DC-motor

TechTeach has four DC motors including tachometer (which gives a voltage proportional to the rotanional speed), servo amplifier and power supply as shown in the figure below. The motor is produced by Faulhaber. The control signal is in the range of ±10V, and the tachometer voltage is in the range of approximately ±10V, corresponding to a speed of ± 2krpm. A load inertia has been added to the motor. The time constant of the motor including load and tachometer is approximately 0.3s. The gain from control signal [V] to tachometer measurement [V] is approximately 0.85. A load torque can be applied to the motor by simply braking the motor (the load) by hand.

Mathematical model

A mathematical model of the motor can be expressed in terms of a transfer function:

S(s) = H(s)*[C(s) + L(s)]          (1)

where S [krpm] is the speed. C [V] is the control signal. L [V] is an equivalent voltage representing the load torque. L is in the range of ± 10 V. H(s) is

H(s) = K/(T*s+1)

where K = 0.17 krpm/V, and T = 0.3 s.

Alternatively, the model (1) can be expressed with the equivalent differential equation model:

T*dS/dt + S = K*(C + L)      (2)

In simulations of the motor you may use either (1) or (2) as the model to represent the motor. If you want to include the intitial value of the speed, S₀, in the simulator, I suggest you use model (2) since this initial value can then be defined in the integrator of S.

In practical applications with the motor the motor can be calculated from the speed sensor (tachometer) signal, which is a voltage. The relation between the speed measurement S_m [V] and the speed S [krpm] is

S_m = K_mS

where K_m = 5 V/krpm.

Connecting to controller

A speed control system (speed servo) can be implemented using any external controller with voltage control signal and voltage measurement signal, e.g.

• an industrial PID controller

• a PLC

• a PC with for example LabVIEW software and implementing the control function and an I/O device as FieldPoint or USB-6008.

(The servo amplifier also contains an inbuilt speed controller. However in the labs that TechTeach has prepared an external controller is used in stead.)

[TechTeach]

Updated 26. October 2008. Finn Haugen (finn@techteach.no).