DIGITAL CONTROL SYSTEMS

What device is used to convert analog signals to digital signals within a control loop containing a digital computer?

What is the stability criterion for a digital control system in the z-plane?

According to the derivation in Example 13.1, what is the closed-form z-transform, F(z), for a sampled unit ramp f(kT) = kT?

The transfer function of a zero-order hold, which holds the last sampled value over the sampling interval, is given by which Laplace transform?

In the context of analog-to-digital conversion, what is quantization error?

What is the primary purpose of the Tustin transformation in the design of digital compensators?

In Example 13.12, a digital lead compensator Gc(z) is designed for a plant Gp(s) = 1/(s(s+6)(s+10)). What is the chosen sampling time, T, for this design?

For a digital compensator to be physically realizable, what must be true about the relationship between the order of its numerator and denominator polynomials?

What is the z-transform, R(z), for a unit step input R(s) = 1/s?

In the Antenna Control Case Study, the design gain K is calculated to achieve a 0.5 damping ratio. What is the value of K?

How is the static velocity error constant, Kv, for a digital system defined?

In Example 13.6, a missile control system is analyzed. For a gain of K = 100, where are the poles of the closed-loop system located, and is the system stable?

A bilinear transformation s = (z-1)/(z+1) is used for stability analysis. Where does this transformation map points from the left half of the s-plane (where alpha < 0)?

In gain design on the z-plane, how are lines of constant settling time, Ts, represented?

What is the steady-state error e*(infinity) for a unity feedback digital system with a unit step input?

What is the result of sampling a time waveform f(t) with an ideal sampler?

In Example 13.9, what is the steady-state error for a ramp input for the system with G1(s) = 10/(s(s+1))?

What is one of the main advantages of using digital computers for control over analog controllers?

When reducing block diagrams for sampled-data systems, the z-transform of a product of two continuous-time transfer functions, z{G1(s)G2(s)}, is generally not equal to what?

In Example 13.8, the denominator of a digital transfer function is given as D(z) = z^3 - z^2 - 0.2z + 0.1. After applying the bilinear transformation, what is the resulting polynomial in s?

What is the minimum sampling frequency required to avoid distortion when sampling a signal, according to the principle mentioned in the text?

What does the z-transform theorem f(infinity) = lim(z->1) (1-z^-1)F(z) represent?

In Example 13.7, a digital system becomes unstable for sampling intervals T > 0.2 seconds. What sampling frequency does this correspond to?

When using the power series method to find the inverse z-transform of F(z), what do the coefficients of the resulting power series in z^-k represent?

In the Antenna Control Digital Cascade Compensator Design case study, what is the design requirement for the settling time of the compensated system?

How does placing a pole at z=1 in the open-loop pulse transfer function G(z) affect the steady-state error of a digital system?

In Example 13.10, the root locus for the system G(z) = K(z+1)/((z-1)(z-0.5)) is analyzed for stability. What is the approximate gain K at which the system becomes unstable?

In the digital compensator implementation flowchart shown in Figure 13.28, what do the 'Delay T seconds' blocks represent?

How are curves of constant damping ratio, zeta, represented on the z-plane?

In the Antenna Control Case Study for digital cascade compensator design, a lead compensator zero is placed at s = -1.71. What is the reason for this placement?

For the system in Example 13.11 with a designed gain of K=0.0627, what is the approximate overshoot of the sampled step response?

What is the maximum quantization error for an analog-to-digital converter using n binary bits and a maximum analog voltage of M?

What is the inverse Tustin transformation used for?

When deriving the pulse transfer function, C(z) = G(z)R(z), what conceptual component is assumed to be at the system output?

In the digital compensator implementation shown by the difference equation in (13.99), the current output x*(t) depends on what combination of signals?

Which of the following z-transforms from Table 13.1 corresponds to the time function f(t) = sin(omega*t)?

According to the guideline from Astrom and Wittenmark mentioned in Section 13.10, the sampling interval T should be in what range, relative to the zero dB frequency (omega_phi_M) of the compensated analog system?

In the inverse z-transform method via partial-fraction expansion, why is F(z)/z expanded instead of F(z) directly?

For the digital system in Figure 13.9(c), with two cascaded subsystems G1(z) and G2(z) each with a sampler at its input, what is the overall pulse transfer function for the output C(z)?

In the context of the z-transform, what is the significance of the variable T?

A continuous system pole at s = -a is transformed into the z-plane using z = e^(sT). What is the location of the corresponding pole in the z-plane?

What is the primary effect of decreasing the sampling interval, T, when using the Tustin transformation to design a digital compensator?

In the digital control system of Figure 13.25(a), what components does the 'Digital controller' block represent?

In Figure 13.18, which shows performance characteristics on the z-plane, what do radial lines emanating from the origin represent?

For the cascade of G1(s) and a zero-order hold in Example 13.4, the pulse transfer function G(z) is found using the relation G(z) = (1 - z^-1) * Z{G1(s)/s}. What is G1(s)/s in this example?

In the final step of Example 13.4, with T=0.5, what is the final expression for the pulse transfer function G(z)?

What is the primary trade-off involved in choosing the sampling rate for a digital control system?

If a digital system's closed-loop poles are found to be at 0.5 + j0.5 and 0.5 - j0.5, is the system stable?

In the digital compensator flowchart of Figure 13.29, which implements Gc(z) = (z+0.5)/(z^2 - 0.5z + 0.7), what value is multiplied by the e*(t-T) sample?

What is the key difference in plotting a root locus for a digital system on the z-plane compared to a continuous system on the s-plane?