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computer sciences
systems analysis and design

Questions and Answers of Systems Analysis And Design

Consider the spring and mass shown in Figure 3.3 where M = 1 kg, k = 100 N/m, and b = 20 Ns/m.(a) Find the state vector differential equation.(b) Find the roots of the characteristic equation for
The manual, low-altitude hovering task above a moving landing deck of a small ship is very demanding, particularly in adverse weather and sea conditions. The hovering condition is represented by the
A multi-loop block diagram is shown in Figure E3.9.The state variables are denoted by x1 and x2.(a) Determine a state variable representation of the closed-loop system where the output is denoted by
An RLC circuit is shown in Figure P3.1.(a) Identify a suitable set of state variables.(b) Obtain the set of first-order differential equations in terms of the state variables.(c) Write the state
Many control systems must operate in two dimensions, for example, the x- and the y-axes. A two-axis control system is shown in Figure P3.10, where a set of state variables is identified. The gain of
A system is described byx = Ax + Buwhereand x1(0) = x2(0) = 10. Determine x1(t) and x2(t).
A system is described by its transfer function(a) Determine a state variable model. (b) Determine Î¦(t), the state transition matrix.
Consider again the RLC circuit of Problem P3.1 when R = 2.5, L = 1/4, and C = 1/6.(a) Determine whether the system is stable by finding the characteristic equation with the aid of the A matrix.(b)
Determine a state variable representation for a system with the transfer function
Obtain a block diagram and a state variable representation of this system.
The dynamics of a controlled submarine are significantly different from those of an aircraft, missile, or surface ship. This difference results primarily from the moment in the vertical plane due to
A system is described by the state variable equationsDetermine G(s) = Y(s)/U(s).
Consider the control of the robot shown in Figure P3.18.The motor turning at the elbow moves the wrist through the forearm, which has some flexibility as shown [16]. The spring has a spring constant
Consider the system described bywhere x(t) = [x1(t) x2(t)]T.(a) Compute the state transition matrix Î¦(t, 0).
A balanced bridge network is shown in Figure P3.2.(a) Show that the A and B matrices for this circuit are(b) Sketch the block diagram. The state variables are (x1, x2) = (vc, iL).
A nuclear reactor that has been operating in equilibrium at a high thermal-neutron flux level is suddenly shut down. At shutdown, the density X of xenon 135 and the density I of iodine 135 are 7
Consider the block diagram in Figure P3.21.(a) Verify that the transfer function is(b) Show that a state variable model is given by
Determine a state variable model for the circuit shown in Figure P3.22. The state variables are x1 = i, x2 = v1, and x3 = v2. The output variable is v0(t).
The two-tank system shown in Figure P3.23(a) is controlled by a motor adjusting the input valve and ultimately varying the output flow rate. The system has the transfer functionfor the block diagram
It is desirable to use well-designed controllers to maintain building temperature with solar collector space-heating systems. One solar heating system can be described by [10] dx1/dt = 3x1 + u1 +
A system has the following differential equation:Determine Î¦(t) and its transform Î¦(s) for the system.
A system has a block diagram as shown in Figure P3.26. Determine a state variable model and the state transition matrix Î¦(s).
A gyroscope with a single degree of freedom is shown in Figure P3.27. Gyroscopes sense the angular motion of a system and are used in automatic flight control systems. The gimbal moves about the
A two-mass system is shown in Figure P3.28. The rolling friction constant is b. Determine a state variable representation when the output variable is y2(t).
There has been considerable engineering effort directed at finding ways to perform manipulative operations in space-for example, assembling a space station and acquiring target satellites. To perform
An RLC network is shown in Figure P3.3. Define the state variables as x1 = iL and x2 = vc. Obtain the state differential equation.
Obtain the state equations for the two-input and one-output circuit shown in Figure P3.30, where the output is i2.
