MAE488 Quiz
Consider the control system shown below with C(s)=K and P(s)=1/s+a where a= 16. What should the gain KK be so that the closed loop pole is s= -35?
19
The voltage across a capacitor is vC(t)=1/C∫(t0)i*dt assuming no initial charge on the capacitor. What is the impedance? 1 . C 2. 1/Cs 3. C/s 4. sC 5. None of these
2
Which of the following is the equation for Ohm's law? 1. V=i/R 2. V=iR 3. i=VR 4. None of these
2
A circuit constants of a voltage source in series with a resister, capacitor and inductor. How many states are required for the state space model? 1 2 3 4
2 (Voltage, Current)
The settling time for a step response is the time required to reach the fist peak the time to go from 10% to 90% of the final value the time after which the response remains within 5% of the final value the time after which the response remains within 5% of the step input magnitude
the time after which the response remains within 5% of the final value
If all of the stable poles of a system lie on a vertical line in the complex plane (not necessarily passing through the origin), the poles have the same damping ratio natural frequency damped natural frequency time constant
time constant
A "root locus" is the path taken by all of the open loop poles (roots of the characteristic equation) while satisfying a particular condition True False
False
A BOde plot consists of the magnitude and phase plotted versus damping ratio. True False
False
The equivalent spring constant of two springs in series is the sum of the spring constants. True False
False
The initial value theorem will always provide the correct initial condition, regardless of the input or transfer function of the system. True False
False
The integral of the unit step function is a parabolic function. True False
False
The resonant frequency is always the same as the natural frequency. True False
False
The roots of a 2nd order system resukt in an undamped oscillatory free response. Therefore the imaginary part of the roots is zero. True False
False
The units of electrical charge are Henrys. True False
False
The controllability matrix only depends on the A and C matrix. True False
False (C = [B AB A^2B ・・・ A^(n-1)B])
In a system is represented as a matrix of transfer functions. all of the denominators of the transfer functions are the same. True False
True
One of the advantages of block diagrams is that provided a visual representation of the subsystems and their interconnections in a complex system. True False
True
One of the advantages of the state space model is that it can handle non-zero initial conditions. True False
True
One of the advantages of the state space model is that the equations are in the time domain. True False
True
The characteristic equation of the standard 2nd order system is s2+2ζωns+ω2n=0 What are the roots? s=±ζωn s=−ζωn±ωn√ζ2−1 s=−ζωn±2ωn√ζ2−1 s=−ζωn±ωn√1−ζ2 Not possible to determine
s=−ζωn±ωn√ζ2−1
Match the letters in boxes in the figure below to the corresponding number in the parameter list following the figure. 1. Time constant, τ 2. Natural frequency, ωn 3. Rise time, tr 4. Damped natural frequency, jωd 5. Overshoot 6. Real part of the pole, −ζωn 7. Critical damping value 8. ζ=cosθ A B C D E
A 4 B 2 C 1 D 6 E 8
Suppose that you have a non-linear system. What can you do to obtain a linear model? Linearize the model using partial fraction expansion Nothing Linearize the model using Taylor Series Linearize the model using the Bode plot method
Linearize the model using Taylor Series
What happens to the magnitude of a transfer function T(s)if it is evaluated at s=a, where a is a pole of the transfer function nothing it has a local minimum it goes to zero it tends to infinity
it tends to infinity
The Laplace transform of the hyperbolic sin is sinh(at)u(t)⟺as2−a2 What is the Laplace transform of y(t)=t*sinh(4t)u(t) Choose from the following: 1. 4/s2−164s2−16 2. s2−16/(s2+16)2s2−16(s2+16)2 3. 8s/(s2−16)28s(s2−16)2 4. s/s2+16
3
Which of the following is the equation for comobining 2 resister, R1 and R2, in series into an equivalent resistance, Req? 1. Req=R1+R2/R1R2 2. 1/Req=1/R1+1/R2 3. Req=R1+R2 4. Req=R1R2
3
What is the size of the matrix of transfer functions for a system with 5 states, 2 inputs, and 3 outputs?
3 x 2 matrix
The voltage across an inductor is vL(t)=L*di/dt. What is the impedance? 1 . L 2. 1/Ls 3. L/s 4. sL 5. None of these
4
A system is described by the following transfer function T(s) = 100/(s2+10s+100) What is the resonant frequency in rad/sec? Enter your answer with 4 digits to the right of the decimal point.
