Industrial process control
In this experiment, you will give step inputs to the open-loop system to determine the nature of the transfer function between the set value and the output of the temperature sensor. Set the proportional band to 100% and the set value to 2. Use the appropriate switches to select "continuous control" and "proportional band". Perform this experiment by placing the sensor at each of the three locations P1, P2 and P3. For each sensor location, repeat the experiment at the three values 40, 65 and 90 of throttle setting. For every combination of the sensor position and throttle setting, give a set-value disturbance by throwing the switch marked "internal". This gives a step input voltage of a certain fixed magnitude, which can be seen on.
A typical control objective in thermal systems is to maintain the temperature of some component at a user specified value called the set point. Figure 4 below depicts a closed-loop system designed to maintain the output temperature of the PT326 apparatus at a desired set point.
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Loosely speaking, the controller uses the error signal between the desired temperature and actual temperature to manipulate the heater input voltage in such a way that the actual temperature converges to the set point value.
A cost effective means of implementing a controller in thermal systems is a relay, which gives full heater input voltage when the error signal is positive and gives zero heater input voltage when the error signal is negative. Such a controller is called an on-off controller. Figure 5 below shows the input-output characteristic of an on-off controller.
Practical relays suffer from hysteresis, where, for decreasing input, the relay output switches off at a lower value of the input than the value at which the relay output switches to its maximum when the input is increasing. Figure 6 below shows the input-output characteristics of a relay with hysteresis.
The oscilloscope at the terminal marked "trigger CRO. The output of the temperature sensor can be seen at the terminal marked "Y". By observing both signals on the oscilloscope, determine the DC gain, transport lag, and time constant of the open-loop transfer function between the set value and the sensor output.
In this experiment, you will investigate how the open-loop behavior influences the behavior of the closed-loop system under on-off control.
Place the sensor at the middle location. Set the proportional band to 100%, the set value to 2, throttle setting to 40, and overlap to 0. Select "two-step control" and switch off the internal set-value disturbance. Close the loop by connecting the terminals "X" and "Y". Use the oscilloscope to observe the heater input voltage at terminal "C", and the temperature sensor output at terminal "Y". From the oscilloscope, measure the threshold value of sensor output below which the heater turns on, threshold value of sensor output above which the heater turns off, maximum and minimum values of the sensor output voltage, maximum and minimum values of the heater input voltage, cycle time, heater-on time and heater-off time in each cycle. Repeat the above steps by setting the overlap to 0.5 and 1.
On-off controllers, though inexpensive to implement, suffer from the disadvantage that they lead to cycling or "hunting" around the desired set point, and thus provide less exact control.
An alternative to an on-off controller is a proportional controller, whose output is proportional to the error between the set point and the actual measured output. Thus, when a proportional controller is used in the closed-loop system in Figure 5, the heater input voltage is related to the error e(s) = r(s) -Vo (s) by
oi p Vs = K r s -V s
where Kp is the proportional gain of the controller.
Equation (12) implies that the closed-loop response becomes faster as the proportional gain increases. Equation (11) implies that the DC gain approaches 1 as the proportional gain Kp increases. In other words, the steady-state value of the temperature approaches the set point as Kp increases. Thus, the closed-loop system responds faster and more accurately to constant set point commands as Kp increases. However, for no value of the gain Kp is the response completely accurate. This can be physically explained by observing that, if the error is zero, then the heater voltage commanded by the controller is zero, causing the air to start cooling immediately. In other words a proportional controller cannot maintain a state of zero error (unless the set point equals the room temperature!).
Iterative feedback tuning algorithm has been successfully implemented for the optimization of time delay controller. The gradient of the cost function can be obtained by performing three experiments on the closed-loop process. In setting the step size to 0.7, the bandwidth of the filter function to 5 times the estimated system bandwidth, the duration of the optimization to apparent time delay plus ten times the apparent time constant and the tolerance to stop the optimization to 0.005, optimal solution is reached in two to three iterations. The optimized time delay controller outperforms the Ziegler and Nichols PID controller for dominant time delay processes. The novelty of the tuning technique is that it is model-free, it could be run in closed-loop operation and optimal solution could be reached in two to three iterations.
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