Include space in CCF smoothly

Aug 6th, 2022
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How to Include space in CCF

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hello everyone in this session we will discuss a topic that is ccf and the ocf so what is ccf ccf means controllable canonical form controllable canonical form so what is this meaning so up to now we discussed some problems that is regarding the state model the equations are x dot equal to ax plus bu and y equals cx plus du these equations is called as the controllable canonical form and we can and this ccf controllable canonical form can be converted into the ocf that is observable canonical form so both this controllable and observable canonical form both are similar together but it has a small modification that is this is also this will also represent the same equation x dot equal to ax plus bu [Music] and y equal to cx plus du these are also the same equations but we have a small difference this a is this a is i will write controllable canonical form a okay this b is controllable canonical form b this c is controllable canonical form this d is controllable canonical form here a b

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[ b , a ] = ss2tf( A , B , C , D ) converts a state-space representation of a system into an equivalent transfer function. ss2tf returns the Laplace-transform transfer function for continuous-time systems and the Z-transform transfer function for discrete-time systems.
Controllable canonical form is a minimal realization in which all model states are controllable. Like companion form and observable canonical form, it can be ill-conditioned for computation.
[ b , a ] = ss2tf( A , B , C , D ) converts a state-space representation of a system into an equivalent transfer function. ss2tf returns the Laplace-transform transfer function for continuous-time systems and the Z-transform transfer function for discrete-time systems.
We define the state-space model by using the MATLAB function ss(). Then we transform such a state-space model into a transfer function form by using the command tf().
Probably the most straightforward method for converting from the transfer function of a system to a state space model is to generate a model in controllable canonical form. This term comes from Control Theory but its exact meaning is not important to us.
Consider the third order differential transfer function: We start by multiplying by Z(s)/Z(s) and then solving for Y(s) and U(s) in terms of Z(s). We also convert back to a differential equation. We can now choose z and its first two derivatives as our state variables. Now we just need to form the output.
Direct link to this answer A = [-1.5,-2;1,0]; B = [0.5;0]; C = [0,1]; D = 0; sys = ss(A,B,C,D) sys = A = x1 x2 x1 -1.5 -2 x2 1 0 B = u1 x1 0.5 x2 0 C = x1 x2 y1 0 1 D = u1 y1 0 Continuous-time state-space model. sysastf = tf(sys) sysastf = 0.5 --------------- s^2 + 1.5 s + 2 Continuous-time transfer function.
Create the transfer function G ( s ) = s s 2 + 3 s + 2 : num = [1 0]; den = [1 3 2]; G = tf(num,den); num and den are the numerator and denominator polynomial coefficients in descending powers of s. For example, den = [1 3 2] represents the denominator polynomial s2 + 3s + 2.

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