Extenders are robot manipulators that extend (that is, increase) the strength of the human arm in load-maneuvering tasks (Figure P3.31) [19, 22]. The system is represented by the transfer
A drug taken orally is ingested at a rate r. The mass of the drug in the gastrointestinal tract is denoted by m1 and in the bloodstream by m2. The rate of change of the mass of the drug in the
The attitude dynamics of a rocket are represented byand state variable feedback is used where x1 = y(t), x2 = (t), and u = -x2 - 0.5x1. Determine the roots of the characteristic equation of this
A system has the transfer function(a) Construct a state variable representation of the system. (b) Determine the element Ï•11(t) of the state transition matrix for this system.
Determine a state-space representation for the system shown in Figure P3.35. The motor inductance is negligible, the motor constant is Km = 10, the back electromagnetic force constant is Kb = 0.0706,
Consider the two-mass system in Figure P3.36. Find a state variable representation of the system. Assume the output is x.
Consider the block diagram in Figure P3.37. Using the block diagram as a guide, obtain the state variable model of the system in the formx = Ax + Buy = Cx + DuUsing the state variable model as a
The transfer function of a system isSketch the block diagram and obtain a state variable model.
A closed-loop control system is shown in Figure P3.5.(a) Determine the closed-loop transfer function T(s) = Y(s)/R(s).(b) Sketch a block diagram model for the system and determine a state variable
Determine the state variable matrix equation for the circuit shown in Figure P3.6. Let x1 = v1, x2 = v2, and x3 = i.
An automatic depth-control system for a robot submarine is shown in Figure P3.7.The depth is measured by a pressure transducer. The gain of the stern plane actuator is K = 1 when the vertical
The soft landing of a lunar module descending on the moon can be modeled as shown in Figure P3.8. Define the state variables as x1 = y, x2 = dy/dt, x3 = m and the control as u = dm/dt. Assume that g
A speed control system using fluid flow components is to be designed. The system is a pure fluid control system because it does not have any moving mechanical parts. The fluid may be a gas or a
Consider the electromagnetic suspension system shown in Figure AP3.1. An electromagnet is located at the upper part of the experimental system. Using the electromagnetic force f, we want to suspend
Consider the mass m mounted on a mass less cart, as shown in Figure AP3.2. Determine the transfer function Y(s)/U(s), and use the transfer function to obtain a state-space representation of the
The control of an autonomous vehicle motion from one point to another point depends on accurate control of the position of the vehicle [16]. The control of the autonomous vehicle position Y(s) is
Front suspensions have become standard equipment on mountain bikes. Replacing the rigid fork that attaches the bicycle's front tire to its frame, such suspensions absorb bump impact energy, shielding
Figure AP3.5 shows a mass M suspended from another mass m by means of a light rod of length L. Obtain a state variable model using a linear model assuming a small angle for Î¸. Assume the
Consider the single-input, single-output system described byx(t) = Ax(t) + Bu(t)y(t) = Cx(t)whereAssume that the input is a linear combination of the states, that is, u(t) = -Kx(t) + r(t), where r(t)
A system for dispensing radioactive fluid into capsules is shown in Figure AP3.8(a).The horizontal axis moving the tray of capsules is actuated by a linear motor. The x-axis control is shown in
The traction drive uses the capstan drive system shown in Figure CDP2.1. Neglect the effect of the motor inductance and determine a state variable model for the system. The parameters are given in
A spring-mass-damper system, is used as a shock absorber for a large high-performance motorcycle. The original parameters selected are m = 1 kg, b = 9 N s/m. and k = 20 N/m. (a) Determine the system
A system has the state variable matrix equation in phase variable formIt is desired that the canonical diagonal form of the differential equation be Determine the parameters a, b, and d to yield the
An aircraft arresting gear is used on an aircraft carrier as shown in Figure DP3.3. The linear model of each energy absorber has a drag force fD = KDx3. It is desired to halt the airplane within 30 m
The Mile-High Bungi Jumping Company wants you to design a bungi jumping system (i.e., a cord) so that the jumper cannot hit the ground when his or her mass is less than 100 kg, but greater than 50
Consider the single-input, single-output system described byx(t) = Ax(t) + Bu(t)y(t) = Cx(t)whereAssume that the input is a linear combination of the states, that is, u(t) = -Kx(t) + r(t), where r(t)
Determine a state variable representation for the following transfer functions (without feedback) using the SS function:(a)(b) (c)
Determine a transfer function representation for the following state variable models using the tf function:(a)(b) (c)
Consider the circuit shown in Figure CP3.3. Determine the transfer function V0(s)/Vin(s). Assume an ideal op-amp.(a) Determine the state variable representation when R1 = 1 kÎ©, R2 = 10
Consider the system(a) Using the tf function, determine the transfer function Y(s)/U(s). (b) Plot the response of the system to the initial condition x(0) = [0 -1 1]T for 0 ‰¤ t
Consider the two systemsand (a) Using the tf function, determine the transfer function Y(s)/U(s) for system (1). (b) Repeat part (a) for system (2). (c) Compare the results in parts (a) and (b) and
Consider the closed-loop control system in Figure CP3.6.(a) Determine a state variable representation of the controller.(b) Repeat part (a) for the process.(c) With the controller and process in
Consider the following system:with Using the Isim function obtain and plot the system response (for x1(t) and x2(t)) when u(t) = 0.
