With reference to the error analysis of the control systems, the term 'acceleration error constant' stands for:

Question

Question

This question was previously asked in

PGCIL Diploma Trainee EE Official Paper (Held on 17 Dec 2020)

Answer 1

Acceleration error constant is a measure of the steady-state error of the system when the input is parabolic function.

Positional error constant is a measure of the steady-state error of the system when the input is unit step function.

Velocity error constant is a measure of the steady-state error of the system when the input is ramp function.

Key Points

Type of input	Input: r(t)	ess	Error constant
Step	A.u(t)	\(\frac{A}{{1 + {k_p}}}\)	Position error constant \({k_p} = \mathop {\lim }\limits_{s \to 0} G\left( s \right)\)
Ramp	A.t.u(t)	\(\frac{A}{{{k_v}}}\)	Velocity error constant \({k_v} = \mathop {\lim }\limits_{s \to 0} {s}G\left( s \right)\)
Parabolic	A.u(t).t2/2	\(\frac{A}{{{k_a}}}\)	Acceleration error constant \({k_a} = \mathop {\lim }\limits_{s \to 0} {s^2}G\left( s \right)\)