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computer science
modern database management 13th edition

Modern Control Systems 13th Global Edition Robert Bishop Richard Dorf - Solutions

P3.32 A drug taken orally is ingested at a rate r(t). The mass of the drug in the gastrointestinal tract is denoted by m11t2 and in the bloodstream by m21t2. The rate of change of the mass of the drug in the gastrointestinal tract is equal to the rate at which the drug is ingested minus the rate at
Extenders are robot manipulators that extend (that is, increase) the strength of the human arm in loadmaneuvering tasks (Figure P3.31) [19, 22]. The system is represented by the transfer function where U1s2 is the force of the human hand applied to the robot manipulator, and Y1s2 is the force of
P3.30 Obtain the state equations for the two-input and one-output circuit shown in Figure P3.30, where the output is i21t2. i2(t) www www R R R3 v(1) iz(1) vec(1) v2(t) FIGURE P3.30 Two-input RLC circuit.
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 such tasks, space shuttles carry a remote manipulator system(RMS) in the cargo bay [4, 12, 21].
A two-mass system is shown in Figure P3.28.The rolling friction constant isb. Determine a state variable representation when the output variable is y21t2. yi(t) u(t) Force m2 mi k Rolling friction constant = b FIGURE P3.28 Two-mass system. y2(1)
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 output axis OB. The input is measured around the input axis OA. The equation of motion about the output
P3.26 A system has a block diagram as shown in Figure P3.26. Determine a state variable model and the state transition matrix Φ(s). R(s) 25 25 1 s+3 3 25 FIGURE P3.26 Feedback system. 117 Y(s)
A system has the following differential equation:Determine 1t2 and its transform 1s2 for the system. 2-3 x(t) [H] + x [b } ] = x(t)
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] dx(t) 3x1(t)u(t) + u(t), dt and dx(1) 2x2(t)u2(t) + d(t), dt where x(t) temperature deviation from desired equilibrium, and
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 function 1(s) Input signal Qo(s) 1 = G(s) = I(s) s3+10s2+29s + 20 for the block diagram shown in Figure P3.23(b). Obtain a state
Determine a state variable model for the circuit shown in Figure P3.22. The state variables are x(t)= i(t), x(t)= v(t), and x3(t)=v2(t). The output variable is vo(t). R v(1) R v2(1) 0 + v(t) (1) T C V(1) i(t) FIGURE P3.22 RLC circuit. S C vo(1) Output R3 voltage
Consider the block diagram in Figure P3.21.(a) Verify that the transfer function is Y(s) hs + ho+ah G(s) = U(s) s + as + do (b) Show that a state variable model is given by x(t) -[-% 0 1 -a x(t) + u(t), ho. y(t)= [10]x(t).
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 * 1016 and 3 * 1015 atoms per unit volume, respectively. The half-lives of I135 and Xe135 nucleides are
Consider the system described by x(t) 0 1 x(t), -2-3 where x(t) = (x(t) x2(t)). (a) Compute the state transition matrix (t, 0). (b) Using the state transition matrix from (a) and for the initial conditions x(0) = 1 and x2(0) -1, find the solution x(t) for t 0.
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 k and friction-damping constantb. Let the state variables be x11t2 = f11t2 - f21t2 and x21t2 =
A system is described by the state variable equations 1 1 -1 x(t) 4 3 0 x(t) + 0 u(t), -2 1 10 4 y(t) [100]x(t). Determine G(s): = Y(s)/U(s).
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 the buoyancy effect. Therefore, it is interesting to consider the control of the depth of a
Obtain a block diagram and a state variable representation of this system. Y(s) T(s) R(s) 14(s + 4) 3+10s231s+16
Determine a state variable representation for a system with the transfer function Y(s) R(s) == T(s) = $ + 50 s+12s3+10s2 + 34s +50
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 the transition matrix of the network.(c) When the initial inductor current is 0.1
A system is described by its transfer function Y(s) T(s) R(s) 8(s + 5) s3+12s2+44s + 48 (a) Determine a state variable model. (b) Determine the state transition matrix, (1).
P3.11 A system is described by x(t) = Ax(t) + Bu(t) where A = = [23] B B= and x(0)=x2(0)= 10. Determine x(t) and x2(t).
