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systems analysis and design

Questions and Answers of Systems Analysis And Design

A PID controller is used in the system in Figure 12.1, whereThe gain KD of the controller (Equation (12.33)) is limited to 200. Select a set of compensator zeros so that the pair of closed-loop roots
A system has a process functionwith K = 10 and negative unity feedback with a PD compensator Gc(s) = Kp + KDs. The objective is to design Gc(s) so that the overshoot to a step is less than 5% and the
Consider the control system shown when G{s) - \/{s + 5)2, and select a PID controller so that the settling time (with a 2% criterion) is less than 1.5 second for an ITAE step response. Plot y(t) for
For the control system with G(s) = \/(s + 4)2, select a PID controller to achieve a settling time (with a 2% criterion) of less than 1.0 second for an ITAE step response. Plot y(t) for a step input
Repeat Exercise 12.6, striving to achieve a minimum settling time while adding the constraint that |u(t)| < 80 for t > 0 for a unit step input, r(t) = l , l > 0.
A system has the form shown in Figure E12.6 with
Consider the unmanned underwater vehicle (UUV) problem presented in DP4.7. The control system is shown in Figure P12.1, where R(s) - 0, the desired roll angle, and Td[s) = 1/s. We select Gc(s) = K(s
A plant has a transfer functionWe want to use a negative unity feedback with a PID controller and a prefilter. The goal is to achieve a peak time of 1 second with ITAE-type performance. Predict the
Consider the three dimensional shown. This problem was first introduced in DP5.7. The control of x may be achieved with a DC motor and position feedback of the form shown, with the DC motor and load
Consider the closed-loop second-order systemy = [2 0]x + [0]µ. Compute the sensitivity of the closed-loop system to variations in the parameter K.
Consider the mobile, remote-controlled video camera system presented in DP4.8.The control system is shown, where TX - 20 ms and TI - 2 ms. (a) Select K so that Mpw = 1.84. (b) Plot 20 log|T| and
Magnetic levitation (maglev) trains may replace airplanes on routes shorter than 200 miles. The maglev train developed by a German firm uses electromagnetic attraction to propel and levitate heavy
An automatically guided vehicle is shown in Figure P12.4(a) and its control system is shown in Figure P12.4(b). The goal is to track the guide wire accurately, to be insensitive to changes in the
A roll-wrapping machine (RWM) receives, wraps, and labels large paper rolls produced in a paper mill [9, 16]. The RWM consists of several major stations: positioning station, waiting station,
The function of a steel plate mill is to roll reheated slabs into plates of scheduled thickness and dimension [5, 10). The final products are of rectangular plane view shapes having a width of up to
A motor and load with negligible friction and a voltage- to-current amplifier Ka is used in the feedback control system, shown in Figure P12.7. A designer selects a PID controllerwhere KP = 5, Kt =
A unity feedback system has a nominal characteristic equation q(s) = s3 + 3s2 + 3s + 6 = 0. The coefficients vary as follows: 2 ≤ a2 ≤ 4, 1 ≤ a1 ≤ 4, 4 ≤ a0 ≤ 5. Determine whether the
Future astronauts may drive on the Moon in a pressurized vehicle that would have a range of 620 miles and could be used for missions of up to six months. Boeing Company engineers first analyzed the
To minimize vibrational effects, a telescope is magnetically levitated. This method also eliminates friction in the azimuth magnetic drive system. The photo detectors for the sensing system require
A system of the form shown in Figure 12.1 haswhere 3 ‰¤ p ‰¤ 5,0 ‰¤ q ‰¤ 1, and 1 ‰¤ r ‰¤ 2. we will use a compensator with all real poles and zeros. Select an appropriate
One promising solution to traffic gridlock is a magnetic levitation (maglev) system. Vehicles are suspended on a guide way above the highway and guided by magnetic forces instead of relying on wheels
Antiskid braking systems present a challenging control problem, since brake/automotive system parameter variations can vary significantly (e.g., due to the brake-pad coefficient of friction changes
A robot has been designed to aid in hip-replacement surgery. The device, called RoBoDoc, is used to precisely orient and mill the femoral cavity for acceptance of the prosthetic hip implant. Clearly,
Consider the system of Figure 12.1 withwhere K = 1 under normal conditions. Design a PID controller to achieve a phase margin of 50°. The controller is with complex zeros. Determine the effect of
Consider the system withwhere K1 = 1.5 and T ‰ˆ 0.001 second, which may be neglected. (Check this later in the design process.) Select a PID controller so that the settling time (with a 2%
Consider the system withThe goal is to select a PI controller using the ITAE design criterion while constraining the control signal as |µ(t) ‰¤ 1 for a unit step input. Determine the appropriate
A machine tool control system is shown. The transfer function of the power amplifier, prime mover, moving carriage, and tool bit isThe goal is to have an overshoot less than 25% for a step input
Consider a system with the structure withwhere 1 ‰¤ a ‰¤ 3 and 2 ‰¤ K ‰¤ 4. Use a PID controller and design the controller for the worst-case
A position control system for a large turntable is shown, and the block diagram of the system is shown. This system uses a large torque motor with Km = 15. The objective is to reduce the steady-state
Consider the closed-loop system depicted in Figure DPI 2.2. The process has a parameter K that is nominally K = 1 Design a controller that results in a percent overshoot P.O. ≤ 10% for a unit step
Many university and government laboratories have constructed robot hands capable of grasping and manipulating objects. But teaching the artificial devices to perform even simple tasks required
Objects smaller than the wavelengths of visible light are a staple of contemporary science and technology. Biologists study single molecules of protein or DNA; materials scientists examine
The system described in DP12.4 is to be designed using the frequency response techniques described in Section 12.6 withSelect the coefficients of Gc(s) so that the phase margin is approximately 45°.
