Two quadrant armature controlled DC drive; closed loop

A two-quadrant armature controlled drive feeds the armature of a separately excited dc motor from a fully controlled converter (single-phase or three-phase), with the field kept constant. The converter can give positive or negative average voltage but current in one direction only, so the drive works in quadrant I (forward motoring) and quadrant IV (reverse regenerative braking).

Open-loop operation

$$V_a = V_{do}\cos\alpha, \quad N = \frac{V_{do}\cos\alpha - I_a R_a}{K}$$

• $0 < \alpha < 90^\circ$: $V_a > 0$, $I_a > 0$; power flows from ac supply to motor: motoring (quadrant I). Speed is set by $\alpha$.
• $90^\circ < \alpha < 180^\circ$: $V_a < 0$. If the load drives the motor in reverse (e.g. lowering a hoist load), $E_b$ reverses, current is still positive, and the converter works as an inverter, returning energy to the supply: reverse regenerative braking (quadrant IV).
• The operator simply sets $\alpha$ through a potentiometer and firing circuit.

 ac --[full converter]--+--La--[ M ]   field: const
          ^ alpha       |
   [firing circuit] <-- V_c (set by potentiometer)

Limitations of open loop

1. Speed falls as load increases ($I_aR_a$ drop); poor speed regulation.
2. Speed changes with supply voltage variation and temperature (resistance change).
3. No current limit: a sudden change in $\alpha$ or a heavy load causes very high current, damaging thyristors and commutator.
4. Slow and oscillatory dynamic response; no protection against stall.
5. Discontinuous conduction at light load makes speed rise sharply.

Closed-loop scheme (speed loop with inner current loop)

 w*  +   +------+ Ia* +-----+  +   +------+ Vc  +-------+    +---------+
 --->(O)-|speed |-|lim|-->(O)-|curr. |---->|firing |--->|converter|-> M
     -|  | PI   |  +-----+  -| | PI   |     |circuit|    +---------+   |
      |  +------+            | +------+                     |          |
      |                      +------- Ia (current sensor) <-+          |
      +--------------------------- w (tachogenerator) <----------------+

• Outer speed loop: the speed error is processed by a PI controller to give the current reference $I_a^*$; this corrects speed for load and supply changes (near zero steady-state error).
• Limiter: clamps $I_a^*$ to the maximum safe value (e.g. 1.5–2 × rated), so starting, acceleration and braking take place at constant maximum current.
• Inner current loop: a PI controller compares $I_a^*$ with the measured current and sets the control voltage $V_c$ (hence $\alpha$); it reacts fast and protects the motor and converter.
• Often a cosine-wave firing scheme is used so $V_a$ is linear in $V_c$.

This cascade control gives accurate speed, built-in current limit and fast response.