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 each axis is K1 and K2, respectively. (a) Obtain the state differential equation. (b) Find the
P3.9 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 liquid. A system is desired that maintains the speed within 0.5% of the desired speed by using a
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 1 t2 = y1 t2 , x2 1 t2 =y #1t2, x31t2 = m1t2 and the control as u = m # 1t2.Assume that g is the gravity constant on the moon.Find a state variable model for this
P3.7 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 velocity is 25 m/s.The submarine has the transfer function G(s) (s + 1) 5+1 and the feedback
P3.6 Determine the state variable matrix equation for the circuit shown in Figure P3.6. Let x11t2 = v 11t2, x21t2 = v 21t2, and x31t2 = i1t2. FIGURE P3.6 RLC circuit. 3 1 mH + v(1) v(1) 0.25 mF 2(t)) 0.5 mF ww 1
A closed-loop control system is shown in Figure P3.5. (a) Determine the closed-loop transfer function T1s2= Y1s2>R1s2. (b) Sketch a block diagram model for the system and determine a state variable model. FIGURE P3.5 Closed-loop system. R(s) +1 Controller Voltage s+1 V(s) s+6 s-2 Velocity V(s)
The transfer function of a system is Y(s) T(s) = R(s) s+2s+ 10 s3+45+65 + 10 Sketch the block diagram and obtain a state variable model.
An RLC network is shown in Figure P3.3. Define the state variables as x11t2 = iL1t2 and x21t2 = v c1t2.Obtain the state differential equation. v(1) Partial answer: A iz(t) = [-1/c 0 1/L -1/C -1/(RC) C i (f) L v(t) R FIGURE P3.3 RLC circuit.. + V(1)
A balanced bridge network is shown in Figure P3.2.(a) Show that the A and B matrices for this circuit are -2/((R+R2)C) 0 0 L)]. -2RR2/((R + R)L) B = 1/(R + R) 1/C/CL] -R/L (b) Sketch the block diagram. The state variables are (x1(t), x2(t)) = (vc(t), i(t)). L iz(t) www R2 www R R R + v (1) v(1)
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 differential equation. R i(t) L v(t) + Voltage source v (1) C FIGURE P3.1 RLC circuit.
Consider the block diagram in Figure CP2.10.Create an m-file to complete the following tasks:(a) Compute the step response of the closed-loop system (that is, R1s2 = 1/s and Td1s2 = 02 and plot the steady-state value of the output Y1s2 as a function of the controller gain 0 6 K … 10.(b) Compute
Consider the feedback control system in Figure CP2.9, where G(s) = s + 1 5+2 1 and H(s) = S+1 (a) Using an m-file, determine the closed-loop trans- fer function. (b) Obtain the pole-zero map using the pzmap func- tion. Where are the closed-loop system poles and zeros? (c) Are there any pole-zero
CP2.8 A system has a transfer function X(s) (20/z)(s + z) R(s) s + 35 + 20 Plot the response of the system when R(s) is a unit step for the parameter z = 5, 10, and 15.
