Using any transfer function as an example (e.g. a linear transfer function), explain why for a sensor, the higher the sensitivity, the better.
Write your answers and graphs of transfer functions.
What is the transfer function:
In physics, the transfer function
may be defined as mathematical representation (in terms of
frequency) of interrelation between input and output in linear time
uninterrupted systems with zero pint equilibrium and zero initial
conditions. If talking particularly about control systems then it
can be defined as the ratio of the Laplace transform of the output
variable to the Laplace transform of the input variable, with all
zero initial conditions.
A transfer function is a function of complex variables. The
transfer function can be obtained by simple algebraic jugglery of
differential equations that illustrates the system. A transfer
function can represent higher-order systems also, even infinite
dimensionless systems which regulate on partial differential
equations.
For sensors higher sensitivity is better because the sensors are
fully based on sensing its environment. So more the sensitivity of
a sensor more will be the accurate results that it can give. This
leads the sensor better for future implementation also.
Transfer Function of a Linear System: The Transfer Function An input-output description of a system is essentially a table of all possible input-output pairs. For linear systems, the table can be characterized by one input pair only, for example, the impulse response or the step response. In this section, we will consider another interesting pair of signals.
Consider the linear input-output system, the differential equation (1) that express it will be:
Where u is the input and y is the output the differential equation is completely described by two polynomials:
The characteristic polynomial of the system is polynomial a(s). Taking u (t) = est as input to find transfer function so the output will also be an exponential function that will be y (t) = y0 est. Inserting signals in equation (1), we get:
If a, , it will give,
The transfer function of this linear system thus will be a rational function,
Note that, a(s) and b(s) are given above as polynomial of system.
The graphical representation of Transfer Function of a Linear System,
Using any transfer function as an example (e.g. a linear transfer function), explain why for a...
Question 1 a) Define the term transfer function in relation to a linear control system. [5 marks] Figure Q1 shows a block diagram of a feedback control system, with a plant with transfer function G(s) , a controller with transfer function C(s) , and a sensor with transfer function H(s) . b) Derive from first principles the closed loop transfer function G (s) cl from the reference signal r(t) , to the output signal y(t) . [5 marks] c) Give...
3. Write the expressions for the shape functions for a linear truss element. Explain the following properties (what they are and what they mean): delta function property, partitions of unity property, and property of linear field reproduction. Does the shape function for the linear truss element satisfy these three properties? Why or why not? 3. Write the expressions for the shape functions for a linear truss element. Explain the following properties (what they are and what they mean): delta function...
Using diagram(s) explain why a simple linear regression with a constant term will generally provide a better fit than a simple linear regression which excludes a constant.
1 a the system stable. For example, in Chapter 2 we derived the transfer function for the inverted pendulum, which, for simple values, might be G(s) for which we have bs)1 and as)-s2-1-(s+)(s 1). Suppose we try Dcl (s) = K Istn . The characteristic equation that results for the system is (4.17) This is the problem that Maxwell faced in his study of governors: Under what conditions on the parameters will all the roots of this equation be in...
b) The transfer function of a causal linear time-invariant (LTI) discrete-time system is given by: 1+0.6z1-0.5z1 i Does the system have a finite impulse response (FIR) or infinite 3 impulse response (IIR)? Explain why. ii Determine the impulse response h[n] of the above system iii) Suppose that the system above was designed using the bilinear transformation method with sampling period T-0.5 s. Determine its original analogue transfer function. b) The transfer function of a causal linear time-invariant (LTI) discrete-time system...
1. Complete the two activities below. 1. To create the equation of a linear function in standard form, pick two coordinate points to be the x-intercept and y-intercept. o Write the equation in standard form and graph the equation using the intercepts. • Determine the slope and y-intercept of your line. Explain how to graph the line using the slope and y-intercept. • Discuss which method of graphing is easier and why you chose that one. • Is there a...
Provide an Example for each of the followings. If there is Not any example explain why. A subgroup of (Z,-): A non-commutative ring with a multiplicative identity : • An integral domain that is not a subset of the complex numbers : A subgroup of Z40 that has order 7 : .
In Matlab and not using any built in functions write a function that will take in a word and a specific letter. It will then return a list of all the positions in the word where that letter exists. function indexes = find_letter_positions( word, letter ) Example of output. >> find_letter_positions('hello', 'h') ans = [ 1 ]; >> find_letter_positions('hello', 'l') ans = [ 3 4 ]; >> find_letter_positions('hello', 'z') ans = [ ]; % an empty array
Develop a piecewise linear transfer function for the calibration data shown below (and on your handout) Use a (s,T) coordinate of (5.5,0) as your transition point. Report your answer as an equation using the equation editor function. 225 200 175 150 U 125 2 100 O 75 50 - 25 ト + ト + 25 75 89 10 Stimulus (mV) Develop a piecewise linear transfer function for the calibration data shown below (and on your handout) Use a (s,T) coordinate...
Give an example of a 2x2 system of linear equations which is inconsistent and independent. Explain why your example is inconsistent and independent.