7.0711
Suppose the order of a state space system is 8 and it has 2 inputs and 8 outputs. How many closed loop poles can be placed where they are desired?
8 because B = 8x2
A linear system has a frequency response given by M(ω)=1-ω2 (magnitude) Φ(ω)=90-ω2+2ω(phase) If the input to the system is x(t)=A1sin(ω^t+ϕ1) where A1=5.4 and ω^=5.9 rad/sec, ϕ1=26, what is the amplitude of the output, ϕ2, where the output is given by y(t)=A2sin(ω^t+ϕ2) Round your answer to the nearest integer.
93
Q5 Consider the following block diagram and the corresponding differential equation. Match each of the items on the left from the block diagram A~E with the corresponding items from the differential equation listed below. x¨(t)−5x˙+6x(t)=f(t) 1. x(t) 2. x˙(t) 3. x¨(t) 4. 5 5. -5 6. 6 7. -6
A. 3 B. 2 C. 1 D. 5 E. 6
Capacitors store energy in the form of ______________ but inductors store energy in the form of _______________
Charge Voltage
A commutator changes the direction of the armature current. True False
True
The general form of an exponential signal is y(t)=Ae(tτ) Match the following parameters with their description. A e t tau
amplitude exponential function time time constant
Consider the unit step response for a standard 2nd order system. For a fixed damping ratio, ζζ, as the natural frequency, ωnωn, increases the rise time increase decrease remains constant
decrease
The free response of two 2nd order systems with the same natural frequency are being compared. The free response of system 1 decays faster than the free response of system 2. Therefore, the damping ratio of system 1 is ________ the damping ratio of system2. greater than less than equal to
greater than
The Lorentz Force law describes how a force is generated on a wire carrying current in the presence of a _________ field electric magnetic force
magnetic
If all of the stable poles of a system are the same distance from the origin, the poles have the same damping ratio natural frequency damped natural frequency time constant
natural frequency
For positive values of K, the root locus plot starts at the ________ , ________and ends at the ___________, ____________.
open loop (plant) Poles open loop (plant) Zeros
Consider the following differential equation. 3*d3x/dt3+5t*dx/dt=sin(t) The differential equation is a partial differential equation ordinary differential equation
ordinary differential equation
A fourth order system can be written in term of two 2nd order transfer functions. System 1 has a time constant of τ1=1.5. System 2 has a time constant of τ2=0.15. Which system has the dominant roots? system1 system2
system1
Consider the following differential equation. 3*d3x/dt3+5t*dx/dt=sin(t) The independent variable is t x
t
If all of the stable poles of a system lie on a horizontal line in the complex plane (not necessarily passing through the origin), the poles have the same damping ratio natural frequency damped natural frequency time constant
time constant
A system whose free response always approaches ∞∞ as the time, t⟶∞t⟶∞ is unstable stable marginally stable
unstable
Impedance is a transfer function with voltage output and current input current output and voltage input
voltage output and current input
Q1 Choose the best completion to this statement: A non-causal element is an element where the current output or state depends ONLY on the current input where the current output does not depend on future input where the current output depends on future input
where the current output depends on future input
Choose the best completion to this statement: A dynamic element is an element where the current output or state depends ONLY on the current input where the current output or state depends ONLY on past and current input. where the current output does not depend on future input where the current output depends on future input
where the current output or state depends ONLY on past and current input.
Consider the following differential equation a2x¨(t)+a1x˙(t)+a0x(t)=b0e(t) a0=6.7 a1=4 a2=7 b0=11 1. Calculate the transfer function T(s)=X(s)E(s)T(s)=X(s)E(s). 2. Using this transfer function in the block diagram below, calculate the transfer function X(s)F(s)X(s)F(s) 3. Write the result in normal form. 4. What is the coefficient of the constant term in the denominator? Be sure to enter your answer with 4 decimal places
2.5286
The mass of an object is 21.4 slugs. Using the appropriate units (kg, lbs, slugs, or N), calculate the mass of the object in SI units. Enter your result with 2 decimal places. You must use one of the following values for the acceleration due to gravity: 32.2 ft/s2 = 9.8 m/s2. Also you must use the fact that there are 2.2 lbs/kg. Do not round numbers in your calculation.
