PID Controller

Objective:

To study the performance characteristics of an analog PID controller using simulated system.

Experimental Units:

This is a very well designed and compact unit for class room experiments on the study of proportional-integral-derivative controllers. The front panel diagram of the unit has been shown below. It comprises of a flexible simulated process, a PID controller, signal sources, a DVM, and a stabilized power source for all the sub-systems. The various sections along with their specifications are described below:

Process or Plant:

In a practical situation the process or plant is that part of the system which produces the desired response under the influence of command signal. Usual processes are higher order, nonlinear functions having inherent dead time or pure time delay. In process control studies such plants are commonly modelled by transfer functions of the form

\[{G_p}(s) = \frac{{K{e^{\theta s}}}}{{\tau s + 1}}\]

Where

$\theta$ is the time delay in sec.

τ is the effective time constant

and K is the d.c gain.

In the present system, the process is an analogue simulation through a few basic building blocks which may be connected suitably to form a variety of processes or plants. These blocks are:

• Integrator: Having an approximate transfer function of 10/s.
• Simple Pole: Two identical units, each having a transfer function of 1/(1+0.0155s)
• Pure time delay: A time delay of about 5.64 msec. generated by a high order multiple pole approximation of the delay function.

Note: All the above blocks except the pure delay, have 180⁰ phase shift between input and output.

Controller:

The controller for the process is an analog Proportional-Integral-Derivative (PID) circuit in which the PID parameters are adjustable. The values may be set within the following range through 10 turn calibrated potentiometers:

Proportional Gain, Kc : 0 to 20

Integral Time Constant, Ti  : 5-100 msec.

Derivative Time Constant, Td  : 0-20 msec.

It may be mentioned that although in an industrial PID controller it is common to adjust the above parameters directly, but in the educational environment convenience and simplicity is more important. In the present unit, therefore, it is proportional, integral and derivative gains viz. Kc, Ki and Kd, which are made variable through 10 turn potentiometers calibrated from 0-10. The PID block has a phase angle of 0⁰ between its input and output.

Error Detector:

The error detector is a unity gain inverting adder which adds the input signal with the feedback signal. To ensure negative feedback it would therefore be necessary to have (2n+1)π phase shift in the forward path.

Amplifier:

It is a unity gain inverting amplifier. This amplifier may be inserted in the loop, if required, to ensure proper phase angle.

Signal Sources:

The signal source comprises of a low frequency square and triangular wave generator having adjustable amplitude and frequency. The square wave is used as input signal to the system, while the triangular wave is used for external x-deflection in the CRO. This arrangement gives a perfectly steady display even up to very low frequencies and is convenient for CRO measurement.

Power Supply and DVM:

An IC regulated circuit powers the complete unit. A 3 ½ digit DVM of $ \pm $19.99V range mounted on the panel may be used for d.c or steady state measurements. Also a variable d.c in the range $ \pm $ 1V (min) available on the panel may be used as a d.c input or set-point for the system.

Apparatus Required:

DSO

Trace sheet/ pen drive of 4 GB or less. 

Experiments procedure:

• Connect the output of controller to the input of the summation unit. Output of the sum to the input of delay unit. And output of delay unit to any one of the time constant unit for first order system.
• The output of time constant is connected to the negative node of the error detector through amplifier.
• For second order system two time constant unit should be connected in cascade and the output of second time constant is directly connected to the negative node of the error detector.
• Make sure that all the controllers knob position is initially at ‘0’.
• Set the peak to peak value of square wave at 1 volt and frequency at 5Hz. Connect the square wave signal to the positive node of the error detector.

Calibration:

The digits written in the controller potentiometer are not their actual values. There is a calibrated value of controller parameter correspond to their knob or potentiometer value. These are:

Kc = Knob value of P x 2

Ki = Knob value of I x 91.42/sec

Kd = Knob value of D x 0.00104 sec

Proportional control:

• Connect one channel of DSO to the input signal and other channel to the output of time constant.
• Change the value of P potentiometer only in step of 0.2. All other potentiometer should be at 0. 
• Observe the effect on overshoot, oscillation and steady state error of the response. Trace or save three-five waveforms. follow the link to know how to save waveform in pen drive (click here)
• Calculate the steady state error and % overshoot.

   Steady State Error $ = \frac{{(p - p)input - X}}{{(p - p)input}}$

Peak percent Overshoot $ = \frac{{Y - X}}{X}X100\% $

where

X= 2 times of steady state value

Y = 2 times of peak response

Note: X and Y can be calculated from x-y mode display of the DSO, by connecting one channel of the DSO with time constant output and other channel with triangular wave.

Table 1:

Scale reading (POT value)	Kc value	X	Y	Steady state error	% overshoot

PI Controller:

Here keep the value of Kc constant at 0.8 and change the value of Ki with Kd at 0. Observe the effect on response by changing the value of Ki. Calculate the steady state error and peak percent overshoot. Trace or save 3-5 waveform.

Table 2:

Scale reading (POT value)	Ki value	X	Y	Steady state error	% overshoot

PID Controller:

Here keep the value of Kc constant at 0.8 and Ki at 73.14 and change the value of Kd. Observe the effect on the response. Calculate the steady state error and peak percent overshoot. Trace or save 3-5 waveform. By using trial and error method change all the control parameters so that the response will perfectly match with the input (perfectly tuned). Note down the controller values at which you get the optimised response and trace the waveform too.