CP2.7 For the simple pendulum shown in Figure CP2.7, the nonlinear equation of motion is given by (t) + sin e(t) = 0, L where L = 0.5 m, m = 1 kg, and g = 9.8 m/s. When the nonlinear equation is linearized about the equilib- rium point 000, we obtain the linear time-invariant model, = (1) + (0) =
CP2.6 Consider the block diagram in Figure CP2.6.(a) Use an m-file to reduce the block diagram in Figure CP2.6, and compute the closed-loop transfer function.(b) Generate a pole–zero map of the closed-loop transfer function in graphical form using the pzmap function.(c) Determine explicitly the
CP2.5 A satellite single-axis attitude control system can be represented by the block diagram in Figure CP2.5.The variables k,a, and b are controller parameters, and J is the spacecraft moment of inertia. Suppose the nominal moment of inertia is J = 10.8E 81slug ft22, and the controller parameters
CP2.4 Consider the mechanical system depicted in Figure CP2.4. The input is given by f1t2, and the output is y1t2. Determine the transfer function from f1t2 to y1t2 and, using an m-file, plot the system response to a unit step input. Let m = 10, k = 1, and b = 0.5. Show that the peak amplitude of
Consider the differential equationwhere y102 = y # 102 = 0 and u1t2 is a unit step. Determine the solution y1t2 analytically and verify by co-plotting the analytic solution and the step response obtained with the step function. y+4y(t) + 3y u,
Consider the feedback system depicted in Figure CP2.2.(a) Compute the closed-loop transfer function using the series and feedback functions.(b) Obtain the closed-loop system unit step response with the step function, and verify that final value of the output is 2/5. Controller Plant s+2 R(s)' Y(s)
Consider the two polynomials and p(s) = s + 7s+ 10 q(s) = s +2. Compute the following (a) p(s)q(s) (b) poles and zeros of G(s) q(s) == P(s) (c) p(-1)
DP2.5 Consider the clock shown in Figure DP2.5. The pendulum rod of length L supports a pendulum disk.Assume that the pendulum rod is a massless rigid thin rod and the pendulum disc has mass m. Design the length of the pendulum, L, so that the period of motion is 2 seconds. Note that with a period
An operational amplifier circuit that can serve as a filter circuit is shown in Figure DP2.4. Determine the transfer function of the circuit, assuming an ideal op-amp. Find v 01t2 when the input is v 11t2 = At, t Ú 0. R www a b R2 v(1) R www + FIGURE DP2.4 Operational amplifier circuit. 0+ vo(1)
DP2.3 An input r1t2 = t, t Ú 0, is applied to a black box with a transfer function G1s2. The resulting output response, when the initial conditions are zero, is 3 y(t) = e -21 4 Determine G(s) for this system. + 1 N
DP2.2 The television beam circuit of a television is represented by the model in Figure DP2.2. Select the unknown conductance G so that the voltage v is 24 V.Each conductance is given in siemens (S). FIGURE DP2.2 Television beam circuit. www Reference 2i2 20 A www 0.
A control system is shown in Figure DP2.1. The transfer functions G21s2 and H21s2 are fixed. Determine the transfer functions G11s2 and H11s2 so that the closed-loop transfer function Y1s2/R1s2 is exactly equal to 1. FIGURE DP2.1 Selection of transfer functions. R(s)' 5 G + H H2 G YO
We want to accurately position a table for a machine as shown in Figure CDP2.1. A traction- drive motor with a capstan roller possesses several desirable characteristics compared to the more popular ball screw. The traction drive exhibits low friction and no backlash. However, it is susceptible to
Consider the inverting operational amplifier in Figure AP2.9. Find the transfer function Vo1s2>Vi1s2.Show that the transfer function can be expressed as Vo(s) K G(s) = Kp + + Kps, V(s) S where the gains Kp, K, and Kp are functions of C, C2, R, and R2, This circuit is a proportional-integral-
AP2.8 Consider the cable reel control system given in Figure AP2.8. Find the value of A and K such that the percent overshoot is P.O. … 10% and a desired velocity of 50 m/s in the steady state is achieved. Compute the closed-loop response y1t2 analytically and confirm that the steady-state
AP2.7 Consider the unity feedback system described in the block diagram in Figure AP2.7. Compute analytically the response of the system to an impulse disturbance.Determine a relationship between the gain K and the minimum time it takes the impulse disturbance response of the system to reach y1t2 6
Consider the hanging crane structure in Figure AP2.6. Write the equations of motion describing the motion of the cart and the payload. The mass of the cart is M, the mass of the payload is m, the massless rigid connector has length L, and the friction is modeled as Fb1t2 = -bx # 1t2 where x1t2 is
For the three-cart system (Figure AP2.5), obtain the equations of motion. The system has three inputs u11t2, u21t2, and u31t2 and three outputs x11t2, x21t2, and x31t2. Obtain three second-order ordinary differential equations with constant coefficients. If possible, write the equations of motion
AP2.4 Consider a thermal heating system given bywhere the output 1s2 is the temperature difference due to the thermal process, the input q1s2 is the rate of heat flow of the heating element. The system parameters are Ct, Q, S, and Rt. The thermal heating system is illustrated in Table 2.5. (a)
Consider the feedback control system in Figure AP2.3. Define the tracking error as E1s2 = R1s2 - Y1s2.(a) Determine a suitable H1s2 such that the tracking error is zero for any input R1s2 in the absence of a disturbance input (that is, when Td1s2 = 0). (b) Using H1s2 determined in part (a),
AP2.2 A system has a block diagram as shown in Figure AP2.2. Determine the transfer function Y(s) T(s) = R(s) It is desired to decouple (s) from R(s) by obtaining T(s) = 0. Select Gs(s) in terms of the other G,(s) to achieve decoupling. R(s) G($) H(s) G5($) G(s) Y(s) + R(s) G3($) +G4(s) G6(5) H(s)
An armature-controlled DC motor is driving a load. The input voltage is 5 V. The speed at t = 2 s is 30 rad/s, and the steady speed is 70 rad/s when t S .Determine the transfer function v1s2>V1s2.