313.22
What is the locus of all possible stable roots with a constant natural frequency?
A half circle
Q3 For each of the following kinds of force, indicate whether it is conservative or non-conservative Gravitational .................... Frictional .................... Any force that is path independent ............................ Any force that is path dependent ........................... Elastic Force (AKA Spring Force) ...........................
Force conservative Force non-conservative conservative non-conservative conservative
What is the name for the linear force-deflection model for springs? Hooke's Law Pirate's Law Newton's 2nd Law Euler's Equation
Hooke's Law
Recall the bicycle chain example from class. The kinetic energy of the system was given as: KE=12I1ω21+12I2(r1r2ω1)2+12m(r1ω1)2 What is the equivalent inertia of this system? I1+I2(r1/r2)2+m(r1)2 I1+I2 m(r1)2 I1+I2+m(r1)2
I1+I2(r1/r2)2+m(r1)2
Q9 Consider the root locus plot below obtained for the plant transfer function (s^2+22s+40)/(s^3-5s^2-175s+1875) Is it possible to stabilize this system with a gain K>0? [ >----- ] Yes No
No
A damper resists velocity whereas a spring resists displacement. True False
True
Pole placement is a controller design method in which the values of adjustable parameters in the controller are chosen so that a desired closed characteristic equation is obtained for the closed loop system. True False
True
Q8 One of the reasons we use control is to provide robustness in the case of modeling error, variation in the parameters, etc. True False
True
The eigenvalues of the A maxrix in the state space equations determine the number of outputs are the same as the roots of the characteristic equation are always complex conjugates None of these will always be positive
are the same as the roots of the characteristic equation
Which of the following is the steady-state response for the following equation: x(t)=b2/a+(xo−b2/a)e−at
b2/a
The damping ratio ______ affect the magnitude of the oscillations of a system at resonance does does not
does
What is a technique that can be used when your problem has both translational and rotational elements? Hint: this technique allows you to convert the problem into a purely translational or purely rotational model. equivalent mass and inertia parallel axis theorem conservation of mass Newton's 2nd Law
equivalent mass and inertia
What is the technique that can be used when your problem has both translational and rotational elements? Hint: this technique allows you to convert the problem into a purely translational or purely rotational model. equivalent mass and inertia parallel axis theorem conservation of mass Newton's 2nd Law
equivalent mass and inertia
One of the reasons why we use control is to modify the dynamic response. True False
True
The eigenvalues of the A matrix are the same as the roots of the corresponding characteristic equation. True False
True
The equations for the state space (state variable) model are: dx/dt=Ax(t)+Bu(t) y(t)=Cx(t)+Du(t) True False
True
The frequency response of a system describes how the system responds to a sinusoidal input as the frequency of the input changes from 0 to infinity. True False
True
The frequency transfer function is a complex function. True False
True
The frequency transfer function is obtained by setting s=jω in the transfer function. True False
True
The function f(t)=3e(−4t)sin(3t+π2)f(t)=3e(−4t)sin(3t+π2) is a damped sinusoid. True False
True
The relationship to obtain the transfer function from the state space equations is C[sI=A]^-1B+D True False
True
The transfer function can be used to obtain the free response True False
True
When using pole placement and full state feedback to design a controller, the desired closed loop eigenvalues are obtained by adjusting the values in the gain matrix. True False
True
Operational amplifiers can be used to create an integrator, differentiator, or gain stage in a circuit. True False
True
Resistors, capacitors, and inductors are passive elements True False
True
Since electrons are negatively charged, a positive current flows in the opposite direction of the electrons. True False
True
The free response of a stable system approaches __________________ as t⟶∞t⟶∞ Infinity Not possible to determine A constant Zero
Zero
A linear system has a frequency response given by M(ω)=100−ω2+5ω (magnitude) Φ(ω)=200−ω3+45ω2 (phase) If the input to the system is x(t)=A1sin(ω^t) where A1=1.2 and ω^=7.2 rad/sec, what is the amplitude of the output, A2, where the output is given by y(t)=A2sin(ω^t+ϕ2) Round your answer to the nearest integer.
