REDUCTION OF MULTIPLE SUBSYSTEMS

What are the three basic topologies for interconnecting subsystems in block diagrams?

What is the equivalent transfer function, Ge(s), for three subsystems G1(s), G2(s), and G3(s) connected in a non-loading cascade form?

For a standard negative feedback system with a forward-path transfer function G(s) and a feedback-path transfer function H(s), what is the equivalent closed-loop transfer function Ge(s)?

What is the primary difference between a signal-flow graph and a block diagram?

In the context of Mason's Rule, what is a 'loop gain'?

According to Mason's Rule, what is the formula for the transfer function G(s) of a system?

What is the significance of a state-space representation that results in a diagonal system matrix (A matrix)?

In state-space, what is the relationship between the Controller Canonical Form and the Observer Canonical Form?

What are the poles of a system represented in state space equivalent to?

To find the eigenvalues of a system matrix A, which equation must be solved?

For the system in Example 5.3 with a forward path transfer function of 25 / (s(s+5)), what is the closed-loop transfer function T(s)?

In Example 5.4, a system with a forward transfer function G(s) = K / (s(s+5)) is designed to have a 10 percent overshoot. What is the required value of gain K?

For the signal-flow graph in Figure 5.20, which of the following is NOT a valid loop gain?

In the system from Figure 5.15, analyzed in Example 5.3, what is the calculated percent overshoot?

What does the 'loading effect' in cascaded systems imply?

For the system in Skill-Assessment Exercise 5.2, a unity feedback system with forward-path transfer function G(s) = 16 / (s(s+a)) is designed to have a 5 percent overshoot. What is the value of 'a'?

What is the equivalent transfer function for the parallel system shown in Figure 5.5(a), where the outputs of G1(s), G2(s), and G3(s) are summed with positive signs?

For the system in Example 5.11, the matrix A = [[-3, 1], [1, -3]] is diagonalized. What is the resulting diagonal matrix D = P^(-1)AP?

What is the primary characteristic of a system represented in the Jordan canonical form?

What transformation matrix P is used to diagonalize a system matrix A?

In the block diagram reduction shown in Figure 5.10, what is the equivalent transfer function for the three parallel feedback paths with transfer functions H1(s), -H2(s), and H3(s)?

The system described by the transfer function C(s)/R(s) = 24 / ((s+2)(s+3)(s+4)) is represented in parallel form in Example 5.7. What is the resulting state-space system matrix A?

What is the result of moving a block G(s) to the right past a summing junction, where the other input to the junction is X(s)?

For the signal-flow graph in Example 5.7 (Figure 5.21), what is the value of the cofactor Δ1, corresponding to the single forward path?

What is the defining characteristic of an eigenvector xi of a matrix A?

For the matrix A = [[-3, 1], [1, -3]] in Example 5.10, what are the eigenvalues?

A system has a transfer function G(s) = (s^2 + 7s + 2) / (s^3 + 9s^2 + 26s + 24). What is the state-space matrix A in controller canonical form?

What is the structure of the input matrix B in the controller canonical form for the transfer function G(s) = (s^2 + 7s + 2) / (s^3 + 9s^2 + 26s + 24)?

A system is represented by the state equations x_ = Ax + Br and y = Cx. A similarity transformation z = P^(-1)x is applied. What is the new state equation for z_?

In the state-space representation for the antenna azimuth position control system derived in the case study (Figure 5.35), the state vector is defined as x = [x1, x2, ea]^T. What does the state variable 'ea' represent?

What is the equivalent transfer function T(s) = C(s)/R(s) for the system in Skill-Assessment Exercise 5.1, as shown in Figure 5.13?

For the system in Example 5.8, with forward transfer function G(s) = 100(s+5) / ((s+2)(s+3)) in a unity feedback loop, what is the state equation for x_1 assuming a cascade form with poles at -3 and -2?

How is a system with transfer function C(s)/R(s) = (s+3)/((s+4)(s+6)) represented as a signal-flow diagram in parallel form?

What is the open-loop transfer function, or loop gain, for the feedback system shown in Figure 5.6?

For the UFSS vehicle pitch control system in Figure 5.37, which state variable represents the pitch angle?

For the system in Skill-Assessment Exercise 5.7, with A = [[1, 3], [-4, -6]], what are the eigenvalues?

In the signal-flow graph of Figure 5.20, which pair of loops is considered 'nontouching'?

How is the state-space representation of a system with transfer function C(s)/R(s) = 24/((s+2)(s+3)(s+4)) derived in cascade form?

For the system in Figure 5.14, with forward-path transfer function G(s) = K / (s(s+a)), for what range of K is the system underdamped?

What is the result of moving a block G(s) to the left past a pickoff point?

In the antenna control case study (Figure 5.34), what is the first step performed to simplify the block diagram?

What is the equivalent forward transfer function G(s) for the antenna control system after converting it to a unity feedback system, as shown in Figure 5.34(c)?

When a system with transfer function G(s) = C(s)/R(s) is represented in observer canonical form, where are the coefficients of the characteristic polynomial located in the system matrix A?

In the signal-flow graph of Example 5.6 (Figure 5.19c), how is the negative feedback from H1(s) represented?

For the system in Skill-Assessment Exercise 5.6, representing the feedback system from Figure 5.29 in controller canonical form, what is the value of the top-left element of the A matrix?

What are 'companion matrices' in the context of state-space forms?

For the system reduction in Example 5.2 (Figure 5.12), what is the equivalent transfer function of the feedback system with forward path G3(s) and feedback H3(s)?

In the case study, the simplified antenna control system of Figure 5.34d is analyzed with K=1000. What is the resulting percent overshoot?

How many nontouching loops taken two at a time exist in the signal-flow graph of Example 5.7 (Figure 5.21)?

What is the final closed-loop transfer function T(s) = C(s)/R(s) for the block diagram in Example 5.1 (Figure 5.9)?