Analog Controller for Speed Control of DC Servo Motor

One option is to purchase a "feedback controller" intended for 12VDC model railway applications, available in the UK for a few tens of pounds Sterling. http://www.gaugemaster.co.uk/controls.html

Feedback control is used in battery electric drills to maintain bit speed. So another option is to dissect a drill and use its controller.

Behaviour of any feedback control loop depends on the gain, the integral action and the derivative action applied to the system of which the controller is only a part. These parameters are determined by the user by "tuning" the loop or by a pre-programmed tuning algorithm according to principles established by Zeigler & Nicholls and repeated by controls engineers ever since.

Something most people forget is that a DC motor has inherent feedback with its back EMF. If positive feedback is applied to cancel out the losses caused by the motors resistance, the motor and load is far easier to stabilize because this "inner" feedback is instantaneous. This means the "outer" feedback loop is doing far less to control the motor speed and is nowhere near as critical for the phase and gain needed to stabilize the loop. In fact, if you don't need high accuracy in the absolute motor speed, you don't even need an "outer" feedback loop at all. Here is a link from an application note. http://focus.ti.com/lit/an/sboa043/sboa043.pdf

A simple PID contol loop should be used. No. 3 is not a reasonable expectation. Please note No. 3 (directly following) conflicts with No. 2 (20% overshoot)

#3 does not conflict with #2. What he's saying is that after the overshoot, when the speed settles down to a steady value, that speed should be exactly what is requested/set by the input.

Student's project?

No 3 suggest at least PI type controller.

No 1 suggest more: PID.

Simple Voltage Divider "represents" P type control so if you are in charge to design analog controller the Operational Amplifier is the one with capacitors. First of course must be calculted Kp, Ki, Kd parameters so remarks about the load (final elementin the loop) parameters (DC motor + inertia + voltage/current as a function of the speed/or maybe position? ..) are significant to calculate dynamics (requirements in No 2).

Your "input" (as a set point) is added to error signal from the PID controller.

PID controller is the feedback in the control loop. Its input is an electrical value representing speed and output is the error signal

I believe you have a book about process control (automation) so my notes are just a simple piece of info to avoid confusion in the beginning of the designing.

If this is a project to existing DC servo... buy one of available contollers with ability to wide setting adjustments.

Since you are controlling a DC motor you automatically get #3 (because you have a pole at DC). All you need is a proportional controller; so an op-amp with two resistors is all you need. I have one question for you, do you have a DC motor driver or did you want to build or buy one of these. I can help with that too.

If you know how to do pole placement design it's pretty easy to design this controller. The open loop poles of your dc motor are at zero and 1/tau, where tau depends on your dc motor. With I proportional controller, as you increase K the poles come together and slit (this is a root locus plot). To meet #2 of your demands, the angle that your poles make (with the intersection of the real and imaginary axis) can not be more than 62.8 degrees. So this will limit your maximum gain value that you can use. The more gain that you use the faster the motor will move but the more ringing and overshoot you will have in your motor. If you increase the gain so that the poles make more than the 62.8 degrees the motor will overshoot more than 20%. You have to know your motor to meet #1.

You can do better if you do a PID. It's easy to do this with one op-amp, 3 caps, and 3 resistors. It's more complicated but it can give you a little bit better results.

The saturation problem should be thought about after you understand how to control the motor with a proportional controller. If you use too much K then your motor can saturate faster when there is more speed error. It's easiest to matlab it and see how much power you have to use. You can calculate "regions" where the poles should lie to give optimal power but if you don't really know root locus then it's easier to try picking gains and check it to see what you get.

If you tell me a little bit more about your motor, motor driver, and tach that you are using, I might be able to help out more.

B

Proportional (P) controller CANNOT make error = 0(zero) which is required for steady state! Again: PID controller is the solution. To select elements to OpAmp you MUST do calculation to find Kp (for P regulation), Ti for Integral and Td for Derivative parts (your design)/or settings (controller selected from catalogs) of the controller. Remember that power supply voltages (+/-) must be over the span of adjustement/setting to avoid saturation. Process control teachers easily would find the errors!

The transfer function of a DC motor looks something like A/(s*(tau*s+1). If I use a proportional controller with a gain of K and I look at the closed loop response from the input (r) to the Input of the controller (e) some like 1/(1 + K*A/s*(tau*s+1)) or s*(tau*s +1)/(s*(tau*s+1)+K*A). If I put a step input then it looks something like (1/s)* s*(tau*s +1)/(s*(tau*s+1)+K*A). If I do the final value theorem ( taking the limit as s->0 and multiplying the closed loop transfer function by s) I get the limit as (s->0) pf s*(tau*s +1)/(s*(tau*s+1)+K*A)=0. So the steady state value of the error is indeed 0. All you need is a P controller for a steady state error of 0.

