Motion profile generator.

[HenrikOlsson]

Richard,
Slow down, I can't keep up at the moment! ;-)

The PID routine works with the error between the desired motor position and the actual motor position, the error magnitude it's able to handle depends on how aggressively it's tuned. Ie with low gain it'll handle large errors without overflowing the internal registers, with high gains it won't be able to handle an equally large error. But generally speaking yes, it'll handle an error of 255 without problems.

If the PID is executed 1000 times per second "stepping it" 255 counts each tick would equal a velocity of 255000 encoder counts per second. Using a 500 line encoder that equals a velocity of 7650rpm, pretty decent.

Looking at the code in your latest post I can't seem to see where you specify the distance to be moved.... (?) But that says more about my abillity to read others code than anything else :-)

I appreciate your ideas very much but at this time I don't see how precalculating the move is going to work in real life. One move might last 100ms while another 100s. One move might travel 25 counts while another might travel 100000 counts.

An example:
I'm at position 0.
* I want to go to position 4690
* I want the velocity to be 123 counts per tick
* I want the acceleration to be 8 counts/tick/tick

Tick	Accel	Vel	Pos	
1	8	8	0	
2	8	16	8	
3	8	24	24	
4	8	32	48	
5	8	40	80	
6	8	48	120	
7	8	56	168	
8	8	64	224	
9	8	72	288	
10	8	80	360	
11	8	88	440	
12	8	96	528	
13	8	104	624	
14	8	112	728	
15	8	120	840	
16	3	123	960	<---Velocity clamped at 123

At tick 16 increasing the velocity by the set acceleration would violate the set velocity so the velocity is clamped at that point. No problems with that or the code to do it.
At this point I know that it took 16 ticks and a total distance of 960 counts to get up to speed. So all that is needed is to start decelerating 960 counts from the desired target position, ie at position 4690-960=3730.

The problem is that when moving at 123 counts/tick the target position will never be exactly 3730 at a specific tick. It'll be either 3675 at tick 38 and 3798 at tick 39:

Tick	Accel	Vel	Pos
17	0	123	1083	
18	0	123	1206	
19	0	123	1329	
20	0	123	1452	
21	0	123	1575	
22	0	123	1698	
23	0	123	1821	
24	0	123	1944	
25	0	123	2067	
26	0	123	2190	
27	0	123	2313	
28	0	123	2436	
29	0	123	2559	
30	0	132	2682	
31	0	123	2814	
32	0	123	2937	
33	0	123	3060	
34	0	123	3183	
35	0	123	3306	
36	0	123	3429	
37	0	123	3552	
38	0	123	3675	<---Should I start here?
39		123	3798	<---Or should I start here?

So, if I start decelerating (8 counts/tick/tick) at position 3675 I end up short. If start accelerating (8 counts/tick/tick) at position 3798 I end up overshooting - that's the issue with this.

What I'm currently doing in my code is detecting when the distance to target is equal to or less than the distance traveled during the acceleration phase (that would be at tick 39 above) and then recalculate the needed acceleration (deceleration) in order to end up at target. That, however, isn't a one shot kind of thing since the needed acceleration (deceleration) might be 8.324 counts/tick/tick which obviously won't work with PBP. So, next tick I recalculate again and again and again - all the way to the end. The acceleration (deceleration) will toggle between 8 and 9, something like 8,8,8,8,9,8,8,8,9,8,8,8,8,9 - perhaps.

This seems to work in simulation, I have yet to try it on real hardware. The drawback of course is it takes a lot processing power due the division involved in the math.

The above numbers are just an example. The desired acceleration can be "any" number, the desired velocity can be "any" number and distance to move can be anything between 0 and several million counts. And they can change from one move to another.

Thanks Richard!

/Henrik.

[Ioannis]

If you are, as in your example, between tick 38 and 39, you are almost on target position.

Why not change acceleration to 1 count/tick/tick sinc the drop in speed will not be noticed and you will get the exact steps you need?

I am not an expert on this, just droped my idea.

Ioannis

[HenrikOlsson]

Hi,
I'm definitely no expert either, hence this thread ;-)

I'm not sure I follow your reasoning though. Where should I change acceleration to 1 (-1 actually), at step 38?
If I do that the velocity becomes 122 instead of 123 and the position at tick 39 becomes 3797 instead of 3798....then what should I do?

In order to "hit" 3730 at tick 39 the acceleration at step 38 would have to be 68 (8.5 times that of the programmed rate!) so that the velocity becomes 123-68=55 and the position at tick 39 becomes 3675+55=3730.

