Signals normally pass through interconnections of subsystems.
Feedback provides an opportunity to use and to integrate material we have learned (Laplace transform, frequency response, step response) in an important application area.Stability is an important issue with feedback systems.
Unstable systems can be stabilized with feedback.
Lecture #12:
INTERCONNECTED SYSTEMS AND FEEDBACK
Motivation:
Signals normally pass through interconnections of subsystems.
Feedback is widely used in both man-made and natural systems to enhance performance.
Feedback provides an opportunity to use and to integrate material we have learned (Laplace transform, frequency response, step response) in an important application area.
Stability is an important issue with feedback systems
Unstable systems can be stabilized with feedback
Outline:
Interconnection of systems
Simple feedback system — Black’s formula
Effect of feedback on system performance
Review properties of feedback
Dynamic performance of feedback systems
BIBO stability
Roots of second-order and third-order polynomials
Root locus plots of position control systems
Stabilization of unstable systems
Conclusion
I. INTERCONNECTION OF SYSTEMS
Systems are interconnections of sub-systems. For example, consider the cascade of LTI systems shown below.
The presumption in such a cascade is that H1(s) and H2(s) do not change when the two systems are connected.
1/ Cascade of a lowpass and a highpass filter
Suppose
and
have the following form.
2/ Loading
Now cascade
and
.
l
Note that
3/ Isolation
With the use of an op-amp, the two systems can be isolated from each other or buffered so that the system function is the product of the individual system functions.
Note that
4/ Conclusion
When we draw block diagrams of the form
we assume that the individual systems are buffered or that the loading of system 1 by system 2 is taken into account in
II. FEEDBACK EXAMPLES
1/ Man-made system — robot car
2/ Robot car block diagram
To drive the robot car to the target we use the camera to compare the measured target position with the desired target position. The difference is an error signal whose value is used to change the wheel position. Therefore, the output variable, the angle of the wheels, is fed back to the input to control the new output variable.
3/ Wheel position controller block diagram
The wheel controller system is itself a feedback system. A voltage proportional to the angular position of the motor shaft is subtracted from the desired value and the difference signal is used to drive the motor.
4/ Physiological control systems examples
Voluntary everyday activities
Driving a car
Filling a glass with water
Involuntary everyday occurrences
Pupil reflex
Blood glucose control
Spinal reflex
5/ Spinal reflex
Tapping the patella stretches muscle receptors that, through a neural feedback system, results in muscle contraction. This reflex is used in the maintenance of posture.
Questions & Answers
differentiate between demand and supply
giving examples
In economics, a perfect market refers to a theoretical construct where all participants have perfect information, goods are homogenous, there are no barriers to entry or exit, and prices are determined solely by supply and demand. It's an idealized model used for analysis,
When MP₁ becomes negative, TP start to decline.
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of lab
Kelo
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of labour (APL) and marginal product of labour (MPL)
Quantity demanded refers to the specific amount of a good or service that consumers are willing and able to purchase at a give price and within a specific time period. Demand, on the other hand, is a broader concept that encompasses the entire relationship between price and quantity demanded
Ezea
ok
Shukri
how do you save a country economic situation when it's falling apart
Economic growth as an increase in the production and consumption of goods and services within an economy.but
Economic development as a broader concept that encompasses not only economic growth but also social & human well being.
Shukri
production function means
Jabir
What do you think is more important to focus on when considering inequality ?
sir...I just want to ask one question... Define the term contract curve? if you are free please help me to find this answer 🙏
Asui
it is a curve that we get after connecting the pareto optimal combinations of two consumers after their mutually beneficial trade offs
Awais
thank you so much 👍 sir
Asui
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities, where neither p
Cornelius
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities,
Cornelius
Suppose a consumer consuming two commodities X and Y has
The following utility function u=X0.4 Y0.6. If the price of the X and Y are 2 and 3 respectively and income Constraint is birr 50.
A,Calculate quantities of x and y which maximize utility.
B,Calculate value of Lagrange multiplier.
C,Calculate quantities of X and Y consumed with a given price.
D,alculate optimum level of output .
the market for lemon has 10 potential consumers, each having an individual demand curve p=101-10Qi, where p is price in dollar's per cup and Qi is the number of cups demanded per week by the i th consumer.Find the market demand curve using algebra. Draw an individual demand curve and the market dema
suppose the production function is given by ( L, K)=L¼K¾.assuming capital is fixed find APL and MPL. consider the following short run production function:Q=6L²-0.4L³ a) find the value of L that maximizes output b)find the value of L that maximizes marginal product