Digital Control System

Theory:

The digital control systems are going popular because of readily available inexpensive microcomputers and peripheral devices. A digital controller has versatility to change or modify its control function by changing or modifying its programme instructions where as in analog controllers it is modified by changing its hardware. It has disadvantages of computing errors due to finite word length, error in sampling and reconstruction, unstabilized sample and register overflow. 

Setup:

• Signal source
• Process or plant
• Digital controller

Signal source: the system performance is studied by applying an internal square wave of 1Vpp amplitude at frequency 10Hz approximately. This signal is reasonable for experiment and displayed upon good DSO.

Process or Plant: It is an Op-Amp simulation of 2^nd order type-0 transfer function. The simulation has predictable characteristics and suited for this experiment.

Digital controller: It is basically a microprocessor 8085 with some peripheral interface ICs like 8255, EEPROM, ROM etc. The controller programme for different experiment has been stored in ROM. It is accessed by some set of commands and executed.

Apparatus Required:

• DSO
• Trace sheet/pen drive of 4 GB or less.

Procedure:

1. The process response:

• Switch ON the power supply. Connect a patch cord between SIG and SIG IN. Put the toggle switch for cro test block in DIR mode.
• Switch ON the DSO. Connect one channel between SIG and ground to see the input wave form, and other channel between TP4 and ground to see the output waveform. Adjust the V/D and T/D of DSO so that the wave form will visible clearly.
• Observe the overshoot and steady state error ${e_{ss}}$. And calculate them by taking cursor of the DSO.
• The transfer function of the plant is :

\[G(s) = \frac{{K{a^2}}}{{{{(s + a)}^2}}}\]

The parameters are calculated as:

\[K=\frac{{C_{ss}}}{{V_{input}}}\]

and
\[a = \frac{{1.68}}{{{t_{\frac{1}{2}}}}}\]

where
${C_{ss}}$ = peak to peak value of response at steady state.
${t_{\frac{1}{2}}}$ = time to approach half value of steady state value.

2. Fixed proportional gain and variable delay:

• Now put the toggle switch for CRO Test Block in CONT mode.
• Connect one channel of DSO between TP2 and ground to measure the time delay, and other channel between TP4 and ground to observe the output waveform.
• Execute the programme stored at address 5000h. Keep the value PC constant at 4 and observe the effect of delay by changing the value DEL.

The procedure is:

• Press the reset button---->then del go---->then type the address 5000----->nemc next----->give the PC value 4------>nemc next-------->give delay value 0-------->then press fill
• The DSO channel connected to TP2 shows the square waveform. The time period of the wave is actual delay time of the digital delay value DEL entered in the programme. For change in value of DEL the time period will change.
• The other channel of DSO which is connected to TP4 shows the response of the system. Observe the waveform for different delay values.
• Trace the waveform or save it on the pen drive. Calculate Cpeak, Css, and Mp

\[Mp = \frac{{{C_{peak}} - {C_{ss}}}}{{{C_{ss}}}}X100\% \]

Observation table: At PC or Kp=4

Sl no	Delay	Delay time T (mS)	C peak (V)	Css (V)	Mp%

3. Fixed delay and variable forward path gain:

Exactly do the same thing what is done in above. But here keep the delay DEL constant at ‘0’ and vary the forward path gain PC in the programme. No need to connect DSO channel at TP2 to measure the delay rather connect it to input signal SIG IN.

Observation table: At constant  Delay(DEL)=0

Sl no	Forward path Proportional Gain(PC)	C peak (V)	Css (V)	Mp%

4. Digital control system, P.I.D controller:

• Connect the DSO channel one at TP4 and other at input signal SIG IN.
• Execute the programme from the address location 5030h. Here you have to enter the value of three variable i.e Proportional gain (PC), Derivative gain(DC) and Integral Time(IC)
• Here you have to tune the controller, means you have to adjust the parameter value (PC,IC,DC) in such a value that the response would match the input.
• Observe the response first and the effect of each parameter on the response. Accordingly change the parameter value to achieve the desired objective.

The range of the parameters are:

Gain	Digital value	Analog Value
PC	0-9, and A-F (all hex digits)	0-15
DC	0-9, and A-F (all hex digits)	0-15
IC	0-9, and A-F (all hex digits)	0,1/16,2/16----------13/16,14/16,15/16

Note: Attach some of the waveform traced or saved in pen drive. Follow the link to know how to save waveform in pen drive click here