BUT, even if I could live with that gross violation of the programmed acceleration (which I just can't) the velocity is now 55 so if I now continue to decelerate at the programmed rate of 8 counts/tick/tick I would end up WAY short since the "deceleration sweet spot" of 3730 was "based" on a velocity of 123.... (Velocity will reach zero at tick 45 at which the position will be 3892 when I shooting for 4690).

I hope that makes sense and if there's something I'm missing (which by no means is unlikely) please elaborate!

/Henrik.

[richard]

its mainly the idea's I'm experimenting with at this stage . this one is to increment the setpoint not at the pid update rate but a rate that suits the acceleration / velocity . in the example that would be every 8 mS. it would be fairly simple to clamp the velocity at any rate after the acceleration move (the pid offset is constant), short moves can easily be accommodated by calculatining a lower vmax, the decelerate phase would begin when distance remaining = or less than the total accelerate displacement and then the accelerate parameter blocks are fed into pid setpoint in reverse leaving no doubt at all for the final move. assuming of course that you can sync the real position with where the ramp-generator thinks it is but you have plenty of steps here to adjust out any error.
speed wise after the initial "move" parameters are calculated the array could be filled in on the fly if you have the processing time, I like the array idea because it applies easily to both acceleration phases for the move. biggest problem I can see is that the block rate could vary with each "move " (this keeps the numbers manageable) so you would to be able to provide an accurate but variable timebase for the block clock
its a work in progress

[HenrikOlsson]

Hi Richard,

this one is to increment the setpoint not at the pid update rate but a rate that suits the acceleration / velocity

Yes, I'd probably not run it at the PID rate either but for the purpose of the discussion it makes it easier. I probably wouldn't want to run it slower than say 50 times per second though since that would make the motion jerky. So, with a fixed array size of 64 the longest move possible is 1.28s

the decelerate phase would begin when distance remaining = or less than the total accelerate displacement and then the accelerate parameter blocks are fed into pid setpoint in reverse leaving no doubt at all for the final move

Exactly, but that's the big problem. Because if you don't start "playing back" the accelerate parameter block in reverse at exactly the right position you will reach zero velocity either before or after you reach the target position. And since the motor is moving at a velocity of 240 counts (in your example .pdf) per update the likelyhood of hitting (target position - 7620) (where 7620 is the total displacement during acceleration in your example) is slim.

Accelerating is easy, clamping the velocity is easy, moving at velocity is easy, even decelerating is easy. The hard part is ending up at exactly the desired position.
Your .pdf shows a nice ramp from 0 to 30000 in velocity. Now see if you can keep moving at the velocity and then, at any given "tick", start playing back the acceleration ramp in reverse and get to position 55727. To do that you need to start playing back the acceleration ramp in reverse exactly at position 55727-7620 but since the motor is moving at 240 counts per update you're never going to hit that exact location.

I'm obviously too far into my own thinking and can't see the forest due to the trees.....prove me wrong will you ;-)

/Henrik.

[richard]

I understand what your saying , but the array data is only required for the acceleration phases of each move the constant velocity part if one is required can easily just be a loop terminating when actual_position is less than or equal to target-ramp_length. so moves of any length are possible. I envision the deceleration would need error correction applied as
error = (actual_position - (target-(ramp_length-array[])) , each iteration would be adjusted by that error and the ramp_length decremented by the array [] increment . with potentially 60 odd iterations the final movement should be pretty good. (ramp_length=0 and error=0)=good
I agree about the jerkiness I'm hoping inertia will smooth some out , tell me if you feed a 200 step increment into the pid how many iterations till the error is 0 ? . my guess is that its more the 1 ,this may also do a bit of smoothing.

[HenrikOlsson]

Hi Richard,

tell me if you feed a 200 step increment into the pid how many iterations till the error is 0 ? my guess is that its more the 1 ,this may also do a bit of smoothing.

Yes, of course it's more than one, perhaps 20-200.
Exactly HOW many depends on the inertia of the system, the tuning of the PID parameter, encoder resolution, current limit of the drive etc etc etc. Aggressive tuning will cause overshoot and ringing, "loose" tuning will cause slow risetime and so on - as I'm sure you know.

I think that what you're aiming to do with recalcuating the array is basically what I'm doing as well - except I do it on the fly at each tick. What your method have going for it, provided it works of course, is that you don't use a division in the recalculation phase which will make it run fast. Then, on the other hand, if you need to recalcute the what's left of the array each tick (not sure if you need that or not?) then it might not be more effecient, I don't know.

Please do keep posted and I'll do the same - if I could just find the time to sit down and actually get it running...

Thanks Richard!
/Henrik.