# How to make sense of speed vs Torque curves in speed control mode

I am operating my motor in closed loop speed control mode using motor controller. Toque vs speed curves gives us a relation between them which is one-one correspondence. But in a closed loop speed control operation by keeping the load constant when one can always vary the set speed. Which means that for a given load(torque) there can be multiple speeds ?

Is torque Vs speed curves apply only in open loop ? Do it make sense to look at them in closed loop control.

Am I missing something in here ?

Thanks

Speed/torque curves tell you what the motor hardware will do.

Your closed loop controller can control anything it's been programmed to control, within the boundaries set by the motor speed/torque curve.

Consider how you'd drive a car. You could test it with several constant throttle openings, and measure its speed on different inclines, to get a set of speed/gradient curves. However, when you sit in the driving seat and close the control loop, you can choose to drive it at any speed within the speed/gradient limits of the hardware you're controlling.

You are only missing the Laws of Applied Physics.

e.g. energy conversion with the moving mass and inertia of the motor+ rotating mass to the servo power required.

This is only a "hand waving" answer not intended to be a classroom theoretical training for proper motor servo design.

Converting rotary to linear, motor+load mass inertia p=mv and motor acceleration F=ma = k*I= k * V/DCR for some motor constant k and current limited by I=V/R for some total series R including the DCR= DC winding resistance + driver resistance, Ron at DC=Vol/Iol from datasheet or some linear V/I =R drop from feedback control voltage and series current.

No load motor speed is proportional to voltage applied or generated.

i.e. kV/RPM or volts per radian/s or per RPM.

The bottom line is that the acceleration must be controlled or the heat dissipation must be removed to support the acceleration and braking of the servo loop mechanical energy into electrical energy and conduction losses in series.

The apparent motor voltage V = ( Vdc + Vbemf) where the generated back EMF voltage Vbemf=Vdc at some speed with no load or acceleration. i.e. servo motor has Vdc applied no load then open loop voltage as a generator is the same voltage. then when reverse voltage is applied you get twice the voltage apparent inside the servo motor at that instant.

Thus for any given DC servo motor when you change directions abruptly, the motor sees 2x Vdc/DCR and the power dissipation in any loop current series resistance ( such as the driver transistors) Pd=I^2 Ron with an associated temp rise * Rja [C/W] reduced by a possible heatsink.

Can you define all your variables with your understanding of Physics?. e.g. Vdc, I , DCR, driver R, mass, velocity, acceleration position error.

There must be a closed loop acceleration limit, max velocity spec and a closed loop position error curve to design the transfer functions (2). Then consider the current as acceleration feedback and voltage as a speed at a steady state then position error on arrival to servo closed loop resting with minimum overshoot and shortest possible seek time.

So there are several standard ways to design this with a PID loop but better to use linear feedback for acceleration=current and linear feedback error for the position. Then integrate only if the linear loop gain error is too high. Integration causes overshoot in the step response. Intermediate lead-lag compensation filters then optimize the servo design.

The phase-lead RC filter is partial D or derivative and I is partial low pass filter or integrate and P is the proportional loop gain which reduces the feedback error in steady state.

My rule of thumb for Servo Design, is always focus on linear feedback 1st ( the P in PID) for whatever you want to control whether it is acceleration, velocity, or position error, or for that matter temperature, vibration, etc etc. in any Control System design.

You regulate acceleration with current feedback, RPM with voltage control or tach feedback, and position with position feedback.

You can always differentiate sensors to get acceleration from velocity of a tach feedback and combine with current feedback. So choose your feedback to be linear or the P in PID loop. e.g. tach sensor for RPM velocity.

Advanced servo design uses "Vector feedback"

Then 2nd, the steady-state error and step response or settling time constraints can be optimized by tuning the "ID" in PID feedback using a variety of "control system theory methods" such as Root Locus, Nyquist methods, Body Plots etc.

• I don't think it's useful to consider inertia in this case. Inertia is only relevant for acceleration/deceleration, but torque (and thus speed and power) is relevant in every phase including steady state. Apr 12, 2019 at 10:05
• Maybe BUT in controlling torque in any Servo design, to some step response for damping factor, you need to know for PID parameters while accel/brake and computing power losses over time for temp rise. Apr 12, 2019 at 14:10

Which means that for a given load(torque) there can be multiple speeds ?

Yes, of course. Note that power = force * speed ~ torque * rpm. So, for any given (input) power, you can vary the load (torque) and the speed will respond 'automatically'; or you can vary the input power, and for a given torque you will get higher or lower speeds. In your case, it seems that you try to keep the speed constant, varying the (input) power to match the output torque requirement.

Is torque Vs speed curves apply only in open loop ?

Kind of. The torque-speed curves from e.g. datasheets indicate the maximum torque for a given speed, or vice-versa.

Of course, you can drive any load (torque) with any desired speed, up to the maximum (power) the motor can provide for the required torque.

Imagine if this weren't the case: Then you could control the speed of any motor in no other way than by varying the load, which is obviously not how motors work.

• The torque-speed curves from e.g. datasheets indicate the maximum torque for a given speed, or vice-versa. Datasheets I've seen give the torque/speed graphs for the rated voltage. Applying a higher voltage than the rated voltage (not recommended) gives a higher speed at given torque (and vise-versa) than shown in the datasheet. So, the don't indicate a max values, nor a minimum values, just the values at rated voltage. Apr 11, 2019 at 18:51
• @Huisman Yes, of course, you can get more than the rated power out of a given motor if you drive it with higher voltage than what it's rated for. Apr 12, 2019 at 10:00