Q1 (a) Use Laplace Transform to find the response x(t) of the system governed by the following equation, where y(t) is the input: d?x(t) dy(t) + 4y(t) dt dx(t) +5 +4x(t) 6.5- dt2 dt Assume zero output initial conditions i.e.r(0)- 0, (0)-0 and given that: y(1)-2 for /20 (b) The following equations represent a system, having an input r(t) and an output v(t). Put these equations in transfer function form. d?v(t) + 6 dr(t) + 3r(t) dt dv(t) + 5v(t) = 7- dt %3D dt2
Transfer function
A transfer function (also known as system function or network function) of a system, subsystem, or component is a mathematical function that modifies the output of a system in each possible input. They are widely used in electronics and control systems.
Convolution Integral
Among all the electrical engineering students, this topic of convolution integral is very confusing. It is a mathematical operation of two functions f and g that produce another third type of function (f * g) , and this expresses how the shape of one is modified with the help of the other one. The process of computing it and the result function is known as convolution. After one is reversed and shifted, it is defined as the integral of the product of two functions. After producing the convolution function, the integral is evaluated for all the values of shift. The convolution integral has some similar features with the cross-correlation. The continuous or discrete variables for real-valued functions differ from cross-correlation (f * g) only by either of the two f(x) or g(x) is reflected about the y-axis or not. Therefore, it is a cross-correlation of f(x) and g(-x) or f(-x) and g(x), the cross-correlation operator is the adjoint of the operator of the convolution for complex-valued piecewise functions.
Trending now
This is a popular solution!
Step by step
Solved in 6 steps