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systems analysis and design

Questions and Answers of Systems Analysis And Design

A capstan drive for a table slide is described in CDP2.1. The position of the slide x is measured with a capacitance gauge, as shown in Figure CDP4.1, which is very linear and accurate. Sketch the
A closed-loop speed control system is subjected to a disturbance due to a load, as shown in Figure DP4.1. The desired speed is Ï‰d(t) = 100 rad/s, and the load disturbance is a unit step
The control of the roll angle of an airplane is achieved by using the torque developed by the ailerons. A linear model of the roll control system for a small experimental aircraft is shown in Figure
The speed control system of Figure DP4.1 is altered so that G(s) = l/(s + 5) and the feedback is K1 as shown in Figure DP4.3.(a) Determine the range of K1 allowable so that the steady state is ess
Lasers have been used in eye surgery for more than 25 years. They can cut tissue or aid in coagulation [17]. The laser allows the ophthalmologist to apply heat to a location in the eye in a
An op-amp circuit can be used to generate a short pulse. The circuit shown in Figure DP4.5 can generate the pulse v0(t) = 5e-100t, t > 0, when the input v(t) is a unit step [6]. Select appropriate
A hydrobot is under consideration for remote exploration under the ice of Europa, a moon of the giant planet Jupiter. Figure DP4.6(a) shows one artistic version of the mission. The hydrobot is a
Interest in unmanned underwater vehicles (UUVs) has been increasing recently, with a large number of possible applications being considered. These include intelligence-gathering, mine detection, and
A new suspended, mobile, remote-controlled video camera system to bring three-dimensional mobility to professional football is shown in Figure DP4.8(a) [29]. The camera can be moved over the field,
Consider a unity feedback system withObtain the step response and determine the percent overshoot. What is the steady-state error?
Consider the closed-loop system is depicted in Figure CP4.10. The controller gain K can be modified to meet the design specifications.(a) Determine the closed-loop transfer function T(s) =
Consider the non-unity feedback system is depicted in Figure CP4.11.(a) Determine the closed-loop transfer function T(s) = Y(s)/R(s).(b) For K = 10, 12, and 15, plot the unit step responses.
Consider the transfer function (without feedback)When the input is a unit step, the desired steady-state value of the output is one. Using the step function, show that the steady-state error to a
Consider the closed-loop transfer functionObtain the family of step responses for K = 10, 200, and 500. Co-plot the responses and develop a table of results that includes the percent overshoot,
Consider the feedback system in Figure CP4.4. Suppose that the controller isGc(s) = K = 10.Figure CP4.4Unity feedback system with controller gain K.(a) Develop an m-file to compute the closed-loop
Consider the closed-loop control system shown in Figure CP4.5. Develop an m-file script to assist in the search for a value of k so that the percent overshoot to a unit step input is greater than 1%,
Consider the closed-loop control system shown in Figure CP4.6. The controller gain is K = 2. The nominal value of the plant parameter is a = 1. The nominal value is used for design purposes only,
Consider the torsional mechanical system in Figure CP4.7(a). The torque due to the twisting of the shaft is -kÎ¸; the damping torque due to the braking device is -bÎ¸; the
A negative feedback control system is depicted in Figure CP4.8. Suppose that our design objective is to find a controller Gc(s) of minimal complexity such that our closed-loop system can track a unit
Consider the closed-loop system in Figure CP4.9, whose transfer function is(a) Obtain the closed-loop transfer function T(s) = Y(s)/R(s) and the unit step response; that is, let R(s) = l/s and assume
A second-order control system has the closed-loop transfer function T(s) = Y(s)/R(s). The system specifications for a step input follow: (1) Percent overshoot P.O. ≤ 5%. (2) Settling time Ts <
A system with unity feedback is shown in Figure E5.11. Determine the steady-state error for a step and a ramp input whenFigure E5.11 Unity feedback system.
We are all familiar with the Ferris wheel featured at state fairs and carnivals. George Ferris was born in Galesburg, Illinois, in 1859; he later moved to Nevada and then graduated from Rensselaer
For the system with unity feedback shown in Figure E5.l l, determine the steady-state error for a step and a ramp input whenFigure E5.11 Unity feedback system.
