of a pid temperature control system by analyzing its settling time, deviation from steady state value, and delay in output signal. The study involves adjusting the proportionality gain and observing the system's response using graphs and observations.

Typology: Exercises

2011/2012

Uploaded on 07/09/2012

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Introduction
There is no industry which doesn’t include some kind of boiler in its
structure. A boiler is a closed vessel in which water or other fluid is heated.
The heated or vaporized fluid exits the boiler for use in various processes or
heating applications. Because of boilers importance there is a strong need
to control boilers temperature by some control system. Such control
systems include some heat sensors, comparators and signal generators.
These control systems act differently for different temperature and stability
conditions. There is always a need to study their behavior before
incorporating control system to practical. Behavioral study of temperature
control system include dependence of its settling time (time required to
reach steady state) and frequency response over systems parameters
which include proportionality gain, systems max power etc.
Objective
Over main objective is to study the optimization of following
performance parameters of a PID temperature control system
Time to reach the steady state
Deviation from steady state value
Delay in the output signal
Procedure
At first gain of the system was reduced to 1 for the tuning purpose.
After this open loop response of system was plotted using plotter.
After tuning, loop was closed and gain was adjusted to unity. Closed
loop response at unity gain was plotted using plotter.
Gain was increased to 3, and again close loop response was plotted
on graph paper.
Gain was increased to 20 and then close loop response was plotted
using plotter.
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Introduction

There is no industry which doesn’t include some kind of boiler in its structure. A boiler is a closed vessel in which water or other fluid is heated. The heated or vaporized fluid exits the boiler for use in various processes or heating applications. Because of boilers importance there is a strong need to control boilers temperature by some control system. Such control systems include some heat sensors, comparators and signal generators. These control systems act differently for different temperature and stability conditions. There is always a need to study their behavior before incorporating control system to practical. Behavioral study of temperature control system include dependence of its settling time (time required to reach steady state) and frequency response over systems parameters which include proportionality gain, systems max power etc.

Objective

Over main objective is to study the optimization of following performance parameters of a PID temperature control system

 Time to reach the steady state  Deviation from steady state value  Delay in the output signal

Procedure

 At first gain of the system was reduced to 1 for the tuning purpose. After this open loop response of system was plotted using plotter.  After tuning, loop was closed and gain was adjusted to unity. Closed loop response at unity gain was plotted using plotter.  Gain was increased to 3, and again close loop response was plotted on graph paper.  Gain was increased to 20 and then close loop response was plotted using plotter.

 After these reading, temperature sensor was removed from its original position and placed away from heating fan.  Gain was adjusted to 20 w/c, and close loop response was plotted on the same graph paper previously used for 20 w/c gain.

Observations

As shown in figure 1, when proportionality gain is increased then time required for reaching steady state become small. This can be seen in the given graphs that steady sate transition time is smallest for 20 w/ , and largest for proportionality gain of 3.

Fig 1

Reference Signal

Gain=

Gain=

Conclusion

There are exceptions we have to make if we want a fast responding system. Increasing the gain of the system decrease the settling time of the transient but correspondingly it make system under damped. So we have to compensate for speed over stability. Temperature difference in the vessel causes delay in system response. This delay can be reduced by designing the vessel for uniform temperature difference or by using more than one sensor at different points in the vessel and then couple their outputs. By increasing the proportionality gain we can achieve certain degree of accuracy for output temperature. This accuracy increases with increasing gain.