Change design in CCF smoothly

Aug 6th, 2022
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How to Change design 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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The Controllability Matrix is defined as. — recall that A is n×n and B is n×1, so C(A,B) is. n×n; — the controllability matrix only involves A. and B, not C. We say that the above system is controllable if.
More generally, for a class of objects on which an equivalence relation is defined, a canonical form consists in the choice of a specific object in each class. For example: Jordan normal form is a canonical form for matrix similarity.
Notice that observable canonical form can be obtained from the controllable canonical form simply by transposing the A matrix and by transposing and swapping the b and c vectors.
y = [a0 a1 a2 ··· an−1]x . This form is called the controllable canonical form (for reasons that we will see later). Note how the coefficients of the transfer function show up in the matrix: each of the denominator coefficients shows up negated and in reverse order in the bottom row of A.
Controllability measures the ability of a particular actuator configuration to control all the states of the system; conversely, observability measures the ability of the particular sensor configuration to supply all the information necessary to estimate all the states of the system.
[ 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.
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.
Notice that observable canonical form can be obtained from the controllable canonical form simply by transposing the A matrix and by transposing and swapping the b and c vectors.
Obtaining Controllable Canonical Form There is no MATLAB® command for directly computing controllable canonical form. However, if you can obtain the system in the transfer-function form H(s), then you can use the coefficients ɑ0,…,ɑn–1, β0,…,βn–1, and d0 to construct the controllable canonical-form matrices in MATLAB.
y = [a0 a1 a2 ··· an−1]x . This form is called the controllable canonical form (for reasons that we will see later). Note how the coefficients of the transfer function show up in the matrix: each of the denominator coefficients shows up negated and in reverse order in the bottom row of A.

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