101
Consider the following differential equation with input f(t) x...(t) +a2x¨(t) +a1x˙(t) +a0x(t) = bf(t) where a2= 2 a1= 3 a0= 2 b= 3 Put the differential equation in state space form with the states, x1,x2,andx3 defined as: x1=x(t) x2=x˙(t) x3=x¨(t) Multiply the elements in the last row of the A matrix together and enter as your answer.
-12
Consider a state space model with A=[2 5;1 0] and B=[2;1] Design a full state feedback controller to obtain a response with ζ=0.6 and τ=1/3 . Calculate the product of the gains and enter your result as an integer. For example, if your gain matrix is K=[k1k2k3] your answer should be k1∗k2∗k3
-24
Consider the following differential equation with input f(t) x...(t) +a2x¨(t) +a1x˙(t) +a0x(t) = bf(t) where a2= 4 a1= 6 a0= 2 b= 9 Put the differential equation in state space form with the states, x1,x2,andx3 defined as: x1=x(t) x2=x˙(t) x3=x¨(t) Multiply the elements in the last row of the A matrix together and enter as your answer.
-48
Consider the function f(x)=Axnf(x)=Axn where A=A=6.5 n=n=2 Calculate the constant term in the linear approximation f(x)=mx+bf(x)=mx+b to the function at the point a=a=3.1 Enter your your answer with up to 2 decimal places. For example, if your answer is enter 5 5 5.2 5.2 5.22 5.22 5.25 5.23 If your answer is 5.2, enter 5.2. If your answer is 5.223, enter 5.22. If your answer is 5.225, enter 5.23.
-62.47
The Lorentz force equation is F=iL*B. IF the current is in the direction of the +x axis and the magnetic field is in the direction of the +z axis, what is the direction of the force?
-y axis direction
Match each of the values for the damping ratio on the left with the corresponding type of response on the right 0 <0 >1 Between 0 and 1 1
0 Oscillatory(sinusoidal) <0 Unstable >1 Overdamped Between 0 and 1 Underdamped 1 Critically damped
Obtain the impulse response of the following ODE assuming zero initial conditions. 0.25x¨(t)+2.75x˙(t)+6x(t)=f(t) Calculate the value of the response at t=t= 0.125, in other words, calculate xx(0.125) Enter your answer with 4 decimal points.
0.2555
Consider the transfer function T(s)=A/(s2+a1s+a0) with A=7 a1= 3 a0= 2 Determine the frequency transfer function and write it in the form α(ω)+jβ(ω) Calculate the real part for ω= 1 rad/sec. Enter your answer with all digits to the right of the decimal point (up to 4). For example, Answer Enter 1.11111111 - 1.1111 (rounded to 4 decimal places) 1.1 - 1.1 1 - 1 (not 1.0)
0.7
Consider the root locus plot below and answer the questions below the plot. Be sure to carefully think about your answers. 1. The open loop system (plant) is ___1____order 2. The open loop (plant) poles are ___2_____, _____3____, ______4_____. You must enter your answers starting with the most negative value, and then the next higher value, etc. For example, if the poles are 1, -3, and 7, you must enter -3 for the first one, 1 for the second, and 7 for the third. 3.The zeros of the open loop system (plant) are ____5____, _____6____, ____7_______. Same instructions as above. 4. The closed loop system is _____8_____order 5. For what range of K is the closed loop system stable? ____9_____<K<______10_____ 6. For what range of K is the closed loop system response underdamped?____11_____<K<______12_____ 7. The system is critically damped for K=_____13______ 8. The system is marginally stable for K=_____14______ 9. The x's in the plot correspond to _____15______ 10. The o's in the plot correspond to _____16_____
1. 2nd 2. -1 3. 5 4. N/A (there are not 3 poles) 5. -2 6. N/A (only one zero) 7. N/A (there are not 3 zeros) 8. 2nd 9. 4 10. infinity 11. 4 12. 13.3 13. 13.3 14. 4 15. Both 16. Both
A system is described by the following transfer function T(s) = 4/(s2+10s+4) What is the resonant frequency in rad/sec? Enter your answer with 4 digits to the right of the decimal point.
1.8708
Suppose we want to convert a frequency expressed in Hz. into radians per second. To do so we would multiply the frequency in Hz. by which of the following? pi 1/(2*pi) 2*pi 1/pi
2*pi
A 5 input, 4 state, and 2 output system can be represented in transfer function form. The size of the matrix of transfer functions is _____ rows by _____ columns.
