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systems analysis and design

Questions and Answers of Systems Analysis And Design

The asymptotic log-magnitude curves for two transfer functions are given in Figure P8.6. Sketch the corresponding asymptotic phase shift curves for each system. Determine the transfer function for
Driverless vehicles can be used in warehouses, airports, and many other applications. These vehicles follow a wire embedded in the floor and adjust the steerable front wheels in order to maintain
A feedback control system is shown in Figure P8.8.The specification for the closed-loop system requires that the overshoot to a step input be less than 15%. (a) Determine the corresponding
Sketch the logarithmic-magnitude versus phase angle curves for the transfer functions (a) and (b) of Problem P8.1.
A spring-mass-damper system is shown in Figure AP8.1(a).The Bode diagram obtained by experimental means using a sinusoidal forcing function is shownFIGURE AP8.1 A spring-mass damper system.
A system is shown in Figure AP8.2. The nominal value of the parameter b is 4.0. Determine the sensitivityFIGURE AP8.2 System with parameter b.
As an automobile moves along the road, the vertical displacements at the tires act as the motion excitation to the automobile suspension system [16]. FigureFIGURE AP8.3 Auto suspension system
A helicopter with a load on the end of a cable is shown in Figure AP8.4 (a).The position control system is shown in Figure AP8.4 (b), where the visual feedback is represented by H(s). Sketch the Bode
A closed-loop system with unity feedback has a transfer function(a) Determine the loop transfer function Gc(s) G(s). (b) Plot the log-magnitude-phase (similar to Figure 8.27), and identify the
Î¼(t) = sin(Ï‰t) is less than 1 for all co. For the values you selected for k and b, what is the frequency at which the peak response occurs?
An op-amp circuit is shown in Figure AP8.7. The circuit represents a lead compensator discussed in more detail in Chapter 10.(a) Determine the transfer function of this circuit.(b) Sketch the
In this chapter, we wish to use a PD controller such that Gc(s) = K(s + 2). The tachometer is not used (see Figure CDP4.1). Plot the Bode diagram for the system when K = 40. Determine the step
Understanding the behavior of a human steering an automobile remains an interesting subject [14,15, 16, 21]. The design and development of systems for four-wheel steering, active suspensions, active,
The unmanned exploration of planets such as Mars requires a high level of autonomy because of the communication delays between robots in space and their Earth-based stations. This affects all the
A table is used to position vials under a dispenser head, as shown in Figure DP8.3(a). The objective is speed, accuracy, and smooth motion in order to eliminate spilling. The position control system
Anesthesia can be administered automatically by a control system. For certain operations, such as brain and eye surgery, involuntary muscle movements can be disastrous. To ensure adequate operating
Consider the control system depicted where the plant is a "black box" for which little is known in the way of mathematical models. The only information available on the plant is the frequency
A single-input, single-output system is described b y (t) = [0 l]x(/) (a) Determine p and K such that the unit step response exhibits a zero steady-state error and the percent overshoot meets
Consider the system of Figure DPS.7. Consider the controller to be a proportional plus integral plus derivative (PID) given byDesign the PID controller gains to achieve (a) an acceleration constant
Consider the closed-loop transfer functionDevelop an m-file to, obtain the Bode plot and verify that the resonant frequency is 5 rad/s and that the peak magnitude M pÏ‰ is 14 dB.
For the following transfer functions, sketch the Bode plots, then verify with the bode function:
For each of the following transfer functions, sketch the Bode plot and determine the crossover frequency (that is, the frequency at which 20 log10 |G(jÏ‰) | = OdB):
A unity negative feedback system has the loop transfer functionDetermine the closed-loop system bandwidth. Using the bode function obtain the Bode plot and label the plot with the bandwidth.
A block diagram of a second-order system is shown in Figure CP8.5.FIGURE CP8.5 A second-order feedback controlsystem.
Consider the feedback system in Figure CP8.6. Obtain the Bode plots of the loop and closed-loop transfer functions using an m-file.FIGURE CP8.6 Closed-loop feedback system.
