# Which one of the following coefficient is associated with Unit Ramp function?

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Which one of the following coefficient is associated with Unit Ramp function?
1. Static stationary error coefficient
2. Static velocity error coefficient
3. Static position error coefficient
4. Static acceleration error coefficient

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Correct Answer - Option 2 : Static velocity error coefficient

Explanation:

Type

It is defined as the number of poles at the origin in the open-loop transfer function.

Error: It is the deviation of output from the input.

• If the actual output of an open-loop system during the steady-state deviates from the reference input then the system is said to have a steady-state error.
• It is the index of accuracy of the control system.
• It is also called a ‘static error’.

${e_{ss}} = \mathop {\lim }\limits_{t \to \infty } e\left( t \right) = \mathop {\lim }\limits_{s \to 0} sE\left( s \right)$

Error constant and ess

The below table gives all information about the ess and error constant.

 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 ${k_v} = \mathop {\lim }\limits_{s \to 0} sG\left( s \right)$ Parabolic A.u(t).t2/2 $\frac{A}{{{k_a}}}$ Acceleration error constant ${k_a} = \mathop {\lim }\limits_{s \to 0} {s^2}G\left( s \right)$

Hence Static velocity error coefficient  is associated with the Unit Ramp function.