Consider the two-mass system in Figure P2.51.Find the set of differential equations describing the system. k T x(f) W K2 M2 y(f) u(t) FIGURE P2.51 Two-mass system with two springs and one damper.
P2.49 A closed-loop control system is shown in Figure P2.49.(a) Determine the transfer function T1s2 = Y1s2>R1s2.(b) Determine the poles and zeros of T1s2.(c) Use a unit step input, R(s) = 1>s, and obtain the partial fraction expansion for Y1s2 and the value of the residues.(d) Plot y1t2 and
P2.48 The circuit shown in Figure P2.48 is called a leadlag filter.(a) Find the transfer function V21s2>V11s2. Assume an ideal op-amp.(b) Determine V21s2>V11s2 when R1 = 250 k, R2 = 250 k, C1 = 2 mF, and C2 = 0.3 mF.(c) Determine the partial fraction expansion for V21s2>V11s2. C C R + R
P2.47 The water level h1t2 in a tank is controlled by an open-loop system, as shown in Figure P2.47.A DC motor controlled by an armature current ia turns a shaft, opening a valve. The inductance of the DC motor is negligible, that is, La = 0. Also, the rotational friction of the motor shaft and
A load added to a truck results in a force F1s2 on the support spring, and the tire flexes as shown in Figure P2.46(a). The model for the tire movement is shown in Figure P2.46(b). Determine the transfer function X11s2>F1s2. FIGURE P2.46 Truck support model. F(s) F(t) Force of material placed in
P2.45 To exploit the strength advantage of robot manipulators and the intellectual advantage of humans, a class of manipulators called extenders has been examined [22].The extender is defined as an active manipulator worn by a human to augment the human’s strength. The human provides an input
P2.44 An ideal set of gears is connected to a solid cylinder load as shown in Figure P2.44. The inertia of the motor shaft and gear G2 is Jm. Determine (a) the iner -tia of the load JL and (b) the torque T at the motor shaft. Assume the friction at the load is bL and the friction at the motor shaft
An ideal set of gears is shown in Table 2.4, item 10.Neglect the inertia and friction of the gears and assume that the work done by one gear is equal to that of the other. Derive the relationships given in item 10 of Table 2.4. Also, determine the relationship between the torques Tm and TL.
In many applications, such as reading product codes in supermarkets and in printing and manufacturing, an optical scanner is utilized to read codes, as shown in Figure P2.42. As the mirror rotates, a friction force is developed that is proportional to its angular speed. The friction constant is
The lateral control of a rocket with a gimbaled engine is shown in Figure P2.41. The lateral deviation from the desired trajectory is h and the forward rocket speed is V. The control torque of the engine is Tc1s2 and the disturbance torque is Td1s2. Derive the describing equations of a linear model
P2.40 A damping device is used to reduce the undesired vibrations of machines. A viscous fluid, such as a heavy oil, is placed between the wheels, as shown in Figure P2.40. When vibration becomes excessive, the relative motion of the two wheels creates damping.When the device is rotating without
P2.39 For the circuit of Figure P2.39, determine the transform of the output voltage V01s2. Assume that the circuit is in steady state when t 6 0. Assume that the switch moves instantaneously from contact 1 to contact 2 at t = 0. FIGURE P2.39 Model of an electronic circuit. 6V t=0 2 10e-21 V 1.5 H
P2.38 A winding oscillator consists of two steel spheres on each end of a long slender rod, as shown in Figure P2.38. The rod is hung on a thin wire that can be twisted many revolutions without breaking. The device will be wound up 4000 degrees. How long will it take until the motion decays to a
A two-mass system is shown in Figure P2.37 with an input force u1t2. When m1 = m2 = 1 and K1 = K2 = 1, find the set of differential equations describing the system. K K x(t) m2 y(t) FIGURE P2.37 Two-mass system.