A unity feedback system has the loop transfer functionGenerate a plot of the bandwidth versus the parameter p as 0
Consider the problem of controlling an inverted pendulum on a moving base, as shown in Figure CP8.8 (a).The transfer function of the system isThe design objective is to balance the pendulum (i.e.,
Design a filter, G(s), with the following frequency response: 1. For ω < 1 rad/s, the magnitude 20 log1() |G(jω)|< OdB 2. For 1 < ω < 1000 rad/s, the magnitude 201og10 | G(jω) | ≥ OdB 3. For co
A system has the loop transfer functionPlot the Bode diagram. Show that the phase margin is approximately 17.5° and that the gain margin is approximately 26.2 dB.
Consider the wind tunnel control system of Problem P7.31 for K = 326. Obtain the Bode diagram and show that the P.M. = 25° and that the G.M. = 10 dB. Also, show that the bandwidth of the closed-loop
Consider a unity feedback system with the loop transfer function(a) Plot the Bode diagram, (b) Find the gain margin and the phase margin.
A unity feedback system with the loop transfer functionwhere T1 = 0.02 and T2 = 0.2 s. (a) Select a gain K so that the steady-state error for a ramp input is 10% of the magnitude of the ramp function
A unity feedback system has a loop transfer function(a) Find the maximum magnitude of the closed-loop frequency response using the Nichols chart, (b) Find the bandwidth and the resonant frequency of
A Nichols chart is given in Figure E9.14 for a system with Gc(jÏ‰)G(jÏ‰)). Using the following table, find (a) the peak resonance MpÏ‰) in dB; (b) the resonant frequency
Consider a unity feedback system with the loop transfer functionFind the bandwidth of the closed-loop system.
The pure time delay e-sT may be approximated bya transfer function asfor 0
A unity feedback system has a loop transfer function(a) Plot the Bode diagram and (b) determine the gain K required to obtain a phase margin of 30°. What is the steady-state error for a ramp
An actuator for a disk drive uses a shock mount to absorb vibrational energy at approximately 60 Hz [14]. The Bode diagram of G(.(s)G(s) of the control system is shown in Figure E9.18. (a) Find the
A unity feedback system with Gc(s) = K hasSelect a gain K so that the phase margin of the system is 50°. Determine the gain margin for the selected gain,K.
A system has the loop transfer functionwhere K = 10.5. Show that the system crossover (O dB) frequency is 5 rad/s and that the phase margin is 40°.
Consider a simple model of an automobile driver following another car on the highway at high speed. The model shown in Figure E9.20 incorporates the driver's reaction time, T. One driver has T = 1 s,
A unity feedback control system has a loop transferFunctionDetermine the phase margin, the crossover frequency, and the gain margin when K - 1300.
A unity feedback system has a loop transfer function(a) Using a Bode diagram for K = 10, determine the system phase margin, (b) Select a gain K so that the phase margin is at least 60°.
Consider again the system of E9.21 when K = 438. Determine the closed-loop system bandwidth, resonant frequency, and Mpω using the Nichols chart.
A unity feedback system has a loop transfer functionwhere K = 1 / 2and T = 1. The polar plot for Gc(jÏ‰)G(jaÏ‰) is shown in Figure E9.24. Determine whether the system is stable by
A unity feedback system has a loop transfer functionDetermine the phase margin and the crossover frequency.
For the system of E9.25, determine Mpω, and ωB for the closed-loop frequency response by using the Nichols chart.
A unity feedback system has a loop transfer function
A unity feedback system has the loop transfer function(a) Determine the phase margin of the system when K = 0.16. (b) Use the phase margin to estimate £ and predict the overshoot, (c) Calculate
A loop transfer function isUsing the contour in the .y-plane shown in Figure E9.29, determine the corresponding contour in the F(s)-plane (B = - 1 + /). FIGURE E9.29 Contour in the s-plane.