A closed-loop system is used to track the sun to obtain maximum power from a photovoltaic array. The tracking system may be represented by Figure 4.3 with H(s) = 1 and G(s) = 100/тs + 1 where т = 3
Consider the feedback control system shown in Figure E4.10.(a) Determine the steady-state error for a step input in terms of the gain, K.(b) Determine the overshoot for the step response for 40
Consider the closed-loop system in Figure E4.11, whereG(s) = K / s + 10 and H(s) = 14 / s2 + 5s + 6 (a) Compute the transfer function T(s) = Y(s)/R(s). (b) Define the tracking error to be E(s) = R(s)
In Figure E4.12, consider the closed-loop system with measurement noise N(s), whereIn the following analysis, the tracking error is defined to be E(s) = R(s) - Y(s): (a) Compute the transfer function
A closed-loop system is used in a high-speed steel rolling mill to control the accuracy of the steel strip thickness. The transfer function for the process shown in Figure E4.13 can be represented
Consider the unity feedback system shown in Figure E4.14. The system has two parameters, the controller gain K and the constant K1 in the process.(a) Calculate the sensitivity of the closed-loop
Reconsider the unity feedback system discussed in E4.14. This time select K = 120 and K1 = 10. The closed-loop system is depicted in Figure E4.15.(a) Calculate the steady-state error of the
A digital audio system is designed to minimize the effect of disturbances as shown in Figure E4.2. As an approximation, we may represent G(s) = K2.(a) Calculate the sensitivity of the system due to
A robotic arm and camera could be used to pick fruit, as shown in Figure E4.3(a). The camera is used to close the feedback loop to a microcomputer, which controls the arm [8, 9]. The transfer
A magnetic disk drive requires a motor to position a read/write head over tracks of data on a spinning disk, as shown in Figure E4.4. The motor and head may be represented by the transfer
A feedback system has the closed-loop transfer function given by(a) Compute the sensitivity of the closed-loop transfer function to changes in the parameter p, where p > 0. (b) Compute the
A unity feedback system has the loop transfer functionDetermine the relationship between the steady-state error to a ramp input and the gain K and system parameter b. For what values of K and b can
Most people have experienced an out-of-focus slide projector. A projector with an automatic focus adjusts for variations in slide position and temperature disturbances [11]. Draw the block diagram of
Four-wheel drive automobiles are popular in regions where winter road conditions are often slippery due to snow and ice. A four-wheel drive vehicle with antilock brakes uses a sensor to keep each
Submersibles with clear plastic hulls have the potential to revolutionize underwater leisure. One small submersible vehicle has a depth-control system as illustrated in Figure E4.9.(a) Determine the
The open-loop transfer function of a fluid-flow system can be written aswhere Ñ‚ = RC, R is a constant equivalent to the resistance offered by the orifice so that 1/R = ½kH0-1/2
For a paper processing plant, it is important to maintain a constant tension on the continuous sheet of paper between the wind-off and wind-up rolls. The tension varies as the widths of the rolls
One important objective of the paper-making process is to maintain uniform consistency of the stock output as it progresses to drying and rolling. A diagram of the thick stock consistency dilution
Two feedback systems are shown in Figures P4.12(a) and (b).(a) Evaluate the closed-loop transfer functions T1 and T2 for each system.(b) Compare the sensitivities of the two systems with respect to
One form of a closed-loop transfer function is(a) Use Equation (4.16) to show that [1] (b) Determine the sensitivity of the system shown in Figure P4.13, using the equation verified in part
A proposed hypersonic plane would climb to 100,000 feet, fly 3800 miles per hour, and cross the Pacific in 2 hours. Control of the aircraft speed could be represented by the model in Figure P4.14.
