- Chapter 2.1: Very few physical systems are linear within some range of the varia...
- Chapter 2.2: The s-plane plot of the poles and zeros graphically portrays the ch...
- Chapter 2.3: The roots of the characteristic equation are the zeros of the close...
- Chapter 2.4: A linear system satisfies the properties of superposition and homog...
- Chapter 2.5: The transfer function is the ratio of the Laplace transform of the ...
- Chapter 2.6: Consider the system in Figure 2.79 where Gc(*) = 10, H(s) = l, and ...
- Chapter 2.7: Consider the system in Figure 2.79 with Gc(s) = 20, H{s) = 1, and G...
- Chapter 2.8: Consider a system represented by the block diagram in Figure 2.80. ...
- Chapter 2.9: The closed-loop transfer function T(s) = Y(s)/R(s) is: TV ^ 5 0 a. ...
- Chapter 2.10: The closed-loop unit step response is: a. y{t) =i r + 20 20 _, 5' _...
- Chapter 2.11: The final value of y(t) is: a. y = lim y(t) = 0.8 r-*oo b. yw = lim...
- Chapter 2.12: Consider the differential equation y + 2y + y = u where y(0) = y(0)...
- Chapter 2.13: A cart of mass m = 1000 kg is attached to a truck using a spring of...
- Chapter 2.14: Consider the closed-loop system in Figure 2.79 with 1000 Gc(s) = 15...
- Chapter 2.15: Consider the feedback system in Figure 2.79 with K(s + 0.3) 1 Gc(s)...
- Chapter 2.E2.1: A unity, negative feedback system has a nonlinear function y = /(e)...
- Chapter 2.E2.2: A thermistor has a response to temperature represented by R = /^-01...
- Chapter 2.E2.3: The force versus displacement for a spring is shown in Figure E2.3 ...
- Chapter 2.E2.4: A laser printer uses a laser beam to print copy rapidly for a compu...
- Chapter 2.E2.5: A noninverting amplifier uses an op-amp as shown in Figure E2.5. As...
- Chapter 2.E2.6: A nonlinear device is represented by the function y = /{X) = e*, wh...
- Chapter 2.E2.7: A lamp's intensity stays constant when monitored by an optotransist...
- Chapter 2.E2.8: A control engineer, N. Minorsky, designed an innovative ship steeri...
- Chapter 2.E2.9: A four-wheel antilock automobile braking system uses electronic fee...
- Chapter 2.E2.10: One of the most potentially beneficial applications of an automotiv...
- Chapter 2.E2.11: A spring exhibits a force-versus-displacement characteristic as sho...
- Chapter 2.E2.12: Off-road vehicles experience many disturbance inputs as they traver...
- Chapter 2.E2.13: Consider the feedback system in Figure E2.13. Compute the transfer ...
- Chapter 2.E2.14: Find the transfer function Yj(s) R2(s) for the multivariate system ...
- Chapter 2.E2.15: Obtain the differential equations for the circuit in Figure E2.15 i...
- Chapter 2.E2.16: The position control system for a spacecraft platform is governed b...
- Chapter 2.E2.17: A spring develops a force /represented by the relation / = kx2 , wh...
- Chapter 2.E2.18: The output y and input x of a device are related by y = x + 1.4x3 ....
- Chapter 2.E2.19: The transfer function of a system is Y(s) _ 15(.f + 1) R(s) ~ s 2 +...
- Chapter 2.E2.20: Determine the transfer function VQ(s)/V{s) of the operational ampli...
- Chapter 2.E2.21: A high-precision positioning slide is shown in Figure E2.21. Determ...
- Chapter 2.E2.22: The rotational velocity &> of the satellite shown in Figure E2.22 i...
- Chapter 2.E2.23: Determine the closed-loop transfer function T(s) = Y(s)/R(s) for th...
- Chapter 2.E2.24: The block diagram of a system is shown in Figure E2.24. Determine t...
- Chapter 2.E2.25: An amplifier may have a region of deadband as shown in Figure E2.25...
- Chapter 2.E2.26: Determine the transfer function X2(s)/F(s) for the system shown in ...
- Chapter 2.E2.27: Find the transfer function Y(s)/Td(s) for the system shown in Figur...
- Chapter 2.E2.28: Determine the transfer function \&(s)/V(s) for the op-amp circuit s...
- Chapter 2.E2.29: A system is shown in Fig. E2.29(a). (a) Determine G(s) and H(s) of ...