P2.36 A system is represented by Figure P2.36. (a) Determine the partial fraction expansion and y1t2 for a ramp input, r1t2 = t, t Ú 0. (b) Obtain a plot of y1t2 for part(a), and find y1t2 for t = 1.0 s. (c) Determine the impulse response of the system y1t2 for t Ú 0. (d) Obtain a plot of y1t2
P2.35 A feedback control system has the structure shown in Figure P2.35. Determine the closed-loop transfer function Y1s2/R1s2 (a) by block diagram manipulation and (b) by using a signal-flow graph and Mason’s signal-flow gain formula. (c) Select the gains K1 and K2 so that the closed-loop
The suspension system for one wheel of an oldfashioned pickup truck is illustrated in Figure P2.34.The mass of the vehicle is m1 and the mass of the wheel is m2. The suspension spring has a spring constant k1 and the tire has a spring constant k2. The damping constant of the shock absorber isb.
Find the transfer function for Y1s2/R1s2 for the idle-speed control system for a fuel-injected engine as shown in Figure P2.33. Air bypass H($) R(s) Speed command Manifold Fuel Ks K6 gain Dynamics + G(s) G($) G3($) Pressure Y(s) Engine H(s) speed Spark gain K4 FIGURE P2.33 Idle speed control system.
A system consists of two electric motors that are coupled by a continuous flexible belt. The belt also passes over a swinging arm that is instrumented to allow measurement of the belt speed and tension. The basic control problem is to regulate the belt speed and tension by varying the motor
An interacting control system with two inputs and two outputs is shown in Figure P2.31. Solve for Y11s2>R11s2 and Y21s2>R11s2 when R2 = 0. + R(s) R(s) + G(5) H(s) G3($) G(s) G5($) + + G(s) Y(s) H(s) FIGURE P2.31 Interacting system. G6($) Y2(s).
P2.30 The measurement or sensor element in a feedback system is important to the accuracy of the system [6].The dynamic response of the sensor is important.Many sensor elements possess a transfer function H(s) = k TS+1 Suppose that a position-sensing photo detector has T = 5 s and 0.999 < k <
P2.29 We desire to balance a rolling ball on a tilting beam as shown in Figure P2.29. We will assume the motor input current i controls the torque with negligible friction. Assume the beam may be balanced near the horizontal 1f = 02; therefore, we have a small deviation of f1t2. Find the transfer
A multiple-loop model of an urban ecological system might include the following variables: number of people in the city (P), modernization (M), migration into the city (C), sanitation facilities (S), number of diseases (D), bacteria/area (B), and amount of garbage/area (G), where the symbol for the
Magnetic levitation trains provide a high-speed, very low friction alternative to steel wheels on steel rails. The train floats on an air gap as shown in Figure P2.27 [25]. The levitation force FL is controlled by the coil current i in the levitation coils and may be approximated bywhere z is the
P2.26 A robot includes significant flexibility in the arm members with a heavy load in the gripper [6, 20]. A two-mass model of the robot is shown in Figure P2.26.Find the transfer function Y1s2>F1s2.