2,5
Consider the following differential equation a2x¨(t)+a1x˙(t)+a0x(t)=b0e(t) a0=5.7 a1=9 a2=7 b0=10.7 1. Calculate the transfer function T(s)=X(s)E(s)T(s)=X(s)E(s). 2. Using this transfer function in the block diagram below, calculate the transfer function X(s)F(s)X(s)F(s) 3. Write the result in normal form. 4. What is the coefficient of the constant term in the denominator? Be sure to enter your answer with 4 decimal places
2.3429
Consider a state space model with A=[2 0;4 1] and B=[0;1] Design a full state feedback controller to obtain a response with ζ=√2/2 and τ=0.5 . Calculate the product of the gains and enter your result as an integer. For example, if your gain matrix is K=[k1k2k3] your answer should be k1∗k2∗k3
35
Consider the following ODE with inputs f(t)and g(t) x...(t)+3x¨(t)−4x˙(t)+2x(t)−2f(t)−3g(t) What is the size of the B matrix? 3x3 2x3 3x2 2x2
3x2
Determine the inverse Laplace transform of X(s)=27s2+63s+90/s3+6s2+9s Choose from 1. x(t)=[17e−3t−48te−3t+10] 2. x(t)=[43t2e−3t−103]u(t) 3. x(t)=[179e−3t−163te−3t+109]u(t) 4. x(t)=[17e−3t−48te−3t+10]u(t)
4
A system is described by the following transfer function T(s) = 100/(s2+10s+100) What is the resonant frequency in rad/sec? Enter your answer with 4 digits to the right of the decimal point.
7.07
A system with 2 inputs, 4 states, and 3 outputs is represented in state space form. The size of the A matrix is _____ rows by _____ columns. The size of the B matrix is _____ rows by _____ columns. The size of the C matrix is _____ rows by _____ columns. The size of the D matrix is _____ rows by _____columns.
A 4,4 B 4,2 C 3,4 D 3,2
A system has 3 inputs, 5 states, and 2 outputs. What is the size of each of the matrices in the state space model? A B C D
A 5 x 5 B 5 x 3 C 2 x 5 D 2 x 3
What is the locus of points comprised of the set of all stable poles in the complex plane with a fixed natural frequency? A semi-circle located to the left of the origin and entered at the origin A circle, centered at the origin A horizontal line A vertical line An oblique line passing through the origin
A semi-circle located to the left of the origin and entered at the origin
Consider the function of time y(t)=8sin(4t+pi/8) Match the quantities on the left hand side with the corresponding description on the right hand side. 8 4 pi/8 4/(2*pi) (2*pi)/4
Amplitude radian frequency phase cyclic frequency period
The step response of several second order systems are shown in the graph below: (W shape) Black Red Green Blue
B Unstable R Underdamped G B Critical Damped
The step response of several second order systems are shown in the graph below: (L shape) Black Red Green Blue
Black Unstable Red Critically Damped Green Overdamped Blue Underdamped
Consider the state space model of a plant given by x˙=Ax+Bu y=Cx+Du Suppose we want to design a full state feedback controller. Which of the following must be true? A matrix must be invertable The system must be controllable C=I and D=0 None of the above
C=I and D=0
Which of the following changes the direction of the armature current so that the torque on the armature is always in the same direction? Rotor Stator Armature Magnetic field Commutator
Commutator
When solving rigid body problems, there are certain steps you should always take. What are these steps?
