- Chapter 3.1: The state variables of a system comprise a set of variables that de...
- Chapter 3.EX3.1: For the circuit shown in Figure E3.1 identify a set ofstate variables.
- Chapter 3.2: The matrix exponential function describes the unforced response of ...
- Chapter 3.EX3.2: A robot-arm drive system for one joint can be represented by the di...
- Chapter 3.3: The outputs of a linear system can be related to the state variable...
- Chapter 3.EX3.3: A system can be represented by the state vector differential equati...
- Chapter 3.4: A time-invariant control system is a system for which one or more o...
- Chapter 3.EX3.4: Obtain a state variable matrix for a system with a differential equ...
- Chapter 3.5: A state variable representation of a system can always be written i...
- Chapter 3.EX3.5: A system is represented by a block diagram as shown in Figure E3.5....
- Chapter 3.6: Consider a system with the mathematical model given by the differen...
- Chapter 3.EX3.6: A system is represented by Equation (3.16), where "0 1 A = 0 0 (a) ...
- Chapter 3.7: The associated state-transition matrix is: a. $(f,0) = [5f] "1 5r" ...
- Chapter 3.EX3.7: Consider the spring and mass shown in Figure 3.3 where M = 1 kg, k ...
- Chapter 3.8: For the initial conditions xt(0) = .*2(0) = 1, the response x(t) fo...
- Chapter 3.EX3.8: The manual, low-altitude hovering task above a moving landing deck ...
- Chapter 3.9: A single-input, single-output system has the state variable represe...
- Chapter 3.EX3.9: A multi-loop block diagram is shown in Figure E3.9.The state variab...
- Chapter 3.10: The differential equation model for two first-order systems in seri...
- Chapter 3.EX3.10: A hovering vehicle control system is represented by two state varia...
- Chapter 3.11: A first-order dynamic system is represented by the differential equ...
- Chapter 3.EX3.11: Determine a state variable representation for the system described ...
- Chapter 3.12: The effect of the input R(s) and the disturbance Td(s) on the outpu...
- Chapter 3.EX3.12: Use a state variable model to describe the circuit of Figure E3.12....
- Chapter 3.13: The state-space representation of the closed-loop system from R(s) ...
- Chapter 3.EX3.13: A system is described by the two differential equations cfy dt + y ...
- Chapter 3.14: The steady-state error E{s) = Y{s) - R(s) due to a unit step distur...
- Chapter 3.EX3.14: Develop the state-space representation of a radioactive material of...
- Chapter 3.15: d. ess = lim e(t) = K + I /oo 15. A system is represented by the tr...
- Chapter 3.EX3.15: Consider the case of the two masses connected as shown in Figure E3...
- Chapter 3.EX3.16: Two carts with negligible rolling friction are connected as shown i...
- Chapter 3.EX3.17: Determine a state variable differential matrix equation for the cir...
- Chapter 3.EX3.18: Consider a system represented by the following differential equatio...
- Chapter 3.EX3.19: A single-input, single-output system has the matrix equations and y...
- Chapter 3.EX3.20: For the simple pendulum shown in Figure E3.20, the nonlinear equati...
- Chapter 3.EX3.21: A single-input, single-output system is described by I x(r) = 0 - 1...
- Chapter 3.EX3.22: Consider the system in state variable form x = Ax + Bit y = Cx + Du...
- Chapter 3.EX3.23: Consider a system modeled via the third-order differential equation...
- Chapter 3.P3.1: An RLC circuit is shown in Figure P3.1. (a) Identify a suitable set...
- Chapter 3.P3.2: A balanced bridge network is shown in Figure P3.2. (a) Show that th...
- Chapter 3.P3.3: An RLC network is shown in Figure P3.3. Define the state variables ...
- Chapter 3.P3.4: The transfer function of a system is T(s) Y(s) s 2 + 2s + 10 R(s) ~...
- Chapter 3.P3.5: A closed-loop control system is shown in Figure P3.5. (a) Determine...
- Chapter 3.P3.6: Determine the state variable matrix equation for the circuit shown ...
- Chapter 3.P3.7: An automatic depth-control system for a robot submarine is shown in...
- Chapter 3.P3.8: The soft landing of a lunar module descending on the moon can be mo...
- Chapter 3.P3.9: A speed control system using fluid flow components is to be designe...
- Chapter 3.P3.10: Many control systems must operate in two dimensions, for example, t...
- Chapter 3.P3.11: A system is described by x = Ax + Bu where A = and X](0) = x2(0) = ...
- Chapter 3.P3.12: A system is described by its transfer function Y(s) _ 8(5 + 5)
