John's Flashcards - Control and Energy resources

What is the difference between an open loop and closed loop system?

Open loop has no feedback

How does a closed loop negative feedback control system work?

subtracts a fraction of the output voltage from the input voltage until the output voltage is the same as the set point

What does an integrator do in a control loop?

eliminates steady state error by accumulating each non-zero value of Ve(s) (which is set point - actual output), until a constant value is reached

What is a PID control system and what does each component represent?

The error signal is multiplied by PID to produce a desired output signal

Proportional: Output voltage is an amplified version of the error voltage (set point - actual output), is scaled

Integrator: eliminates steady state error by accumulating each non-zero value of Ve(s) (which is set point - actual output), until a constant value is reached

Differentiator: subtracts the rate of change from the error signal

rule for success in a proportional amplifier

If Ak / A + k is approximately = to k, where k is the ratio of the (output resistance/input resistance)

Closed Loop Transfer Function

CL(s) = G(s) / 1 + G(s)H(s)

what is the difference between loop gain and closed loop gain function?

Loop Gain - Total gain encountered when going around the loop once

Closed Loop Gain - ratio of input-output relationship that characterises how the system responds

What is the relation between type and order of a control system?

Type - Total number of poles, which are solutions of the polynomial in then denominator when it is equal to 0. number of integrators

Order - highest power of s

What is the integrator equation?

-1/RC * integral (Vi(t)) dt

Loop gain

G(s)*H(s)

Closed loop response of a first order system

K*omega_o / s + omega_o

where omega_o = A/sRC

what is a ramp input?

A signal that changes linearly with time

equation for typical second order dynamic system

( 2𝜁𝜔_𝑛𝑠 + 𝜔^2_𝑛 )/ ( 𝑠^2 + 2𝜁𝜔_𝑛𝑠 + 𝜔^2_𝑛 )

Settling time equation

2pi/omegan

Why is stability needed in a control system?

because if feedback is positive, then any noise at that frequency will steadily build to a large oscillation. This results in a gain magnitude larger than 1, and so the returning signal is larger than the signal originally entering the plant

Gain Margin

How much gain increase the system can tolerate before becoming unstable

Phase Margin

How much phase delay the system can tolerate before becoming unstable

Finding the loop gain

LG(s) = CL(s) / 1 - CL(s)

This is because the feedback gain H(s) is typically 1 in a closed loop

what is the effect of loop delays on stability?

It produces a phase shift, thus creating a smaller phase margin in stability

what is damping in a control system?

Critical damping - prevents overshooting, and allows the signal to settle as fast as possible

Underdamping - system overshoots and then oscillates before settling to its final value

Overdamping - produces the most stable response, but is also the slowest

What is the value of the Betz limit (the maximum theoretical efficiency of a wind turbine)?

16/27

What is the equation for Load Power in a transformer?

VIcos(theta)

power factor

Is lagging for an inductive load, but leading for a capacitive load

Cosine of the angle of the load impedance

Carnot Efficiency Formula

1-(Tcold/Thot)

Chambadal-Novikov efficiency

1-sqrt((Tcold/Thot)) (used in endoreversible dynamics, and with engines)

Why is the efficiency of a wind turbine necessarily less than 100%?

If it was 100% efficient, all the kinetic energy would be extracted from the air, creating a blockade of still air on the other side of the wind turbine. Thus, it must have some velocity. According to Betz's Law, the maximum efficiency for a wind turbine is 59.3%

Why is HVAC used in electricity grid generation and transmission across the world?

High transmission voltage provides efficient transmission over long distances due to low ohmic losses in the conductors, and AC allows the voltage be stepped up and down

Power in a three-phase system

P = 3V_PI_Pcos(pf) = sqrt(3)V_LI_Lcos(pf)

equation relating supply frequency and synchronous rotating speed

f = np

power delivered by all 3 phases of the machine

P = 3VIcos(pf) = 3VEsin(la)/X = V_LE_Lsin(la)/X

Equation to calculate the conductive cross-sectional area

A = (rholP_L/(V_L)^2cos(pf))(efficiency/1-efficiency)

Equation to calculate the conductive total volume

V = (3rho(l^2)P_L)/(V_L)^2cos(pf))*(efficiency/1-efficiency)

what does Carnot efficiency represent?

It represents the maximum possible efficiency that can be achieved in ideal conditions. However the Chambadal-Novikov efficiency equation is much more accurate as it does not assume energy flow to be reversible.

Why must electric grid systems work at close to unity power factor?

this makes most efficient use of the transmission lines, requiring the minimum current for a given power

which units should endoreversible efficiency be calculated in?

Kelvin

what is the difference between simple-cycle, and combined-cycle?

Simple-cycle uses just one heat engine, whereas combined cycle uses two. Combined cycle makes use of the otherwise wasted exhaust heat from the first engine, thus operating at a higher efficiency.

An example of combined cycle is gas turbine stations, as it has a gas turbine followed by a steam turbine.