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These are questions asked by CEFOG

Is it possible to solve an expression like in the picture below?:
I´ve tried to figure it out at maplesoft.com but I could not find anything that worked...

I´ve also attached the equation as a file. 




solve(Y = G__B*D1*G__A*G__f/(G__A*G__B*G__M*G__c+G__A*G__B*G__R+1)+G__B*G__A*G__c*Y__sp/(G__A*G__B*G__M*G__c+G__A*G__B*G__R+1)+G__B*D1*G__d/(G__A*G__B*G__M*G__c+G__A*G__B*G__R+1), Y/D1)

Warning, solving for expressions other than names or functions is not recommended.




Download question_regarding_solve_in_maple.mw



eq1 := 2*(diff(y__1(t), t)) = -2*y__1(t)-3*y__2(t)+2*u__1

eq2 := diff(y__2(t), t) = 4*y__1(t)-6*y__2(t)+2*u__1+4*u__2


We have two coupled differential equations relating two outputs (y__1, y__2 ) with two inputs u__1, u__2

The objective of the exercise is to obtain the four transfer functions relating the outputs to the inputs, in other words, we must find:

To save time, we will from now on write Y__1 instead of Y__1(s) , etc.

In order to find tese relations, we must solve Y__1 and Y__2 as a function of U__1 and U__2

Since our model is defined in the time-domain, the first step is to perform Laplace Transform:

Note tha y__1(0) and y__2(0)are zero because y__1 and y__2 are deviation variables, as indicated in the problem description of this exercise.

Now we have a set of two equations with two unknowns, which can be solved algebraically
(this is the advantage of the Laplace Transform). For example, from equation (3) we can
isolate Y__2:

We can substitute the expression (5) in equation (4) to obtain Y__1, as follows:

We can multiply both sides by -3 and expand the products to get:

Now we must group the factors multiplying Y__1, U__1 and U__2

Note that this relation is analogous to:

Y__1 = G__11*U__1+G__12*U__2

Since the effects of `U__1 ` and U__2 are additive, if we want to obtain the relation between one output and only one input ( for example Y__1 and "`U__1`)" we can set the other input to zero, i.e. U__2 = 0.

We still have to obtan the relation between Y__2 and the inputs. We can use equation (5) and (6):

Finally we can find the relations:



Download Transfer_function.mw



I have this problem:

in which I have to find the four transfer functions relating the outputs(yand y2) to the inputs (u1,u2).

The u and y are deviation variables. 

The objective is to find the four transfer functions:

So I have done it by hand but I was wondering if there are any maple commands, that could be used to solve such a question?


I found the transfer functions to be:

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