P2.25 H. S. Black is noted for developing a negative feedback amplifier in 1927. Often overlooked is the fact that three years earlier he had invented a circuit design technique known as feedforward correction[19]. Recent experiments have shown that this technique offers the potential for yielding
A two-transistor series voltage feedback amplifier is shown in Figure P2.24(a). This AC equivalent circuit neglects the bias resistors and the shunt capacitors.A block diagram representing the circuit is shown in Figure P2.24(b). This block diagram neglects the effect of hre, which is usually an
P2.23 The small-signal circuit equivalent to a commonemitter transistor amplifier is shown in Figure P2.23.The transistor amplifier includes a feedback resistor Rf. Determine the input–output ratio Vce1s2>Vin1s2. Vin(t) + R$ Rf if in hie www + + Ube hrevce Bib vce (1) RL FIGURE P2.23 CE
P2.22 A voltage follower (buffer amplifier) is shown in Figure P2.22. Show that T = Vo1s2>Vin1s2 = 1.Assume an ideal op-amp. -0 + Vin(s) FIGURE P2.22 A buffer amplifier. o+ V(s)
P2.21 Figure P2.21 shows two pendulums suspended from frictionless pivots and connected at their midpoints by a spring [1]. Assume that each pendulum can be represented by a mass M at the end of a massless bar of length L. Also assume that the displacement is small and linear approximations can be
P2.20 A hydraulic servomechanism with mechanical feedback is shown in Figure P2.20 [18]. The power piston has an area equal to A. When the valve is moved a small amount z, the oil will flow through to the cylinder at a rate p # z, where p is the port coefficient. The input oil pressure is assumed
P2.19 The source follower amplifier provides lower output impedance and essentially unity gain. The circuit diagram is shown in Figure P2.19(a), and the small- signal model is shown in Figure P2.19(b). This circuit uses an FET and provides a gain of approximately unity. Assume that R2 W R1 for
P2.18 An LC ladder network is shown in Figure P2.18.One may write the equations describing the network as follows: = (V Va) Y, V = (I-Ia) Z2, La = (Va - V) Y3, V = IZ4- Construct a flow graph from the equations and deter- mine the transfer function V(s)/Vi(s). V(s) L L Va 12=0 Y Ia Y3 V(5) Z2 C ZA
Obtain a signal-flow graph to represent the following set of algebraic equations where x1 and x2 are to be considered the dependent variables and 6 and 11 are the inputs:x1 + 3x2 = 9, 3x1 + 6x2 = 22.Determine the value of each dependent variable by using the gain formula. After solving for x1 by
A mechanical system is shown in Figure P2.16, which is subjected to a known displacement x31t2 with respect to the reference. (a) Determine the two independent equations of motion. (b) Obtain the equations of motion in terms of the Laplace transform, assuming that the initial conditions are
P2.15 Consider the spring-mass system depicted in Fig ure P2.15. Determine a differential equation to describe the motion of the mass m. Obtain the system response x1t2 with the initial conditions x102 = x0 and x # 102 = 0. k, spring constant m, mass x(t) FIGURE P2.15 Suspended spring-mass system.
P2.14 A rotating load is connected to a field-controlled DC electric motor through a gear system. The motor is assumed to be linear. A test results in the output load reaching a speed of 1 rad/s within 0.5 s when a constant 80 V is applied to the motor terminals. The output steady-state speed is
P2.13 An electromechanical open-loop control system is shown in Figure P2.13. The generator, driven at a constant speed, provides the field voltage for the motor. The motor has an inertia Jm and bearing friction bm. Obtain the transfer function uL1s2>Vf 1s2 and draw a block diagram of the
P2.12 For the open-loop control system described by the block diagram shown in Figure P2.12, determine the value of K such that y1t2 S 1 as t S when r1t2 is a unit step input. Assume zero initial conditions. R(s)' Controller K Process 1 Y(s) s+50 FIGURE P2.12 Open-loop control system.
P2.11 For electromechanical systems that require large power amplification, rotary amplifiers are often used [8, 19]. An amplidyne is a power amplifying rotary amplifier. An amplidyne and a servomotor are shown in Figure P2.11. Obtain the transfer function u1s2>Vc1s2, and draw the block diagram
P2.10 Determine the transfer function Y11s2>F1s2 for the vibration absorber system of Problem P2.2. Determine the necessary parameters M2 and k12 so that the mass M1 does not vibrate in the steady state when F1t2 = a sin1v0 t2.
Determine the transfer function X11s2>F1s2 for the coupled spring–mass system of Problem P2.3. Sketch the s-plane pole–zero diagram for low damping when M = 1, b>k = 1, and 1 b 2 kM = 0.1.
A bridged-T network is often used in AC control systems as a filter network [8]. The circuit of one bridged-T network is shown in Figure P2.8. Show that the transfer function of the network is Vo(s) 1+2RCs + RRC Vin(s) 1+ (2R + R)Cs + RRC Sketch the pole-zero diagram when R = 0.5, R2 = 1, and C =

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