Effect of a back-e.m.f. non-linearity on responses of a second-order position control system

In the linearized analysis of control systems containing a d.c. field-excited motor the armature current is assumed constant, allowing motor torque to be taken proportional to field current. Since, in practice, this introduces the complication of current forcing to overcome variations caused by motor back-e.m.f., the question arises of how much armature current forcing, or constancy, is necessary to give desirable system responses. The variation introduces a two-variable (field current, motor speed) non-linearity into the system equation. The paper investigates the effect of the non-linearity on the step function and ramp and frequency responses of an otherwise ideal output-velocity-stabilized second-order position control system. Increase of the non-linearity is initially similar to increased system damping until a heavily non-linear and undesirable type of response is reached; unstable ramp responses can occur. There is, however, a well defined boundary marking the onset of the latter responses; below it responses are comparable with linear, particularly for critical or heavy damping. The range of responses is investigated, together with armature-current behaviour during them. This, together with the boundaries, gives a specification of armature supply requirements for a desirable response. The effects of load viscous friction and field-current saturation are also investigated.