# PCT model of theodolite controller

**URL:** <http://discourse.iapct.org/t/pct-model-of-theodolite-controller/8454>\
**Category:** CSG1997\
**Created:** [February 25, 1997, 5:01pm UTC](http://discourse.iapct.org/t/pct-model-of-theodolite-controller/8454 "1997-02-25T17:01:45Z")\
**Posts on this page:** 1\
**Page:** 1

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**Author:** ![Bill\_Powers1](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/b/8e7dd6/32.png) [@Bill\_Powers1](http://discourse.iapct.org/u/Bill_Powers1)\
**Post date:** [February 25, 1997, 5:01pm UTC](http://discourse.iapct.org/t/pct-model-of-theodolite-controller/8454/1 "1997-02-25T17:01:45Z")

</div>

[From Bill Powers (970225.0930 MST)]

Hans Blom, Rupert Young (970225) and any other interested programmers--

At the end is the Pascal source code for my PCT model of controlling  
theodolite angle. I have added one new condition and changed one, after  
seeing how the simulated theodolite behaves under applied forces. The new  
condition is that the output torque is limited to +/- 750 newton-meters; the  
changed condition is that the disturbance magnitude is 100 newton-meters  
when it is present, instead of 10.

The reason for the torque limit is that when we present the system with a  
step-change in the reference signal, the torque goes instantly to a very  
large magnitude (if the system is set for fast control), like many thousands  
of newton-meters. That would be OK, I suppose, except that scaling the plot  
to show the peak output makes the response to the disturbance invisible.  
I've compromised by limiting the output to 750 newton-meters (about 450  
foot-pounds, which is like attaching a Chevy truck engine to turn the  
theodolite) and increasing the disturbance to 100 newton-meters, to make the  
response to it easily visible. I don't think these changes put any undue  
limits on a realistic design.

I have not put any phase advance into the PCT model. It doesn't seem  
necessary. Any more torque would probably bend the tube of a real theodolite.

It's easy to miss the initial response of the system. The output, in cyan or  
light blue, jumps to the maximum for a few dt's when the reference signal  
jumps to 1 radian, making a dot, and then falls to the maximum negative or  
near it, approaching zero from below as it decelerates the theodolite to its  
final position. When the reference signal drops back to zero, the reverse  
sequence takes place. Note that when the theodolite is stationary (white  
line horizontal), the output torque is zero except when the disturbance is  
present.

The duration of the run is 9 seconds.

Feel free to incorporate any or all of this code into your programs. It  
requires the Borland .bgi files to be in the same directory where the  
program runs. If you don't have the "grutils" unit already, I will post it  
again.

Best,

Bill P.

> **···**
>
> ========================================================================  
> program theodPCT;
> 
> uses dos, crt, graph, grutils;
> 
> var j,u,x,rx,v,rv,d,t,dt,dv,dx,gv,gx,r1,r2,d1,d2: real;  
> &nbsp;&nbsp;&nbsp;&nbsp;i,k,xscale: integer;  
> &nbsp;&nbsp;&nbsp;&nbsp;ch: char;  
> begin  
> initgraphics;  
> dt := 0.002; {time resolution}  
> r1 := 3.0; {start of ref signal change}  
> r2 := 6.0; {end of ref signal change}  
> gv := 500.0; {gain of position control loop}  
> gx := 40.0; {gain of velocity control loop}  
> xscale := round(9.0/dt/450.0); {x scaling for plots}  
> randomize;  
> repeat  
> rv := 0.0; {initialize velocity ref level & other variables}  
> x := 0.0;  
> v := 0.0;  
> t := 0.0;  
> d1 := 1.5 + 6.0\*random; {start of disturbance}  
> d2 := d1 + 2.0; {end of disturbance}  
> clearviewport;  
> setcolor(white);  
> outtextxy(0,0,'Pointing angle');  
> setcolor(lightcyan);  
> outtextxy(0,15,'Output torque');  
> setcolor(lightred);  
> outtextxy(0,30,'Disturbance');  
> setcolor(white);  
> outtextxy(0,240 - 85,'1 radian');  
> outtextxy(0,240 - 104,'----------\>');  
> outtextxy(0,240 - 120,'400 newton-meters');
> 
> {ITERATION LOOP FOR RUN}  
> for i := 1 to round(9.0/dt) do  
> begin
> 
> {CHECK FOR CHANGES IN REF SIGNAL, DISTURANCE}  
> if (t \> r1) and (t \< r2)  
> &nbsp;&nbsp;then rx := 1 else rx := 0.0; {REF SIGNAL, RADIANS}
> 
> if (t \> d1) and (t \< d2) then  
> &nbsp;&nbsp;d := 100 else d := 0; {DISTURBANCE, NEWTON-METERS}
> 
> {CONTROL SYSTEM EQUATIONS}  
> rv := gx\* (rx - x); {velocity ref level = output of position control}  
> u := gv\*(rv - v); {output force = output of velocity control}
> 
> {LIMITS ON OUTPUT}  
> if u \> 750.0 then u := 750.0 else {limit output to +/- 750 n-m}  
> if u \< -750.0 then u := -750.0;
> 
> {ENVIRONMENT EQUATIONS}  
> v := v + (u + d)\*dt; {integrate torque to get angular velocity}  
> x := x + v\*dt; {integrate angular velocity to get angle}
> 
> {PLOT VARIABLES}  
> putpixel(i div xscale, 240,white);  
> putpixel(i div xscale, 240 - round(x\*100),white);  
> putpixel(i div xscale, 240 - round(d/4),lightred);  
> putpixel(i div xscale, 240 - round(u/4),lightcyan);
> 
> {ADVANCE TIME BY DT}  
> t := t + dt;
> 
> end; {END OF RUN LOOP}
> 
> ch := readkey; {pause to view}  
> until ch = 'q'; {repeat on any key but 'q'}
> 
> closegraph;  
> end.