- Chapter 2.E2.30: A system is shown in Figure E2.30. (a) Find the closed-loop transfe...
- Chapter 2.E2.31: Determine the partial fraction expansion for V(s) and compute the i...
- Chapter 2.P2.1: An electric circuit is shown in Figure P2.1. Obtain a set of simult...
- Chapter 2.P2.2: A dynamic vibration absorber is shown in Figure P2.2. This system i...
- Chapter 2.P2.3: A coupled spring-mass system is shown in Figure P2.3. The masses an...
- Chapter 2.P2.4: A nonlinear amplifier can be described by the following characteris...
- Chapter 2.P2.5: Fluid flowing through an orifice can be represented by the nonlinea...
- Chapter 2.P2.6: Using the Laplace transformation, obtain the current I2(s) of P2.1....
- Chapter 2.P2.7: Obtain the transfer function of the differentiating circuit shown i...
- Chapter 2.P2.8: A bridged-T network is often used in AC control systems as a filter...
- Chapter 2.P2.9: Determine the transfer function Xi(s)/F(s) for the coupled spring-m...
- Chapter 2.P2.10: Determine the transfer function Yi{s)jF(s) for the vibration absorb...
- Chapter 2.P2.11: For electromechanical systems that require large power amplificatio...
- Chapter 2.P2.12: For the open-loop control system described by the block diagram sho...
- Chapter 2.P2.13: An electromechanical open-loop control system is shown in Figure P2...
- Chapter 2.P2.14: A rotating load is connected to a field-controlled DC electric moto...
- Chapter 2.P2.15: Consider the spring-mass system depicted in Figure P2.15. Determine...
- Chapter 2.P2.16: Obtain a signal-flow graph to represent the following set of algebr...
- Chapter 2.P2.17: A mechanical system is shown in Figure P2.17, which is subjected to...
- Chapter 2.P2.18: An LC ladder network is shown in Figure P2.18. One may write the eq...
- Chapter 2.P2.19: A voltage follower (buffer amplifier) is shown in Figure P2.19. Sho...
- Chapter 2.P2.20: The source follower amplifier provides lower output impedance and e...
- Chapter 2.P2.21: A hydraulic servomechanism with mechanical feedback is shown in Fig...
- Chapter 2.P2.22: Figure P2.22 shows two pendulums suspended from frictionless pivots...
- Chapter 2.P2.23: The small-signal circuit equivalent to a commonemitter transistor a...
- Chapter 2.P2.24: A two-transistor series voltage feedback amplifier is shown in Figu...
- Chapter 2.P2.25: H. S. Black is noted for developing a negative feedback amplifier i...
- Chapter 2.P2.26: A robot includes significant flexibility in the arm members with a ...
- Chapter 2.P2.27: Magnetic levitation trains provide a high-speed, very low friction ...
- Chapter 2.P2.28: A multiple-loop model of an urban ecological system might include t...
- Chapter 2.P2.29: We desire to balance a rolling ball on a tilting beam as shown in F...
- Chapter 2.P2.30: The measurement or sensor element in a feedback system is important...
- Chapter 2.P2.31: An interacting control system with two inputs and two outputs is sh...
- Chapter 2.P2.32: A system consists of two electric motors that are coupled by a cont...
- Chapter 2.P2.33: Find the transfer function for Y(s)/R(s) for the idlespeed control ...
- Chapter 2.P2.34: The suspension system for one wheel of an oldfashioned pickup truck...
- Chapter 2.P2.35: A feedback control system has the structure shown in Figure P2.35. ...
- Chapter 2.P2.36: A system is represented by Figure P2.36. (a) Determine the partial ...
- Chapter 2.P2.37: A two-mass system is shown in Figure P2.37 with an input force u(t)...
- Chapter 2.P2.38: A winding oscillator consists of two steel spheres on each end of a...
- Chapter 2.P2.39: For the circuit of Figure P2.39, determine the transform of the out...
- Chapter 2.P2.40: A damping device is used to reduce the undesired vibrations of mach...
- Chapter 2.P2.41: The lateral control of a rocket with a gimbaled engine is shown in ...