A feedback system is shown in Figure E5.14.(a) Determine the steady-state error for a unit step when K = 0.4 and Gp(s) = 1.(b) Select an appropriate value for Gp(s) so that the steady-state error is
A closed-loop control system has a transfer function T(s) as follows:Plot y(t) for a step input R(s) when (a) the actual T(s) is used, and (b) using the relatively dominant complex poles. Compare the
A second-order system isConsider the case where 1
A closed-loop control system transfer function T(s) has two dominant complex conjugate poles. Sketch the region in the left-hand 5-plane where the complex poles should be located to meet the given
A system is shown in Figure E5.18(a). The response to a unit step, when K = 1, is shown in Figure E5.18(b). Determine the value of K so that the steady-state error is equal to zero.
A second-order system has the closed-loop transfer function(a) Determine the percent overshoot P.O., the time to peak Tp, and the settling time Ts of the unit step response, R(s) = 1/s. To compute
The engine, body, and tires of a racing vehicle affect the acceleration and speed attainable [9]. The speed control of the car is represented by the model shown in Figure E5.2.(a) Calculate the
Consider the closed-loop system in Figure E5.19, where(a) Determine the closed-loop transfer function T(s) = Y(s)/R(s). (b) Determine the steady-state error of the closed-loop system response to a
New passenger rail systems that could profitably compete with air travel are under development. Two of these systems, the French TGV and the Japanese Shinkansen, reach speeds of 160 mph [17]. The
A feedback system with negative unity feedback has a loop transfer function(a) Determine the closed-loop transfer function T(s) = Y(s)/R(s). (b) Find the time response, y(t), for a step input r(t) =
Consider the feedback system in Figure E5.5. Find K such that the closed-loop system minimizes the ITAE performance criterion for a step input.Figure E5.5Feedback system with proportional controller
Consider the block diagram shown in Figure E5.6 [16].(a) Calculate the steady-state error for a ramp input.(b) Select a value of K that will result in zero overshoot to a step input. Provide the most
Effective control of insulin injections can result in better lives for diabetic persons. Automatically controlled insulin injection by means of a pump and a sensor that measures blood sugar can be
A control system for positioning the head of a floppy disk drive has the closed-loop transfer functionPlot the poles and zeros of this system and discuss the dominance of the complex poles. What
A unity negative feedback control system has the loop transfer function(a) Determine the percent overshoot and settling time (using a 2% settling criterion) due to a unit step input. (b) For what
An important problem for television systems is the jumping or wobbling of the picture due to the movement of the camera. This effect occurs when the camera is mounted in a moving truck or airplane.
A speed control system of an armature-controlled DC motor uses the back emf voltage of the motor as a feedback signal. (a) Draw the block diagram of this system. (b) Calculate the steady-state error
A simple unity feedback control system has a process transfer functionThe system input is a step function with an amplitude A. The initial condition of the system at time t0 is y(t0) = Q, where y(t)
Train travel between cities will increase as trains are developed that travel at high speeds, making the travel time from city center to city center equivalent to airline travel time. The Japanese
We want to approximate a fourth-order system by a lower-order model. The transfer function of the original system isShow that if we obtain a second-order model by the method of Section 5.8, and we do
For the original system of Problem P5.13, we want to find the lower-order model when the poles of the second-order model are specified as -1 and -2 and the model has one unspecified zero. Show that
Consider a unity feedback system with loop transfer functionDetermine the value of the gain K such that the percent overshoot to a unit step is minimized.
A magnetic amplifier with a low-output impedance is shown in Figure P5.16 in cascade with a low-pass filter and a preamplifier. The amplifier has a high-input impedance and a gain of 1 and is used
Electronic pacemakers for human hearts regulate the speed of the heart pump. A proposed closed-loop system that includes a pacemaker and the measurement of the heart rate is shown in Figure P5.17 [2,
Consider the original third-order system given in Example 5.9. Determine a first-order model with one pole unspecified and no zeros that will represent the third-order system.
A closed-loop control system with negative unity feedback has a loop transfer function(a) Determine the closed-loop transfer function T(s). (b) Determine a second-order approximation for T(s). (c)
A specific closed-loop control system is to be designed for an under damped response to a step input. The specifications for the system are as follows: 10% < percent overshoot < 20%, Settling time <
A system is shown in Figure P5.20.(a) Determine the steady-state error for a unit step input in terms of K and K1, where E(s) = R(s) - Y(s).(b) Select K1 so that the steady-state error is zero.
