# Speed control of a direct current motor

## Block diagram of the closed loop control system

This motor is frequently used in control systems as it is quite easy to control its rotational speed.

## Open loop control In the scheme we have:

• K: power amplifier transfer function;
• VR: reference voltage, proportional to the required speed value;
• Vn: engine supply voltage;
• ω: engine speed.

However, this control system is extremely sensitive to changes in load and parameters of the various circuit devices (e.g. amplifier gain) as well as to the presence of any disturbances.

## Closed loop control

These problems can be avoided by introducing a negative reaction ring in order to create a closed loop control system. The feedback block produces a Vf voltage equal to the instantaneous speed of the engine. The VR voltage is proportional to the desired speed. The difference (VR – Vf), amplified by the block gain K, represents the input voltage of the engine. The engine responds to this input by changing its speed in such a way as to reduce the difference (VR – Vf).

As a result, in this control scheme, a change in engine speed caused by load changes, or a change in parameters or disturbances, produces a change in signal (VR – Vf) which, after being amplified, tends to bring the speed back to the desired value.

The system described produces a proportional control, in which the K gain amplifier represents the regulator.

The motor transfer function is given by the expression: where, since there are no poles in the origin, the system is zero type. This means that the error between instantaneous and nominal speed will not be totally eliminated. To eliminate this error it would be necessary to replace the proportional regulator with a proportional-integrative one.

The time constant is called the motor’s mechanical time constant, it has the size of a time and a value that depends on the moment of inertia J of the engine. We will deal in more detail with this transfer function in a future article.

## Complete block diagram of proportional motor speed control The symbols used here are:

• VR: reference voltage, proportional to the speed value you want to obtain;
• Vf: feedback signal, proportional to the actual value of the velocity;
• D: difference signal, proportional to the error signal;
• Vn: engine supply voltage;
• Ω: controlled variable, i.e. angular velocity;
• Ge(s): D signal amplifier transfer function;
• Ga(s): power amplifier transfer function;
• Gm(s): transfer function of the controlled system, i.e. the direct current motor. It is the function seen above;
• H(s)=H: reaction block transfer function, represented by a transducer capable of transforming the angular velocity into a Vf voltage homogeneous to the VR reference signal;
• Da1, Da2: Disturbances that tend to change the operating conditions of the controlled system.

A dynamo, which is in turn controlled by a phase-controlled power amplifier, can be used to power the engine. This is for the control of relevant powers, while for more modest powers (up to a few dozen KW) only the power amplifier is often used.

In a simplified scheme, it can be assumed that the engine is powered directly through a bridge of controlled diods (SCR). Remember that these diodes can lead only if at the moment the gate pulse is provided, the anode is positive with respect to the cathode. In the case of the engine, due to the presence of the counter-electric force E, gate pulses of too short duration should be avoided because they may not be sufficient to trigger the device.

In addition, when the engine acts at high speeds and with low load values, the armature current will have an impulsive course with a high residual ripple. This effect is particularly harmful to the motor as it creates problems in switching and increases electrical power losses. It is possible to limit the effect of this inconvenience by placing in series to the induced circuit an inductance that, reducing the residual undulation of the current, ensures a regular rotation of the engine even in the worst conditions.

We will analyze the transfer functions of the various blocks in a next article.