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What does a Fourier Transform do to a signal?

Transforms the signal from the time domain to the frequency domain.

When would a full PID compensator be used?

If both transient and steady state responses need to be manipulated

For 2nd order systems with complex poles where are the poles located on a Bode plot?

Corner frequency? Or 1?

When would a PI be a good compensator to use?

Very reduced steady state error with minimal impact on transient response characteristics

At the frequency of the pole in a 1st order system what will the magnitude of the output be?

-3dB

What do the different components of PID control do?

How would you analyse a Multi input system?

When will a segment of the real axis be on the root locus?

Left of an odd number of poles

What does pole, or zero, placement mean in the context of designing a control system?

What is system linearization and how is it achieved?

What is the time shift theorem in Laplace Transforms?

e^(-s tau) F(s)

Looks like an underdamped 2nd order

What is the frequency domain design procedure for a phase-lag compensator?

What is the integral theorem in Laplace transforms?

F(s)/s

When would a PD be a good compensator to use?

Gives shorter Tss, reduces steady state error (doesn't get rid of it)

What are the 3 parameters of a sinusoid?

Amplitude, frequency, phase

Frequency domain techniques can still be used to determine stability of non-linear systems

How can a 3rd order system (with no delay) be made stable for all system gains?

s^2 coefficient * s coefficient larger than s^3 coeefficient * constant. Could make constant 0

Have repeated roots. Means the magnitude will go down 40dB/dec at that point

Why is the root locus always symetrical about the real axis?

All heading off to different corners

What are the steady-state step and ramp errors for a type-2 system?

Both: 0

If you needed to reduce the bandwith of a system what sort of compensator would you use and why?

Phase-lag because it decreases the gain at higher frequencies

Why is feedback control used?

What does system approximation mean and when can it be used?

What are the similarities and differences between mechanical and electrical models?

How can required performance be achieved in a system if the goal point is not on the root locus?

Add poles/zeros

What is the difference between SISO and MIMO systems?

What are the steady-state step and ramp errors for a type-0 system?

Step: 1/(1+constant), ramp: inf

What equations are used to model electrical systems?

Kirchhoff's voltage law (KVL) and Kirchhoff's current law (KCL), Ohm, Component rules

What compensator design methodology is best suited when a system has significant time delay and why?

Is an open loop stable 2nd order system (with no delay) always stable for all system gains?

Yes. Poles of the open loop system are not dependent on K

How does a step response relate to its transfer function?

Why do we use the Laplace Transform in Control Systems?

How do you find time to steady state for a 2nd order system?

What does it mean for a system to be unstable?

What is the derivative theorem in Laplace transforms?

sF(s)-f(0)

What is a root locus

A root locus is a plot showing the movement of the pole locations for different gains.

What is the frequency domain design procedure for a phase-lead compensator?

What are some pros and cons of Open Loop control?

Pros

Very simple & easy to design. Are generally stable. Easy to make and use

Cons

Less bandwidth in open loop. Inaccurate & unreliable. Output is affected by disturbances

How can a root locus be used to determine the system gains for stability?

System is stable so long as the poles are on the left half plane

What are the three types of partial fractions that will represent the dynamics of any order system?

A/ax+b, A/ax+b + B/(ax+b)^2, (Ax+B)/(ax^2+bx+c)

What is the main practical difference between Laplace and Fourier Transforms?

How can a Nyquist plot be used to determine the stability margins of a system?

Observe closeness to (-1,0)

Why is the Nyquist plot symetrical about the real axis?

Does a lag compensator increase or decrease the overall magnitude of the system output?

Lag compensator decreases magnitude (dB) of the system output

What does the time to steady-state of a system mean?

Real life issues, like time delays and imperfections

Harder to determine stability

A lag compensator has what net impact on the phase of the system at the phase margin frequency?

What is the root locus angular requirement?

The sum of the angles between the poles and zeros must be equal to 180.

How is a high level of disturbance rejection obtained in a control system?

Same frequency, different amplitude and phase

Less stable because of the time delays inherent in digital systems

If a time delay were inserted into a 2nd order system would the overshoot get larger or smaller?

Larger

Algebraically how does a transfer system with a time delay compare to one without?

