What are the different quadrants of operation and how does it relate to my DC motor control application?

The four quadrants of DC motor operation describe if you are decelerating or accelerating whilst moving forwards or backwards in any combination of the above. Looking at the diagram below we can see the four quadrants where the polarity of one of these vectors changes with respect to the other. We have two motoring quadrants and two generating quadrants:

If we have a single quadrant (often called 1Q) DC drive (or motor controller) then we can only apply the torque in the same vector polarity as the velocity i.e. accelerating forwards (motoring). These drives are commonly used for pumps or fans, as the deceleration is normally controlled by natural friction in the device. 2 quadrant (2Q) drives can apply a negative torque, but only when the velocity is negative i.e. accelerating in reverse (motoring). Four quadrant drives allow a mix of the two components irrespective of their polarity. In other words they can apply a negative torque to a positive velocity to decelerate something that is already in motion and vice versa (generating). To do so the 4Q drive has to overcome the back EMF generated by the motor. Four quadrant drive systems also have the added phenomena of regeneration. The kinetic energy in the decelerating body must be transferred to electrical energy (energy is neither created or destroyed, only converted from one form to another – the conservation of energy 'first law of thermodynamics'). We must also recall Fleming's right and left hand rule i.e. every dc motor is also a generator. This energy transferred to the DC capacitor of the drive and if that capacitor is already saturated with charge, at the rated voltage, the energy is passed upstream to the DC power supply as there is no more "room" in the capacitor for the energy. Most power supplies are not bi-directional and are diode protected. In this circumstance the energy has nowhere to go, so it overloads the capacitor! This is commonly mitigated using a shunt regulator or additional capacitor between the power supply and the drive. Conclusion If your application is dynamic in its deceleration (must be controlled, for example controlling a decent, precise deceleration of a loaded conveyor or perhaps a cutting blade that requires a quick stop) then you will require a four quadrant drive. In choosing this option, allowances must be made to handle regenerated power in the same polarity as the applied voltage. Before 4Q drives were about the way to stop DC motors was to join the phases together of the motor and possibly switch in a resistor bank as well to dissipate the energy. If your application is simple and its deceleration does not have to be critically controlled i.e. coasting to a stop is ok and the motor is not being 'pushed' along by external forces, then you could save money buying a 1Q or 2Q drive. If you were to use a 1Q or 2Q drive and not a 4Q drive in a 4Q application the motor would uncontrollably "run away" as the controller cannot oppose the voltage regeneration from the generating motor.