B

The above prop algro settles out and becomes stable above or below set point with zero error and no method of integrating to set point.

Tuning for a PID controller will be required to achieve the desired amount of stability vs activity. Required Overshoot to meet SP in a single Hz could pitch #1 vs #3.

To properly tune at 6000 Hz, there are two major and completely different approaches. High P and low I vs high I and low P. Values of D correct for a sticky/slicky response ie lack of lube.

The Proportional controller does produce zero error but it also goes to the set point value. Above is the transfer function from the input to the error. The transfer function from output to input looks something like K*A/(s*(tau*s+1)/(1+K*A/(s*(tau*s+1))) or K*A/(s^2*tau+s+K*A). If you do the final value theorem on this, it does go to the exact set point.

B

Oscilloscope observations of PWM feedback controllers on DC motors would suggest that there is no integral or derivative action to be found, and that proportional-only control is used.

Note that a motor-controller system will behave differently depending on the inertia of the motor - its "flywheel effect". Modern coreless motors can behave irritatingly badly when coupled to PWM controllers when applied to model and miniature applications, spoiling illusions of mass and momentum.

The integral is there. If put a DC voltage on the DC motor, the motor will turn at some speed. The position of the dc shaft is the integral of the input voltage. As I increase the DC voltage the DC motor spins faster and faster, integrating more and more signal. The second pole can be seen if you put a sin wave voltage into the motor, at some point the motor doesn't respond to the input. That second pole is a low pass filter. So you can pwm the motor and the motor will filter out the AC component and you will be left with the DC potion of the signal, witch will determine the speed of the motor. (Remember the integral of position is speed).

B

So the motor is doing the integration. Fine, but what about the controller terms?

I guess my point is that all you need is a proportional controller. So the controller terms would be just some gain. If the person doing this design is using a relatively small DC motor, you can use just an op-amp or power op-amp with two resistors to drive the motor to the correct position and settling time. If the motor is bigger and you can not use just an op-amp then other methods have to be used like a power amplifier, PWM or something else. To implement this control, the position has to be fed back. So you must use some shaft encoder or something else like that. To get maximum performance out of the system you can add one resistor and three caps and you can make a PID controller (you might need a few more components for the non-inverting node. I have not thought about that enough).

The signal that drives your motor is the error signal that comes from comparing the setpoint to the actual motor position. This error signal is multiplied by some gain either a proportional gain or a PID gains. It doesn't really matter so much. Both are easy to make. All of this error stuff is done by the op-amp.

B

Usually, one measures the back-EMF from the spinning motor in between each pulse, and uses that as the input for the speed signal. As for the controller, providing it's fast acting, "how" is secondary.

Measuring the back-EMF is one technique to do the position control. It has its advantages and disadvantages. The advantages are its pretty easy to do and you don't need a shaft encoder or anything else like that. A disadvantage is that signal is very noisy. The equations that I was talking about above don't relate to feeding back the speed of the motor. Only the position. You can't just use a P controller feeding back the speed for zero steady state error.

PWSlack, I don't understand your statement "As for the controller, providing it's fast acting, "how" is secondary". Can you elaborate a little more? Thanks.

B

Er, back-EMF is proportional to angular velocity, which is why it is used.

Why, what, where, when and who are primary. How is secondary.

Controllers can use pneumatics, and a "Portsmouth Valve" uses a proportional-only control technique, and there usually isn't a free electron in sight...

How to directly measure back-EMF? We have access to terminals not to "inside world of magnetic field of motor". Of course : EMF = Vmot - Imot * Rmot so you must install two sensors for Vmot and Imot (motor's voltage and current as functions of time)and do calculation.

While one could do that most devices use the 2 wires connected to the motor terminals instead.

The voltage between these two terminals represents the output voltage from the controller not an EMF which is proportional to rpm of motor shaft and, how you stated is good as an input to the controller.

In practical systems the analog tachometers or digital encoders are used to get electrical/or numerical signal to represent a motor speed (rpm).

Having a Data Acquisition you may use two sensing devices and get two voltages, then do calculation (EMF = Vmot - Imot * Rmot) by its program then...do PID in controller but this more expensive way and probably is not the one the initiator of this discussion wanted.

Exactly. As above, it can be done for a few tens of £Sterling using the 2 power supply wires. Why reinvent the wheel (rhetorical question)?

I do agree that the PID is the right answer but a P works too.

B

Quite.

You don't give the vital piece of info required what size of motor, what application do you want, ie: constant torque or constant speed? Fit a opto tacho and pulse width modulate the DC supply. It all works rather well with an op amp or two.