Consider the closed-loop system in Figure P5.21. Determine values of the parameters k and a so that the following specifications are satisfied:(a) The steady-state error to a unit step input is
Consider the closed-loop system in Figure P5.22, where(a) If Ñ‚ = 2.43, determine the value of K such that the steady-state error of the closed-loop system response to a unit step input,
A laser beam can be used to weld, drill, etch, cut. And mark metals, as shown In Figure P5.3(a) [14]. Assume we have a work requirement for an accurate laser to mark a parabolic path with a
The loop transfer function of a unity negative feedback system (see Figure E5.11) isA system response to a step input is specified as follows: peak time Tp = 1.1 s, percent overshoot P.O. = 5%. (a)
A space telescope is to be launched to carry out astronomical experiments [8]. The pointing control system is desired to achieve 0.01 minute of arc and track solar objects with apparent motion up to
A robot is programmed to have a tool or welding torch follow a prescribed path [7, 11]. Consider a robot tool that is to follow a sawtooth path, as shown in Figure P5.6(a). The transfer function of
Astronaut Bruce McCandless II took the first un-tethered walk in space on February 7, 1984, using the gas-jet propulsion device illustrated in Figure P5.7(a). The controller can be represented by a
Photovoltaic arrays (solar cells) generate a DC voltage that can be used to drive DC motors or that can be converted to AC power and added to the distribution network. It is desirable to maintain the
The antenna that receives and transmits signals to the Telstar communication satellite is the largest horn antenna ever built. The microwave antenna is 177 ft long, weighs 340 tons, and rolls on a
A closed-loop transfer function is(a) Determine the steady-state error for a unit step input R(s) = 1/s. (b) Assume that the complex poles dominate, and determine the overshoot and settling time to
A closed-loop system is shown in Figure AP5.2. Plot the response to a unit step input for the system for Ñ‚z = 0, 0.05, 0.1, and 0.5. Record the percent overshoot, rise time, and settling
A closed-loop system is shown in Figure AP5.3. Plot the response to a unit step input for the system with Ñ‚p = 0, 0.5, 2, and 5. Record the percent overshoot, rise time, and settling
The speed control of a high-speed train is represented by the system shown in Figure AP5.4 [17]. Determine the equation for steady-state error for K for a unit step input r(t). Consider the three
A system with a controller is shown in Figure AP5.5. The zero of the controller may be varied. Let Î± = 0, 10, 100.(a) Determine the steady-state error for a step input r(t) for
The block diagram model of an armature-current-controlled DC motor is shown in Figure AP5.6.(a) Determine the steady-state tracking error to a ramp input r(t) = t, t ‰¥ 0, in terms of K, Kb,
Consider the closed-loop system in Figure AP5.7 with transfer functionsGc(s) = 100/s + 100 and G(s) = K/s(s + 50).where1000 ‰¤ K ‰¤ 5000.(a) Assume that the complex poles
A unity negative feedback system (as shown in Figure E5.11) has the loop transfer functionDetermine the gain K that minimizes the damping ratio Î¶ of the closed-loop system poles. What is the
The unity negative feedback system in Figure AP5.9 has the process given byG(s) = 1 / s(s + 15)(s + 25).The controller is a proportional plus integral controller with gains Kp and KI. The objective
The capstan drive system of the previous problems has a disturbance due to changes in the part that is being machined as material is removed. The controller is an amplifier Gc(s) - Ka. Evaluate the
The roll control autopilot of a jet fighter is shown in Figure DP5.1. The goal is to select a suitable K so that the response to a unit step command Ï•d(t) = A, t ‰¥ 0, will
The design of the control for a welding arm with a long reach requires the careful selection of the parameters [13]. The system is shown in Figure DP5.2, where Î¶ = 0.6, and the gain K and
Active suspension systems for modern automobiles provide a comfortable firm ride. The design of an active suspension system adjusts the valves of the shock absorber so that the ride fits the
The space satellite shown in Figure DP5.4(a) uses a control system to readjust its orientation, as shown in Figure DP5.4(b).(a) Determine a second-order model for the closed-loop system.(b) Using the
A deburring robot can be used to smooth off machined parts by following a preplanned path (input command signal). In practice, errors occur due to robot inaccuracy, machining errors, large
The model for a position control system using a DC motor is shown in Figure DP5.6. The goal is to select K1 and K2 so that the peak time is Tp ‰¤ 0.5 second and the overshoot P.O. for a
A three-dimensional cam for generating a function of two variables is shown in Figure DP5.7(a). Both x and y may be controlled using a position control system [31].The control of x may be achieved
Computer control of a robot to spray-paint an automobile is accomplished by the system shown in Figure DP5.8(a) [7]. We wish to investigate the system when K = 1, 10, and 20. The feedback control
Consider the closed-loop transfer function T(s) = 15 / s2 + 8s + 15. Obtain the impulse response analytically and compare the result to one obtained using the impulse function.