- Chapter 3.P3.13: Consider again the RLC circuit of P3.1 when R = 2.5, L = 1/4. and C...
- Chapter 3.P3.14: Determine a state variable representation for a system with the tra...
- Chapter 3.P3.15: Obtain a block diagram and a state variable representation of this ...
- Chapter 3.P3.16: The dynamics of a controlled submarine are significantly different ...
- Chapter 3.P3.17: A system is described by the state variable equations 1 1 4 3 -2 1 ...
- Chapter 3.P3.18: Consider the control of the robot shown in Figure P3.18.The motor t...
- Chapter 3.P3.19: Consider the system described by i(0 = 0 - 2 1 x(0 where x(t) = [*a...
- Chapter 3.P3.20: A nuclear reactor that has been operating in equilibrium at a high ...
- Chapter 3.P3.21: Consider the block diagram in Figure P3.21. (a) Verify that the tra...
- Chapter 3.P3.22: Determine a state variable model for the circuit shown in Figure P3...
- Chapter 3.P3.23: The two-tank system shown in Figure P3.23(a) is controlled by a mot...
- Chapter 3.P3.24: It is desirable to use well-designed controllers to maintain buildi...
- Chapter 3.P3.25: A system has the following differential equation: x + r{t). Determi...
- Chapter 3.P3.26: A system has a block diagram as shown in Figure P3.26. Determine a ...
- Chapter 3.P3.27: A gyroscope with a single degree of freedom is shown in Figure P3.2...
- Chapter 3.P3.28: A two-mass system is shown in Figure P3.28. The rolling friction co...
- Chapter 3.P3.29: There has been considerable engineering effort directed at finding ...
- Chapter 3.P3.30: Obtain the state equations for the two-input and one-output circuit...
- Chapter 3.P3.31: Extenders are robot manipulators that extend (that is, increase) th...
- Chapter 3.P3.32: A drug taken orally is ingested at a rate /-.The mass of the drug i...
- Chapter 3.P3.33: The attitude dynamics of a rocket are represented by where U(s) is ...
- Chapter 3.P3.34: A system has the transfer function Y(s) R(s) T(s) = s1 + 6s2 + lis + 6
- Chapter 3.P3.35: Determine a state-space representation for the system shown in Figu...
- Chapter 3.P3.36: Consider the two-mass system in Figure P3.36. Find a state variable...
- Chapter 3.P3.37: Consider the block diagram in Figure P3.37. Using the block diagram...
- Chapter 3.AP3.1: Consider the electromagnetic suspension system shown in Figure AP3....
- Chapter 3.AP3.2: Consider the mass m mounted on a massless cart, as shown in Figure ...
- Chapter 3.AP3.3: The control of an autonomous vehicle motion from one point to anoth...
- Chapter 3.AP3.4: Front suspensions have become standard equipment on mountain bikes....
- Chapter 3.AP3.5: Figure AP3.5 shows a mass A/ suspended from another mass m by means...
- Chapter 3.AP3.6: Consider a crane moving in the x direction while the mass m moves i...
- Chapter 3.AP3.7: Consider the single-input, single-output system described by x(r) =...
- Chapter 3.AP3.8: A system for dispensing radioactive fluid into capsules is shown in...
- Chapter 3.CDP3.1: The traction drive uses the capstan drive system f-r \ shown in Fig...
- Chapter 3.DP3.1: A spring-mass-damper system, as shown in Figure 3.3, is used as a s...
- Chapter 3.DP3.2: A system has the state variable matrix equation in phase variable f...
- Chapter 3.DP3.3: An aircraft arresting gear is used on an aircraft carrier as shown ...
- Chapter 3.DP3.4: The Mile-High Bungi Jumping Company wants you to design a bungi jum...
- Chapter 3.DP3.5: Consider the single-input, single-output system described by x(0 = ...
- Chapter 3.CP3.1: Determine a state variable representation for the following transfe...
- Chapter 3.CP3.2: Determine a transfer function representation for the following stat...
- Chapter 3.CP3.3: Consider the circuit shown in Figure CP3.3. Determine the transfer ...
- Chapter 3.CP3.4: Consider the system 0 1 o" 1 5_ x + "o" 0 _ 1 _ 0 0 H, - 3 - 2 y = ...
- Chapter 3.CP3.5: Consider the two systems Xl 0 0 4 1 0 - 5 o" 1 - 8 _ xt + ~o" 0 _4_...
- Chapter 3.CP3.6: Consider the closed-loop control system in Figure CP3.6. (a) Determ...
- Chapter 3.CP3.7: Consider the following system:
- Chapter 3.CP3.8: Consider the state variable model with parameter K given by ~ o l o...

# Solutions for Chapter Chapter 3: State Variable Models

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

ISBN: 9780136024583

Solutions for Chapter Chapter 3: State Variable Models

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