Modern Control Engineering 1st. Edition by P.N. Paraskevopoulos | 9780824789817 | 0824789814 | Holooly

Control Systems

Modern Control Engineering

170 SOLVED PROBLEMS

Question: 5.3.2

Consider the network of Figure 5.2a with zero initial conditions.The inputs,the state variables, and the outputs of the network are shown in Figure 5.2b. Determine:(a) The state equations of the network (b) The transition matrix and the output vector of the network, when R1=0 Ω,R2=1.5 Ω, C=1 F,L1=L ...

Verified Answer:

(a) The two loop equations are

R_1(i_1+i_2)...

Question: 9.10.1

Consider the closed-loop system of Figure 9.56, where G(s) = 1/s² and R(s)= 1/s. Find the transfer function Gc(s) of the optimal controller such that Je = minimum and Ju≤1. ...

Verified Answer:

We have

λ+G\overline{G}=λ+\left[\frac{1}{s²...

Question: 12.3.6

For the system of Example 12.3.5, for T = 1 and ω = π/2, find: (a) The transition matrix Φ(kT) (b) The state-space vector x(kT) (c) The output vector y(kT). ...

Verified Answer:

For the given values of ω and T, A, B, and c becom...

Question: 8.5.2

This example refers to the system of automatically adjusting the opening and closing of the pupil of the human eye. A simplified diagram of this system is given in Figure 8.41. Here, the constant a, which is the inverse of the time constant of the pupil of the eye, is usually 0.5 sec; the constant ...

Verified Answer:

The open-loop transfer function has the form [late...

Question: 8.5.1

Consider the transfer function H(jω)=10(jω+1)/(jω)(10^-1jω+1)(3×10^-3jω+1)Plot the Bode diagrams A and φ of H(jω). ...

Verified Answer:

With respect to the diagram A, define

A_1=2...

Question: 9.9.1

Consider a system with transfer function G(s)=K/s(1+0.1s)(1+0.4s)Find a phase lag-lead controller such as to satisfy the following closed-loop specifications:(a) Velocity constant Kv=100 sec^-1(b) Phase margin φp≥45°. ...

Verified Answer:

Using the definition (4.7-3) of the velocity const...

Question: 9.6.3

Consider a system under control, with transfer function G(s)=K/(1+sT1)(1+sT2) Show that using the PID controller (Eq. (9.6-1)), one can achieve arbitrary pole placement and simultaneously drive the position steady-state error to zero. ...

Verified Answer:

Clearly, by choosing a PID controller, the type of...

Question: 9.6.6

The position control system of an object holder robot is shown in Figure 9.36. The block diagram is given in Figure 9.37. Use the stability limit method of Ziegler- Nichols to determine the parameters of the PID controller. Use the Routh stability criterion to calculate the values of Kp and T. ...

Verified Answer:

Using only a proportional controller, as in Figure...

Question: 8.4.6

An automatic control system for controlling the thickness of sheet metal is given in Figure 1.10. A simplified block diagram of this system is given in Figure 8.32.Construct the Nyquist diagram and determine the range of values of K for which the closed-loop system is stable.The controller transfer ...

Verified Answer:

(a) For this case (i.e., when

G_c(s)=K[/lat...

Question: 9.8.1

Design a phase-lag controller that it satisfies the design specifications of the system of Example 9.7.1. ...

Verified Answer:

Consider Figure 9.44b. For the present example, th...

Loading...