Lumped element model is also called
Lumped parameter model
Lumped component model
When there are some physical systems that extend into space then assumptions are made on them. Then, they are supposed to be composed of discrete elements and arranged in a certain topology.
The mathematical implication of lumped element model:
The state space of the system comes to finite dimensions.
A physical system has an infinite dimensional mathematical model in space and time. So, it needs Partial Differential Equations to define it. When the lumped element model is applied to such systems then there are finite parameters and ordinary differential equations can define it.
What is state space representation?
https://en.wikipedia.org/wiki/State-space_representation
Control engg
https://www.tutorialspoint.com/control_systems/index.htm
Control system: A system that provides a desired response by regulating the output is called a control system.
The output is varied by controlling the input. But, what are the ways by which the input can be controlled?
Examples of control engg: Traffic light control systems, washing machines
Traffic lights: One of the lights will be on and the other two will be off at a particular instant. The cycle of on and off depends on time. This time depends on the study of traffic at a particular junction. The input signal controls the output.
Classification of control systems
Continuous time and discrete time control systems:
Continuous time control system: The time signals are continuous.
Discrete time control system: The time signals are discrete.
SISO and MIMO control systems:
SISO: Single input and single output
MIMO: Multiple inputs and single ouitput
Open loop and closed loop control systems:
Open loop control system: The output is not fed back to the input. The input is independent of the desired output.
Ex- traffic light
Closed loop control system: The output is fed back into the input so the input depends on the output.
Error signal: Difference between input and feedback signals.
Feedback
Feedback: If some part of the output or the entire output is returned to the input signal then it is called feedback.
Positive feedback:
The positive feedback adds reference input R(s) and feedback output.
Transfer function of positive feedback control system:
Negative feedback:
Negative feedback reduces the error between R(s) and system input. Transfer function for negative feedback control system is:
G and H are functions of frequency so feedback will decrease or increase depending on the frequency.
Sensitivity:
It is a variation of T wrt G.
Case 1: The GH value is negative and the sensitivity increases
Case 2: The GH value is positive and the sensitivity decreases
What is gain of feedback path and how do we know whether it is positive or negative?
When does a system become unstable?
When the feedback is no longer under control then the system becomes unstable. If GH becomes -1 then transfer function (T) and hence the output will become infinite. The system will be unstable.
Transfer function
Transfer function: Output of a system to input of a system.
Read also: Distributed parameter system
(It is in contrast to the lumped element model)
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