- Chapter 2.P2.42: In many applications, such as reading product codes in supermarkets...
- Chapter 2.P2.43: An ideal set of gears is shown in Table 2.5, item 10. Neglect the i...
- Chapter 2.P2.44: An ideal set of gears is connected to a solid cylinder load as show...
- Chapter 2.P2.45: To exploit the strength advantage of robot manipulators and the int...
- Chapter 2.P2.46: A load added to a truck results in a force F on the support spring,...
- Chapter 2.P2.47: The water level h{t) in a tank is controlled by an open-loop system...
- Chapter 2.P2.48: The circuit shown in Figure P2.48 is called a leadlag filter. (a) F...
- Chapter 2.P2.49: A closed-loop control system is shown in Figure P2.49. (a) Determin...
- Chapter 2.P2.50: A closed-loop control system is shown in Figure P2.50. (a) Determin...
- Chapter 2.P2.51: Consider the two-mass system in Figure P2.51. Find the set of diffe...
- Chapter 2.AP2.1: An armature-controlled DC motor is driving a load. The input voltag...
- Chapter 2.AP2.2: A system has a block diagram as shown in Figure AP2.2. Determine th...
- Chapter 2.AP2.3: Consider the feedback control system in Figure AP2.3. Define the tr...
- Chapter 2.AP2.4: Consider a thermal heating system given by g(') _ 1 q(s) C,s + (QS ...
- Chapter 2.AP2.5: For the three-cart system illustrated in Figure AP2.5, obtain the e...
- Chapter 2.AP2.6: Consider the hanging crane structure in Figure AP2.6. Write the equ...
- Chapter 2.AP2.7: Consider the unity feedback system described in the block diagram i...
- Chapter 2.AP2.8: Consider the cable reel control system given in Figure AP2.8. Find ...
- Chapter 2.AP2.9: Consider the inverting operational amplifier in Figure AP2.9. Find ...
- Chapter 2.CDP2.1: We want to accurately position a table for a machine as shown in Fi...
- Chapter 2.DP2.1: A control system is shown in Figure DP2.1. The transfer functions G...
- Chapter 2.DP2.2: The television beam circuit of a television is represented by the m...
- Chapter 2.DP2.3: An input r(t) = t, t a 0, is applied to a black box with a transfer...
- Chapter 2.DP2.4: An operational amplifier circuit that can serve as a filter circuit...
- Chapter 2.DP2.5: Consider the clock shown in Figure DP2.5. The pendulum rod of lengt...
- Chapter 2.CP2.1: Consider the two polynomials /?(X = .2 s 1 + 7s + 10 and q(s) = s +...
- Chapter 2.CP2.2: Consider the feedback system depicted in Figure CP2.2. (a) Compute ...
- Chapter 2.CP2.3: Consider the differential equation y + 4y + 3y = u, where y(0) = y(...
- Chapter 2.CP2.4: Consider the mechanical system depicted in Figure CP2.4.The input i...
- Chapter 2.CP2.5: A satellite single-axis attitude control system can be represented ...
- Chapter 2.CP2.6: Consider the block diagram in Figure CP2.6. (a) Use an m-file to re...
- Chapter 2.CP2.7: For the simple pendulum shown in Figure CP2.7, the nonlinear equati...
- Chapter 2.CP2.8: A system has a transfer function X(s) (20/z)(s + z) B{s) ~ s 2 + 3s...
- Chapter 2.CP2.9: Consider the feedback control system in Figure CP2.9, where G(s) = ...
- Chapter 2.CP2.10: Consider the block diagram in Figure CP2.10. Create an m-file to co...

# Solutions for Chapter Chapter 2: Mathematical Models of Systems

## Full solutions for Modern Control Systems | 12th Edition

ISBN: 9780136024583

Solutions for Chapter Chapter 2: Mathematical Models of Systems

Get Full SolutionsModern Control Systems was written by and is associated to the ISBN: 9780136024583. This textbook survival guide was created for the textbook: Modern Control Systems, edition: 12. This expansive textbook survival guide covers the following chapters and their solutions. Since 122 problems in chapter Chapter 2: Mathematical Models of Systems have been answered, more than 10392 students have viewed full step-by-step solutions from this chapter. Chapter Chapter 2: Mathematical Models of Systems includes 122 full step-by-step solutions.