Turn on thread page Beta
    • Thread Starter

    I have been working on an assignment and have done some head damaging stuff, feedback control with Matlab modelling mostly with continuous time systems

    Now I have gotten a bit stuck on something I think should be easy

    To cut a long story short I am designing a state feedback control I have done some tricky stuff I have set the poles at 0.5 and -0.5 (for stability) and gotten the K values to give the system

    X(n+1)= (F+GK)X(n) + GV(n)

    X1(n+1)=0.28X1(n) - 0.02288X2(n) + 0.0192V(n)
    X2(n+1)=-7.5X1(n) -0.28X2(2) +0.2(Vn)

    Y(n)=[1 0]X(n)


    Now I am asked to find the values of V(n) so that Y(n) converges to 3 in the steady state


    X1(n) = 3

    Now for a continuous time system it was easy the X1 was a constant so that X(dot)1 = 0 (differential of a constant = 0) and I could easily work the rest out and simulate my result

    My problem is I am used to differential equations not difference so I am unsure if X1(n) = 3 what does X1(n+1) =?????

    My senses tell me it would be 3 also as the output will not have changed anymore one sample time after infinity!!!

    So in a nutshell what do I need to do to calculate V(n)???, obviously set up two simultaneous equations but I don't know what to put in for the X(n+1)

    Any help much appreciated

    is this physics or maths?
    • Thread Starter

    Its engineering, but its really maths!

    I can do everything else except because I know little about difference equations

    I think X1(n+1) is the same as X1(n) in steady state but I still end up with 2 equations and 3 unknowns
    • Thread Starter

    (Original post by Turbo-Dee)
    I have been working on an assignment and have

    X1(n+1)=0.28X1(n) - 0.02288X2(n) + 0.0192V(n)
    X2(n+1)=-7.5X1(n) -0.28X2(n) +0.2(Vn)
    I can't believe its so easy!!

    X(n+1) tends to X(n) as n approaches inf

    1.28X2(n) = -22.5 + 0.2V(n)

    V(n) = 112.5

    For Y(n) to have steady state 3

    Surely that wasn't too hard for this forum!
How are you feeling about GCSE results day?
Useful resources

Make your revision easier


Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here


How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.