In the Antenna Control case study, the final state equation for the motor and load has a system matrix A = [[0, 1], [0, -1.71]]. What physical quantities do the two state variables, x1 and x2, represent?
Explanation
This question checks the understanding of how state variables are chosen to represent physical quantities in a system. In the antenna motor example, the state variables were chosen as the armature's angular position and angular velocity, which is a common practice for mechanical systems.
Other questions
What is the primary disadvantage of the classical, or frequency-domain, approach to system analysis and design?
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What is the typical minimum number of state variables required to describe a system represented by a differential equation?
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What is the key mathematical tool used to linearize nonlinear state equations about an equilibrium point?
For the simple pendulum in Example 3.7, what is the nonlinear state equation for x_2, the angular acceleration?
For the Antenna Control case study, the transfer function of the power amplifier is G(s) = 100/(s + 100). What is its state-space representation if the state variable is the output, ea?
In the Pharmaceutical Drug Absorption case study, what is the state equation for dx3/dt, the rate of change of the drug amount in the blood?
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For the electrical network in Skill-Assessment Exercise 3.1, what is the value of the A[1,3] element in the system matrix?
How is a transfer function with a numerator polynomial, such as (b2*s^2 + b1*s + b0), handled when converting to a state-space representation?
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What is the n-dimensional space whose axes are the state variables called?
In Skill-Assessment Exercise 3.2, for a translational mechanical system with three masses, how many state variables are used in the state-space representation?
When can a state variable, such as the voltage across a resistor vR(t), NOT be chosen as part of the minimal set of state variables if the current i(t) is already chosen?
Given the transfer function G(s) = (2s + 1) / (s^2 + 7s + 9) from Skill-Assessment Exercise 3.3, what is the correct phase-variable state-space representation?
What is the result of the state equation x_ = Ax + Bu if the input u is zero?
In the Case Study on pharmaceutical drug absorption, the system of five state equations has an input matrix B that is a null vector. How can the system have a response?
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In the electrical network of Example 3.2 (with a dependent source), the relationship vL = vC + iR2*R2 is used. How is iR2 expressed in terms of other circuit variables at Node 2?
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What is the primary role of the output equation, y = Cx + Du, in a state-space representation?
For a translational mechanical system as in Example 3.3, if M1=2, M2=1, D=3, and K=4, what is the value of the A[2,2] element in the system matrix?
In the general state-space representation y = Cx + Du, what does a non-zero D matrix imply?
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An 8th-order system would be represented in state space with how many state equations?
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What is meant by the 'phase-variable' choice for state variables?
In the electrical network of Example 3.1, the state variable vC is the voltage across the capacitor. What is the state equation for dvC/dt?
For the system in Skill-Assessment Exercise 3.5, representing a mass with a nonlinear spring, what is the value of the A[2,1] element of the linearized system matrix?
If a system has three independent energy-storage elements, what is the minimum number of state variables required?
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When representing a translational mechanical system in state space, as in Example 3.3, what is a common choice for the state variables?
What is the physical interpretation of the state-vector trajectory in state space?
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For the linearized pendulum in Example 3.7, if T represents a small perturbation torque, what is the linearized state equation for the change in angular acceleration, d(delta_x2)/dt?
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