An integrated circuit is available to serve as a feedback system to regulate the output voltage of a power supply. The Bode diagram of the required loop transfer function Gc(J(ω)G(J(ω). Estimate
Consider the system represented in state variable formv = Cx + Du, where C = [1000 0]. and D = [0] Sketch the Bode plot.
A closed-loop feedback system is shown in Figure E9.31. Sketch the Bode plot and determine the phase margin.FIGURE E9.31 Non unity feedback system.
Consider the system described in state variable form by y(t) = Cx(t) where Compute the phase margin.
Consider the system that compute the loop transfer function L(s), and sketch the Bode plot. Determine the phase margin and gain margin when the controller gain K = 5.
Consider a system with a loop transfer functionWe wish to obtain a resonant peak MpÏ‰) = 3.0 dB for the closed-loop system. The peak occurs between 6 and 9 rad/s and is only 1.25 dB. Plot
An integrated CMOS digital circuit can be represented by the Bode diagram shown in Figure E9.5.(a) Find the gain and phase margins of the circuit.(b) Estimate how much we would need to reduce the
A system has a loop transfer function(a) For K = 4, show that the gain margin is 3.5 dB. (b) If we wish to achieve a gain margin equal to 16 dB, determine the value of the gain K.
A unity feedback system has a loop transfer functionDetermine the range of K for which the system is stable using the Nyquist plot.
Consider a unity feedback system with the loop transfer function(a) For K = 4, show that the gain margin is 3.5 dB. (b) If we wish to achieve a gain margin equal to 16 dB, determine the value of the
For the system of E9.8, find the phase margin of the system for K - 5.
For the Nyquist plots of Problem P8.1, use the Nyquist criterion to ascertain the stability of the various systems. In each case, specify the values of N, P, and Z.
Machine tools are often automatically controlled. These automatic systems are often called numerical machine controls [9]. On each axis, the desired position of the machine tool is compared with the
A control system for a chemical concentration control system. The system receives a granular feed of varying composition, and we want to maintain a constant composition of the output mixture by
A simplified model of the control system for regulating the pupillary aperture in the human eye. The gain K represents the pupillary gain, and r is the pupil time constant, which is 0.5 s. The time
A controller is used to regulate the temperature of a mold for plastic part fabrication. The value of the delay time is estimated at 1.2 s. (a) Using the Nyquist criterion, determine the stability of
Electronics and computers arc being used to control automobiles. An example of an automobile control system, the steering control for a research automobile. The control stick is used for steering. A
Consider the automatic ship-steering system discussed in Problem P8.ll. The frequency response of the open-loop portion of the ship steering control system is shown in Figure P8.ll. The deviation of
An electric carrier that automatically follows a tape track laid out on a factory floor is shown in Figure P9.16(a) [15]. Closed-loop feedback systems are used to control the guidance and speed of
The primary objective of many control systems is to maintain the output variable at the desired or reference condition when the system is subjected to a disturbance [22]. A typical chemical reactor
A model of an automobile driver attempting to steer a course, where K = 5.3. (a) Find the frequency response and the gain and phase margins when the reaction time T is zero, (b) Find the phase margin
In the United States, billions of dollars are spent annually for solid waste collection and disposal. One system, which uses a remote control pick-up arm for collecting waste bags, is shown in Figure
Sketch the Nyquist plots of the following loop transfer functions L(s) - Gc(s)G(s), and determine whether the system is stable by applying the Nyquist criterion:If the system is stable, find the
The Bell-Boeing V-22 Osprey Tilt rotor is both an airplane and a helicopter. Its advantage is the ability to rotate its engines to a vertical position, as shown in Figure P7.33(a), for takeoffs and
Consider a unity feedback system with the loop transfer function(a) Sketch the Bode diagram for K = 4. Determine (b) the gain margin, (c) the value of K required to provide a gain margin equal to 12
The Nichols diagram for Gc(jÏ‰)G(jÏ‰) of a closed loop system is shown in Figure P9.22.The frequency for each point on the graph is given in the following table:Determine (a) the
A closed-loop system has a loop transfer function(a) Determine the gain K so that the phase margin is 60°. (b) For the gain K selected in part (a), determine the gain margin of the system.