Develop an m-file to simulate the response of the system in Figure CP5.10 to a ramp input R(s) = l/s2. What is the steady-state error? Display the output on an x-y graph.
Consider the closed-loop system in Figure CP5.11. Develop an m-file to accomplish the following tasks:(a) Determine the closed-loop transfer function T(s) = Y(s)/R(s),(b) Plot the closed-loop system
A closed-loop transfer function is given by(a) Obtain the response of the closed-loop transfer function T(s) = Y(s)/R(s) to a unit step input. What is the settling time Ts (use a 2% criterion) and
A unity negative feedback system has the loop transfer functionUsing Isim, obtain the response of the closed-loop system to a unit ramp input, R(s) = 1/s2. Consider the time interval 0 ‰¤
A working knowledge of the relationship between the pole locations of the second-order system shown in Figure CP5.3 and the transient response is important in control design. With that in mind,
Consider the control system shown in Figure CP5.4.(a) Show analytically that the expected percent overshoot of the closed-loop system response to a unit step input is about 50%.(b) Develop an m-file
Consider the feedback system in Figure CP5.5. Develop an m-file to design a controller and prefiltersuch that the ITAE performance criterion is minimized. For Ï‰n = 0.45 and Î¶ =
The loop transfer function of a unity negative feedback system is L(s) = Gc(s)G(s) = 25/s(s + 5). Develop an m-file to plot the unit step response and determine the values of peak overshoot Mp, time
An autopilot designed to hold an aircraft in straight and level flight is shown in Figure CP5.7.(a) Suppose the controller is a constant gain controller given by Gc(s) = 2. Using the Isim function,
The block diagram of a rate loop for a missile autopilot is shown in Figure CP5.8. Using the analytic formulas for second-order systems, predict Mpt, Tp, and Ts for the closed-loop system due to a
Develop an m-file that can be used to analyze the closed-loop system in Figure CP5.9. Drive the system with a step input and display the output on a graph. What is the settling time and the percent
A system has a characteristic equation s3 + Ks2 + (1 + K)s + 6 = 0. Determine the range of K for a stable system.
A system has the second-order characteristic equation s2 + as + b = 0, where a and b are constant parameters. Determine the necessary and sufficient conditions for the system to be stable. Is it
Consider the feedback system in Figure E6.13. Determine the range of Kp and KD for stability of the closed-loop system.Figure E6.13Closed-loop system with a proportional plus derivative controller
By using magnetic bearings, a rotor is supported contactless. The technique of contactless support for rotors becomes more important in light and heavy industrial applications [14]. The matrix
A system has a characteristic equation q(s) = s6 + 9s5 + 31.25s4 + 61.25s3 + 67.75s2 + 14.75s + 15 = 0. (a) Determine whether the system is stable, using the Routh-Hurwitz criterion. (b) Determine
A system has a characteristic equation q(s) = s4 + 9s3 + 45s2 + 87s + 50 = 0. (a) Determine whether the system is stable, using the Routh-Hurwitz criterion. (b) Determine the roots of the
The matrix differential equation of a state variable model of a system has(a) Determine the characteristic equation. (b) Determine whether the system is stable. (c) Determine the roots of the
A system has a characteristic equation q(s) = s3 + 20s2 + 5s + 100 = 0. (a) Determine whether the system is stable, using the Routh-Hurwitz criterion. (b) Determine the roots of the characteristic
A system has a characteristic equation s3 + I0s2 + 2s + 30 = 0. Using the Routh-Hurwitz criterion, show that the system is unstable.

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