The use of control theory to provide insight into neurophysiology has a long history. As early as the beginning of the last century, many investigators described a muscle control phenomenon caused by
The goal is to design an elevator control system so that the elevator will move from floor to floor rapidly and stop accurately at the selected floor. The elevator will contain from one to three
A model of the feedback control system is shown for an electric ventricular assist device. This problem was introduced in AP9.11. The motor, pump, and blood sac can be modeled by a time delay with T
One arm of a space robot is shown. The block diagram for the control of the arm is shown. The transfer function of the motor and arm is(a) If Gc(s) = K, determine the gain necessary for an overshoot
A closed-loop feedback system is shown. Use an m-file to obtain a plot of | STK | versus ω. Plot |T(s)| versus ω, where T(s) is the closed-loop transfer function.
An aircraft aileron can be modeled as a first order systemwhere p depends on the aircraft. Obtain a family of step responses for the aileron system in the feedback configuration shown in Figure
Consider the control system,whereThe value of / is known to change slowly with time, although, for design purposes, the nominal value is chosen to be J = 25.(a) Design a PID compensator (denoted by
Consider the feedback control system in Figure CP12.4. The exact value of parameter b is unknown; however, for design purposes, the nominal value is taken to be h = 4. The value of a - 8 is known
A model of a flexible structure is given bywhere Ï‰n is the natural frequency of the flexible mode, and £ is the corresponding damping ratio. In general, it is difficult to know the structural
The industrial process is known to have a time delay in the loop. In practice, it is often the case that the magnitude of system time delays cannot be precisely determined. The magnitude of the time
A unity negative feedback loop has the loop transfer functionWe know from the underlying physics of the problem that the parameter a can vary only between 0 (a) The steady-state tracking error due to
The Gamma-Ray imaging Device (GRID) is a NASA experiment to be flown on a long-duration, high-altitude balloon during the coming solar maximum. The GRID on a balloon is an instrument that will
Design a PID controller for the capstan-slide system. The percent overshoot should be less than 3% and the settling time should be (with a 2% criterion) less than 250 ms for a step input r{t).
State whether the following signals are discrete or continuous: (a) Elevation contours on a map. (b) Temperature in a room. (c) Digital clock display. (d) The score of a basketball game. (e) The
A system has G{z) as described by Equation (13.34) with T = 0.01 s and r = 0.008 s. (a) Find K so that the overshoot is less than 40%. (b) Determine the steady-state error in response to a unit ramp
A system has a process transfer function(a) Determine G(z) for Gp(s) preceded by a zero-order hold with T = 0.05 s. (b) Determine whether the digital system is stable, (c) Plot the impulse response
Find the z-transform ofwhen the sampling period is 1 second.
The characteristic equation of a sampled system is z2 + (K - 4)z + 0.8 = 0. Find the range of K so that the system is stable.
A unity feedback system, has a plantwith T = 0.5. Determine whether the system is stable when K = 5. Determine the maximum value of K for stability.
Consider the open-loop sampled-data system. Determine the transfer function G(z) when the sampling time is T = 1 s.
Consider the open-loop sampled-data system shown in Figure E13.16. Determine the transfer function G (z) and when the sampling time T - 0.5 s.
(a) Find the values y(kT) whenfor k = 0 to 4.
A system has a response y{kT) = kT for k Find Y(z) for this response.
We have a functionUsing a partial fraction expansion of Y(s) and Table 13.1, find Y(z) when T = 0 .1s.
The space shuttle, with its robotic arm,. An astronaut controls the robotic arm and gripper by using a window and the TV cameras [9]. Discuss the use of digital control for this system and sketch a
Computer control of a robot to spray paint an automobile is shown by the system. The system is of the type, whereand we want a phase margin of 45°. A compensator for this system was obtained in
Find the response for the first four sampling instants forThen find y(Q),y(l), y(2), and y(3).
Determine whether the closed-loop system with T(z) is stable whenunstable
(a) Determine y(kT) for k = 0 to 3 when
The input to a sampler is r(t) = sin (ωt), where ω = I/π. Plot the input to the sampler and the output r*{t) for the first 2 seconds when T - 0.25 s.