The steering control of a modern ship may be represented by the system shown in Figure P4.15 [16, 20].(a) Find the steady-state effect of a constant wind force represented by Td(s) = 1/s for K = 10
Figure P4.16 shows the model of a two-tank system containing a heated liquid, where T0 is the temperature of the fluid flowing into the first tank and T2 is the temperature of the liquid flowing out
A robot gripper shown in part (a) of Figure P4.17, is to be controlled so that it closes to an angle Î¸ by using a DC motor control system, as shown in part (b). The model of the control
It is important to ensure passenger comfort on ships by stabilizing the ship's oscillations due to waves [13]. Most ship stabilization systems use fins or hydrofoils projecting into the water to
One of the most important variables that must be controlled in industrial and chemical systems is temperature. A simple representation of a thermal control system is shown in Figure P4.3 [14]. The
A control system has two forward paths, as shown in Figure P4.4.(a) Determine the overall transfer function T(s) = Y(s)/R(s).(b) Calculate the sensitivity, STG, using Equation (4.16).(c) Does the
Large microwave antennas have become increasingly important for radio astronomy and satellite tracking. A large antenna with a diameter of 60 ft, for example, is subject to large wind gust torques. A
An automatic speed control system will be necessary for passenger cars traveling on the automatic highways of the future. A model of a feedback speed control system for a standard vehicle is shown in
A robot uses feedback to control the orientation of each joint axis. The load effect varies due to varying load objects and the extended position of the arm. The system will be deflected by the load
Extreme temperature changes result in many failures of electronic circuits [1]. Temperature control feedback systems reduce the change of temperature by using a heater to overcome outdoor low
A useful unidirectional sensing device is the photo emitter sensor [15]. A light source is sensitive to the emitter current flowing and alters the resistance of the photo sensor. Both the light
A tank level regulator control is shown in Figure AP4.1(a). It is desired to regulate the level h in response to a disturbance change q3. The block diagram shows small variable changes about the
The shoulder joint of a robotic arm uses a DC motor with armature control and a set of gears on the output shaft. The model of the system is shown in Figure AP4.2 with a disturbance torque Td(s)
A machine tool is designed to follow a desired path so thatr(t) = (1 - t)u(t),where u(t) is the unit step function. The machine tool control system is shown in Figure AP4.3.(a) Determine the
An armature-controlled DC motor with tachometer feedback is shown in Figure AP4.4. Assume that Km = 10, J = l, and R = 1.(a) Determine the required gain, K, to restrict the steady-state error to a
A system that controls the mean arterial pressure during anesthesia has been designed and tested [12]. The level of arterial pressure is postulated to be a proxy for depth of anesthesia during
A useful circuit, called a lead network, which we discuss in Chapter 10, is shown in Figure AP4.6.(a) Determine the transfer function G(s) =V0(s)/V(s).(b) Determine the sensitivity of G(s) with
A feedback control system with sensor noise and a disturbance input is shown in Figure AP4.7.The goal is to reduce the effects of the noise and the disturbance. Let R(s) = 0.(a) Determine the effect
The block diagram of a machine-tool control system is shown in Figure AP4.8.(a) Determine the transfer function T(s) =Y(s)/R(s).(b) Determine the sensitivity STb.(c) Select K when 1 ‰¤ K

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