STEADY-STATE ERRORS

What physical scenario is represented by a parabolic input when evaluating the steady-state error of a position control system?

To which type of systems is the discussion of steady-state error analysis primarily limited?

Given a unity feedback system with a forward transfer function G(s), what is the formula for the steady-state error, e(inf), for a generic input R(s)?

For a unity feedback system, what condition on the forward transfer function G(s) is required to have zero steady-state error for a step input?

A unity feedback system has the forward transfer function G(s) = 100(s + 2)(s + 6) / [s(s + 3)(s + 4)]. Calculate the steady-state error for an input of 5tu(t).

What is the definition of the acceleration constant, Ka?

A Type 1 unity feedback system is subjected to a parabolic input, 0.5 * t^2 * u(t). What is the expected steady-state error?

For the system in Figure 7.7(a), with G(s) = 500(s + 2)(s + 5) / [(s + 8)(s + 10)(s + 12)], what is the steady-state error for a unit step input?

A control system has the specification Kp = 1000. What information can be inferred from this specification?

For a unity feedback system with forward transfer function G(s) = K(s + 12) / [s(s + 14)(s + 18)], what value of K will yield a 10 percent error in the steady state?

In the system of Figure 7.13, with G1(s) = 1000 and G2(s) = 1/[s(s+25)], what is the steady-state error component due to a unit step disturbance?

In a nonunity feedback system, what is the term for the signal at the output of the summing junction, such as Ea(s) in Figure 7.15(b)?

For the nonunity feedback system in Figure 7.16, what is the steady-state error e(inf) for a unit step input, given G(s) = 100 / [s(s+10)] and H(s) = 1 / (s+5)?

For the system in Figure 7.19 with T(s) = K / (s^2 + as + K), what is the sensitivity of the closed-loop transfer function T(s) with respect to the parameter 'a'?

For the system in Figure 7.19, with G(s) = K/[s(s+a)], what is the sensitivity of the steady-state error e(inf) with respect to parameter K for a ramp input?

Which method for finding steady-state error in state-space systems avoids taking the inverse of (sI - A)?

Using the input substitution method for a state-space system with a unit step input, what is the final expression for the steady-state error e(inf)?

For the system in Example 7.14 with A=[[-5,1,0],[0,-2,1],[20,-10,-1]], B=[[0],[0],[1]], and C=[1,1,0], what is the steady-state error for a unit step input using the input substitution method?

In the Antenna Control Case Study, the forward transfer function is G(s) = 6.63K / [s(s + 1.71)(s + 100)]. What is the steady-state error for a unit ramp input?

In the Antenna Control Case Study, what value of gain K is required to achieve a 10 percent error in the steady state?

In the Video Laser Disc Recorder Case Study, the system is determined to be Type 2. What is the steady-state error for a parabolic disturbance of 10t^2 micrometers?

In the Video Laser Disc Recorder Case Study, the acceleration constant is given as Ka = 0.0024*K1*K2*K3. A disturbance of 10t^2 micrometers results in an error e(inf) = 20/Ka. To meet a focusing accuracy of 0.1 micrometers, what is the required value for the gain product K1*K2*K3?

What are the two primary sources of steady-state errors discussed in the chapter?

For a unity feedback system with a forward path gain that is a pure integrator G(s) = K/s, what is the steady-state error for a unit step input?

How many pure integrations are required in the forward path of a unity feedback system to achieve zero steady-state error for a ramp input?

What is the primary trade-off involving steady-state error when adjusting only the system gain?

A unity feedback system has a forward transfer function G(s) = 500 / [(s+28)(s^2 + 8s + 12)]. What is the system type?

For the system with G(s) = 500 / [(s+28)(s^2 + 8s + 12)], what is the steady-state error for a ramp input of 60tu(t)?

If a stable unity feedback system has a forward transfer function G(s) = K / [s^2(s+a)], what is its steady-state error for a unit ramp input?

Consider the nonunity feedback system in Figure 7.18 with G(s) = 100/(s+4) and H(s) = 1/(s+1). What is the steady-state actuating signal, ea(inf), for a unit ramp input?

For the system in Figure 7.20 with G(s) = K/[(s+a)(s+b)], what is the sensitivity of the steady-state step error, e(inf), with respect to the gain K?

How is the steady-state error e(inf) related to the closed-loop transfer function T(s) and the input R(s)?

A unity feedback system has a forward transfer function G(s) = 120(s+2)/[(s+3)(s+4)]. What is the steady-state error for an input of 5t^2 u(t)?

What is the relationship between the system type and the static error constants Kp, Kv, and Ka for a Type 1 system?

What is the steady-state error of a Type 2 system for a ramp input?

Why must the final value theorem only be applied to stable systems when calculating finite steady-state errors?

For the system in Figure 7.14 with G1(s) = 1000 and G2(s) = (s+2)/(s+4), what is the steady-state error component due to a unit step disturbance?

To convert a nonunity feedback system (Figure 7.15b) into an equivalent unity feedback system (Figure 7.15e), what is the equivalent forward transfer function, Ge(s)?

For a unity feedback system, what is the steady-state error for a step input if the open-loop transfer function G(s) has a zero at the origin?

If a system has an open-loop transfer function G(s)H(s), and its closed-loop transfer function is unstable, can you meaningfully calculate a finite steady-state error?

What does a sensitivity value of S_F:P = 0 imply?

For the state-space system with input substitution, the steady-state solution for a ramp input is x_ss = Vt + W. What does V represent?

A unity feedback system has an open-loop transfer function with 3 poles and 1 zero. How many integrations are required for the system to have a finite, non-zero steady-state error for a parabolic input?

What is the steady-state error for a unit step input to a unity feedback system with the forward transfer function G(s) = K/[s(s+a)]?

A unity feedback system has a forward transfer function G(s) = 10(s+20)(s+30)/[s^2(s+25)(s+35)(s+50)]. What is the steady-state error for a parabolic input of 15t^2 u(t)?

For the system in Figure 7.7(c), G(s) = 500(s+2)(s+4)(s+5)(s+6)(s+7) / [s^2(s+8)(s+10)(s+12)]. What is the acceleration constant, Ka?

What is the steady-state error for a unit step input for the system in Figure 7.7(c), where G(s) has a factor of s^2 in the denominator?

For the nonunity feedback system in Figure 7.16, what is the steady-state actuating signal, ea(inf), for a unit step input, given G(s) = 100 / [s(s+10)] and H(s) = 1 / (s+5)?

Which statement correctly describes the final value theorem's application to functions with multiple poles at the origin?

A unity feedback system has a forward path G(s) that is a pure gain K. What is the steady-state error for a unit step input?