Define coordinate system and write known(s) Draw free body diagrams Apply Newton's law(s) in each coordinate direction Solve for unknown(s)
Consider the circuit below. What is Kirchoff's Voltage law for the loop? Equation 1: v=i(VR1+VR2) Equation 2: -v +VR1+iVR2=iR1 Equation 3:v=VR1+VR2
Equation 1
Consider the circuit below. What is equation for Kirchoff's current law? Equation 1: i1+i2+i3+i4=0 Equation 2: i1+i3=i2+i4 Equation 3: i1+i2=i3+i4
Equation 2
Q4 Consider the circuit node below. What is the equation for Kirchoff's current law? Equation 1: i1+i2+i3+i4=0i1+i2+i3+i4=0 Equation 2: i1+i3=i2+i4i1+i3=i2+i4 Equation 3: i1+i2=i3+i4
Equation 2
A high pass filter prevents higher frequency signals from passing through the filter. In other words, it only allows low frequency signals to pass. True False
False
A marginally stable system will ALWAYS return to its equibrium position. True False
False
A transfer function is the Laplace transform of the input divided by the Laplace transform of the output. True False
False
A voltage divider is used to increase the voltage at the output. True False
False
An integrator in a PID controller is used to decrease overshoot. True False
False
Back EMF is a consequence of the Lorentz force law. True False
False
Consider the unit step response for a standard 2nd order system. For a fixed damping ratio, ζζ, the natural frequency, ωnωn, has very little effect on the settling time. True False
False
Current is the integral of charge i(t)=∫Qdt True False
False
In a field controlled DC motor, the field current is constant. True False
False
The current flowing in a voltage supply (energy source)moves from the positive terminal to the negative terminal. Conversely, the current flowing in an element that dissipates energy moves from the negative terminal to the positive terminal. True False
False
The equivalent resistance of two resister in parallel is the sum of the resistances. True False
False
If the poles of a stable, 2nd order system are moved horizontally to the left, the free response of the system will be ________ compared to the original system. Faster Slower
Faster
Match the terms on the left with the corresponding description on the right. Free response Transient response Complete response Forced response Steady-state response
Free response: the part of the response that is due to the initial condition Transient response: is the part of the response that disappears (decays to zero) with time Complete response: the sum of the free and forced response Forced response: the part of response due to the input Steady-state response: the part of the response that remains with time
Q10 Consider the state space model of a plant given by x˙=Ax+Bu y=Cx+Du you are to design a controller using pole placement and full state feedback. The input to the closed loop system is an arbitrary input r(t). What is the control law? Note that in Law 1 and Law 2 there is a minus sign between the first and 2nd term that may not show up. Law 1: u(t) = A-BK Law 2: u(t) = r(t)-Kx(t) Law 3: u(t) = Kx(t)+r(t) Law 4: y(t) = Kx(t)+r(t)
Law2
Carefully read the following definition of a transfer function, Is the definition correct? The transfer function is the ratio of the Laplace transform of the input over the Laplace transform of the output, with zero initial conditions
No
Consider the following PID control system. Calculate the transfer function F(s)/E(s). Is this a causal transfer function? Yes No Not possible to determine
No
Is the following block diagram a correct representation of an arbitrary full state feedback control system? Yes No
No (because of K)
Which of the following can be used to estimate the states if they are not available as an output? Observer None of these Estimator Calculator
Observer
Consider the general feedback control system shown below. Match the signal name to the number in the corresponding box. R(s) E(s) F(s) M(s) D(s) C(s)
R(s) : Reference or Command signal E(s) : Error signal F(s) : Control signal M(s) : Actuating signal D(s) : Disturbance C(s) : Controlled variable
For the operational amplifier shown below, there are two golden rules that can be used to analyze circuits containing it. These rules are specified in terms of the two input currents i1i1andi2i2and the differential input voltage Vin. Which of the following statements is equivalent to the two golden rules? Rule 1: Vin=0 and i1+i2=0 Rule 2: Vin=0and i1=i2=0 Rule 3: i1=0 and i2=0
Rule 2
Consider two systems: system 1 with a time constant of τ1 =0.5 and system 2 with a time constant of τ2 =0.25. System 3 is constructed from the serial connection of system 1 and 2. Which system dominates the response of system 3? System 1 System 2 Neither system 1 nor system 2 Not possible to determine
System 2
If the solution of a differential equation is some function, y(t), then the dependent variable in the differential equation has to be y. True False
True
In a DC motor, the back emf opposes the applied armature voltage. True False
True
In a DC motor, the torque constant and the back emf constant are numerically equal assuming they are written with the same units. True False
True
In a multiple input, multiple output system represented as a matrix of transfer functions, the denominator of every transfer function in the matrix is the same. True False
True
For translational motion of rigid bodies, x(t)x(t) was change in position over time. But for linear springs, x(t)x(t) is change in deflection over time. True False
True