A closed-loop system with unity feedback has a loop transfer function(a) Determine the gain K so that the phase margin is 45°. (b) For the gain K selected in part (a), determine the gain margin,
A closed-loop system has the loop transfer function(a) Determine the gain K so that the phase margin is 60° when T - 0.2. (b) Plot the phase margin versus the time delay T for K as in part (a).
A specialty machine shop is improving the efficiency of its surface-grinding process [21]. The existing machine is mechanically sound, but manually operated. Automating the machine will free the
Consider the system that determine the maximum value of K = Kmax for which the closed-loop system is stable. Plot the phase margin as a function of the gain 1 ≤ K ≤ Kmax. Explain what happens to
Consider the feedback system shown in Figure P9.28 with the process transfer function given asThe controller is the proportional controller Gc(s) = KP (a) Determine a value of KP such that the phase
(b) Find a suitable contour Ts in the .v-plane that can be used to determine whether all the roots of the characteristic equation have real parts less than s = -Ïƒ1.(c) Using the contour of
The Nyquist plot of a conditionally stable system for a specific gain K. (a) Determine whether the system is stable, and find the number of roots (if any) in the right-hand s-plane. The system has no
A speed control for a gasoline engine because of the restriction at the carburetor intake and the capacitance of the reduction manifold, the lag T1, occurs and is equal to 1 second. The engine time
A direct-drive arm is an innovative mechanical arm in which no reducers are used between motors and their loads. Because the motor rotors are directly coupled to the loads, the drive systems have no
A vertical takeoff (VTOL) aircraft is an inherently unstable vehicle and requires an automatic stabilization system. An attitude stabilization system for the K-16B U.S. Army VTOL aircraft has been
Electro hydraulic servomechanisms are used in control systems requiring a rapid response for a large mass. An electro hydraulic servomechanism can provide an output of 100 kW or greater [17]. A photo
The space shuttle carries large payloads into space and returns them to earth for reuse [19]. The shuttle uses elevons at the trailing edge of the wing and a brake on the tail to control the flight
Operational spacecraft undergo substantial mass property and configuration changes during their lifetime [25]. For example, the inertias change considerably during operations. Consider the
A multi loop block diagram. (a) Compute the transfer function T(s) = Y(s)/R(s). (b) Determine K such that the steady-state tracking error to a unit step input R(s) = 1/s is zero. Plot the unit step
Patients with a cardio logical illness and less than normal heart muscle strength can benefit from an assistance device. An electric ventricular assist device (EVAD) converts electric power into
Anesthesia is used in surgery to induce unconsciousness. One problem with drug-induced unconsciousness is large differences in patient responsiveness. Furthermore, the patient response changes during
Welding processes have been automated over the past decades. Weld quality features, such as final metallurgy and joint mechanics, typically are not measurable online for control. Therefore, some
The control of a paper-making machine is quite complex [27]. The goal is to deposit the proper amount of fiber suspension (pulp) at the right speed and in a uniform way. Dewatering, fiber deposition,
NASA is planning many Mars missions with rover vehicles. A typical rover is a solar-powered vehicle which will see where it is going with TV cameras and will measure distance to objects with laser
Building elevators are limited to about 800 meters. Above that height, elevator cables and too heavy for practical use. One solution is to eliminate the cable. The key to the cordless elevator is the
A control system is shown. The gain K is greater than 500 and less than 3000. Select a gain that will cause the system step response to have an overshoot of less than 20%. Plot the Nichols diagram,
Consider again the system which uses a PI controller. Letand determine the gain KP that provides the maximum phase margin.
The system of Figure CDP4.1 uses a controller Gc (s) = K0. Determine the value of Ku so that the phase margin is 70°. Plot the response of this system to a step input.

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