How does the impulse response of a system relate to its transfer function?

What are the two main ways to calculate the stability of a system?

What is the damped frequency of a system and how does it relate to the natural frequency?

Damped frequency is the natural frequency multiplied by the square root of 1-zeta

What can a root locus be used for?

What is a transfer function of a system?

Why is it sometimes good to have a high controller gain, irrespective of system dynamics?

What is the fundemental component all signals can be decomposed into?

All signals can be decomposed into a series of sinusoids

What is the time domain formula for general 2nd order systems?

Does a lead compensator increase or decrease the phase at the phase margin frequency and why?

Increases the phase margin, both by increasing the phase

What are the zeros and poles of a system?

The poles and zeros of a system are the points at which the systems response will be calculated as 0.

The poles are found in the denominator of the transfer function and the zeros are found in the numerator of the transfer function.

What are the steady-state step and ramp errors for a type-1 system?

step: 0, ramp: 1/constant

What is the procedure to create a Nyquist plot?

What does it mean for a system to be stable?

What are the gain and phase margins of a system and how would you determine them?

How would you go about creating a digital twin for a mechanical system?

What does the steady-state error of a system mean?

To what temporal charateristic is phase margin most closely related?

Overshoot

Both have all frequencies, but impulse has specific phases where white noise has random phases

Open loop poles are the same as the poles of the characteristic equation, Routh array?

As the system gain gets larger what happens to the branches of the root locus?

Head to infinity or to system zeros

What are some pros and cons of Closed Loop control?

Pros

More accurate in presence of non-linearities, Less affected by noise

Cons

Complex systems. The feedback reduces gain of the system. Can become unstable quite easily

What is an operation you can perform to determine system stability without finding system roots?

Routh Array

How do you find the time to steady-state for a 1st order system?

Why may you want to create a digital twin for a mechanical system?

What does it mean for a system to be LTI?

4. 2 for lead, 2 for lag

If a 1st order system has a pole at w over what frequency range will the phase transition occur?

1/w to 10w

If you can use MATLAB to find system roots why would you need a Routh Array?

How can you tell if a system is stable?

Why is it important to design controllers with possible disturbances in mind?

What is feedback control?

How can you determine the order of a system?

Order of the polynomial in the denominator

What are the three components of PID control?

What affects do lead and lag compensators have on the phase margin frequency?

Lag compensator decreases the phase margin frequency, lead compensator increases it

Why do the block diagram reduction techniques only work for linear systems?

How does the damping ratio of a 2nd order system affect the Bode plot?

How does a time delay affect a system?

What is a block diagram of a system?

What affect will a lead compensator have on the time domain response of a system and why?

fast transient response

What is the Nyquist Stability Criterion?

When will the time domain formula for a 2nd order system step response have a cosine component?

How can you determine the order of a system by looking at the Bode plot?

Number of slope changes (down 20dB/dec for poles, up 20dB/dec for zeros)

At the frequency of the pole in a 1st order system what will the phase of the output be?

-45deg

What is system sensitivity and how is it different between open- and closed-loop control?

How many brances will the root locus of a system have?

What is Contour mapping and why would it be used?

What is the relationship between Nyquist and Bode plots?

Explain how a mass-spring-damper system and a resistor-capacitor-inductor circuit are similar

What is the maximum phase change induced by a 3rd order system with 2 zeros?

neg 270 (from the poles, the zeros would act against it)

What equations are used to model mechanical systems?

Newtons laws of motion (F=ma), component laws

What does it mean to find the impulse response of a system?

If a transfer function of a function I s 2nd order what would it look like?

Depends on the damping ratio

What are the modes that make up any order real system?

What does it mean to find the step response of a system?

What is the time domain fomula for a general 1st order step response?

What is aliasing and why is it detrimental for system analysis and control?

What is pole cancellation and why is it rarely done in practice?

What does it mean for a system to be critically stable?

What is the bandwidth of a system?

What are the three main Input signals used for analysis

impulse, Unit step and ramp (1, 1/s 1/s^2)

When will a system have a complex pole?

The system will have complex conjugate poles when the damping ratio is less than 1

2. 1 for PI 1 for PD