The reference input to a control system is a sinusoid. If the control system is perfect, what is the output? A unit step function The same sinusoid as the input A unit ramp function Not enough information A damped sinusoid
The same sinusoid as the input
If the disturbance is negligible in a control system, the actuator, plant, and sensor may be combined into a single transfer function which may be called the plant. True False
True
A gain controller is a type of PID controller with only the proportional term. You can think of this type of controller as "pushing harder on the plant" as the gain is increased to make the plant respond faster thus reducing the error True False
True
A linear element is an element that obeys the superposition principle True False
True
A locus is a curve or path formed by all the points satisfying a particular condition True False
True
A structure in Matlab is a special data type that can be used to store different data types True False
True
An equilibrium state is a state that will not change unless disturbed. True False
True
Back EMF in an armature controlled DC motor is due to the rotation of the armature winding. If the armature is held fixed, there will be no back EMF True False
True
Consider the state space equations. If the C matrix is the identity matrix and the D matrix is a matrix of zeros, the outputs are the same as the states. True False
True
For mechanical systems, kinetic energy is equivalent to work. True False
True
Q6&7 Consider the free response of a standard 2nd order stable system, As the real part of the poles decreases (becomes more negative) the settling time increases the settling time decreases the frequency decreases the frequency increases the response does not change
the settling time decreases
Consider the state space model of a plant given by x˙=Ax+Bu y=Cx+Du Suppose the plant is 5th order. If the controllability matrix is full rank, is it possible to design a controller for the system so that the response is very nearly a first order response? Not enough information Yes No
Yes
In the following, the variables mm, bb, and aiai for i=0,1,2,⋯,ni=0,1,2,⋯,n are constants. The function y(x)=mx+by(x)=mx+b is ............................ The function y(x)=bxmy(x)=bxm is ............................. The function y(x)=b(10mx)y(x)=b(10mx) is ........................ The function y(x)=anxn+an−1xn−1+⋯+a2x2+a1x+a0y(x)=anxn+an−1xn−1+⋯+a2x2+a1x+a0 is ..........................
a linear function. a power function. a exponential function. a general polynomial function.
What are the the two types of DC motors we discussed in class? armature and commutator controlled armature and lorentz controlled armature and field controlled field and force controlled lorentz and commutator controlled
armature and field controlled
To adjust the speed of an armature controlled DC motor, you adjust the armature voltage field voltage None of these torque constant back emf
armature voltage
Is spring force a conservative force or a non-conservative force? conservative force non-conservative force
conservative force
Consider the mass-spring system shown below: The spring has a spring constant (k), and the attached mass (m) has been moved to the right by a force (f), which displaces it a distance (x) from the equilibrium position. If frictional forces are ignored, the free body diagram of the mass is: At time t=0t=0 the mass is released and oscillates about the equilibrium position forever. What is the equation of motion that describes this mass-spring system? d2x/dt2+k/mx=f/m d2x/dt2+kx=m/f f=kx not enough information
d2x/dt2+k/mx=f/m
If all of the stable poles of a system lie on an oblique line (not vertical or horizontal) passing through the origin in the complex plane, the poles have the same damping ratio natural frequency damped natural frequency time constant
damping ratio
In rotational motion, what is the name of this important equation: Ia = Is+md^2 parallel axis theorem Newton's 2nd Law energy conservation equation continuity equation
parallel axis theorem
Consider the state space model of a plant given by x˙=Ax+Bu y=Cx+Du In order to independently place all of the poles using full state feedback, the system must be state observable state controllable static stable
state controllable
Consider the free response of a standard 2nd order stable system. As the imaginary part of the poles decreases, the settling time increases the settling time decreases the frequency increases the frequency decreases
the frequency decreases
Q2 Match the terms on the left with the corresponding description on the right. Free response Transient response Complete response Forced response Steady-state response
the part of the response that is due to the initial condition is the part of the response that disappears (decays to zero) with time the sum of the free and forced response the part of response due to the input the part of the response that remains with time
OldExam 2018F Definition of transfer function
the ratio of the Laplace transform of the output of a system to the Laplace transform of the input of the system, assuming zero initial condition.
Global stability is a characteristic of the initial conditions the system and the input the system the input the system and the initial conditions the system, initial conditions, and the input the initial conditions and the input
the system
For the mass-spring system seen below: If the mass is m and the spring constant is k and friction is ignored, what is the natural frequency, ωnωn, of this mass-spring system? ωn=√k/m ωn=k/m ωn=km ωn=√km
ωn=√k/m
