Question 12 of 50

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?

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?