Consider a system with a zero-order hold, a processand T = 0.1 s. (a) Let D(z) = K and determine the transfer function G(z)D(z). (b) Determine the characteristic equation of the closed-loop system,
(a) For the system described in Problem P13.10, design a lag compensator Gc(s) using the methods of Chapter 10 to achieve an overshoot less than 30% and a steady-state error less than 0.01 for a ramp
The transfer function of a plant and a zero-order hold is(a) Plot the root locus, (b) Determine the range of gain K for a stable system.
The space station orientation controller described in Exercise E7.6 is implemented with a sampler and hold and has the transfer function.(a) Plot the root locus, (b) Determine the value of K so that
A sampled-data system with a sampling period T = 0.05s is(a) Plot the root locus, (b) Determine K when the two real poles break away from the real axis, (c) Calculate the maximum K for stability.
A closed-loop system with a sampler and hold, has a process transfer functionCalculate and plot y{kT) for 0
A closed-loop system hascalculate and plot y{kT) for 0 ‰¤ k ‰¤ 8 when T = 1 s and the input is a unit step.
A closed-loop system, hasand T = 1 s. Plot the root locus for K ‰¥ 0, and determine the gain K that results in the two roots of the characteristic equation on the z-circle (at the stability limit).
A unity feedback system, hasIf the system is continuous (T = 0), then K = 1 yields a step response with an overshoot of 16% and a settling time (with a 2% criterion) of 8 seconds. Plot the response
The input to a sampler is r{t) = sin(ωt), where (o = l/π. The output of the sampler enters a zero order hold. Plot the output of the hold circuit p(t) for the first 2 seconds when T = 0.25 s.
A unit ramp r(t) = t , t > 0, is used as an input to a process where G(s) = l/(s + 1), as shown in Figure P13.3. Determine the output y (kT) for the first four sampling instants.FIGURE P13.3
A closed-loop system has a hold circuit and process. Determine G(z) when T = 1 and
For the system in Problem P13.4, let r(r) be a unit step input and calculate the response of the system by synthetic division.
For the output of the system in Problem P13.4, find the initial and final values of the output directly from Y(z).
A closed-loop system is shown. This system represents the pitch control of an aircraft. The process transfer function is Gp(s) = K/[ s(0.5s + 1)]. Select a gain K and sampling period T so that the
Consider the computer-compensated system when T = 1 andSelect the parameters K and r of{z) when Select within the range 1
A suspended, mobile, remote-controlled system to bring three-dimensional mobility to professional NFL football is shown. The camera can be moved over the field as well as up and down. The motor
A closed-loop system, has a processwhere a is adjustable to achieve a suitable response. Plot the root locus when a = 10. Determine the range of K for stability when T = 1 s.
A manufacturer uses an adhesive to form a seam along the edge of the material. It is critical that the glue be applied evenly to avoid flaws; however, the speed at which the material passes beneath
A system of the form has D(z) = k andWhen T = 0.05, find a suitable K for a rapid step response with an overshoot less than 10%.
A system of the form hasDetermine the range of sampling period T for which the system is stable. Select a sampling period T so that the system is stable and provides a rapid response.
Consider the closed-loop sampled-data system. Determine the acceptable range of the parameter K for closed-loop stability.
A temperature system has a process transfer functionand a sampling period T of 0.5 second. (a) Using D(z) = K, select a gain K so that the system is stable, (b) The system may be slow and over
A disk drive read-write head-positioning system has a system. The process transfer function isAccurate control using a digital compensator is required. Let T = 10 ms and design a compensator, D(z),
Vehicle traction control, which includes antiskid braking and anti spin acceleration, can enhance vehicle performance and handling. The objective of this control is to maximize tire traction by
A machine-tool system has the form withThe sampling rate is chosen as T = I s . We desire the step response to have an overshoot of 16% or less and a settling time (with a 2% criterion) of 12 seconds
Plastic extrusion is a well-established method widely used in the polymer processing industry [12]. Such extruders typically consist of a large barrel divided into several temperature zones, with a
A sampled-data system closed-loop block diagram is shown in Figure DPI 3.6. Design D{z) to such that the closed-loop system response to a unit step response has a percent overshoot P.O.‰¤ 12% and
Develop an m-file to plot the unit step response of the systemVerify graphically that the steady-state value of the output is 1.
Convert the following continuous-time transfer functions to sampled-data systems using the function. Assume a sample period of 1 second and a zero order hold GQ(S).
The closed-loop transfer function of a sampled data system is given by(a) Compute the unit step response of the system using the step function, (b) Determine the continuous- time transfer function
Plot the root locus for the systemFind the range of K for stability.
Consider the feedback system. Obtain the root locus and determine the range of K for stability.
Consider the sampled data system with the loop transfer function(a) Plot the root locus using the r locus function. (b) From the root locus, determine the range of K for stability. Use the rlocfind
An industrial grinding process is given by the transfer function [15]The objective is to use a digital computer to improve the performance, where the transfer function of the computer is represented
Design a digital controller for the system using the second-order model of the motor-capstan-slide as described. Use a sampling period of T = 1 ms and select a suitable D(z) for the system shown.
What, in general terms, is the distinction between computer organization and computer architecture?

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