Warning: Error while sending QUERY packet. PID=14360 in /home/leakeyB/web/scholarlydissertations.com/public_html/wp-includes/class-wpdb.php on line 2349
The primitive structure of a third order system of ODE’s | ScholarlyDissertations {br} STUCK with your assignment? {br} When is it due? {br} Get FREE assistance. Page Title: {title}{br} Page URL: {url}

The primitive structure of a third order system of ODE’s is defined by the block diagram of Fig. 1. Initial
conditions are zero, and the input, 𝑒, is a unit step.
Initially, the feedback parameter values are set at: 𝒂 = πŸ”. πŸπŸπŸ“; 𝒃 = πŸ–. πŸ•πŸ“
The state equation is:
𝒙̇ = 𝑨𝒙 + 𝑩𝑒
a) Using the states, π‘₯1
, π‘₯2
, and π‘₯3
indicated in the block diagram, derive the system matrix, A, and
the corresponding spectral matrix, S, and modal matrix, M. (15 Marks)
b) Hence, determine the unit step response vector, 𝒙 = [
π‘₯1
π‘₯2
π‘₯3
]. (25 Marks)
c) Check this result via Laplace transform analysis. (15 Marks)
d) Derive the controller canonical realisation of the state equations, and draw the corresponding
block diagram (note, the states will differ from those of the original system). (10 Marks)
e) For the controller canonical realisation, determine a set of state feedback coefficients to
give a unit step response, π‘₯1
, with the following specification:

  1. Zero steady state error for the step input.
  2. Percentage overshoot, 𝑃𝑂 β‰ˆ 20%
  3. Time to first peak, 𝑇𝑝 ≀ 5 sec (12 Marks)
    f) Investigate whether the set of parameter values derived in e), above, are transferrable to
    the original block diagram, through appropriate selection of the β€²π‘Žβ€² and ′𝑏′ parameters.
    (10 Marks)
    g) Now, the system output vector, π’š, is to be defined as follows:
    π’š = π‘ͺ𝒙
    where C is the row vector,
    π‘ͺ = [1, 0, 2]
    Investigate how this modification may be applied to (i) the controller canonical block diagram,
    and (ii) the original primitive block diagram. (13 Marks)
    Dr Colin Morgan NG2S254 Assignment 2021-22
    Fig. 1: Third order state space system
      
    𝑒 + +
    βˆ’ βˆ’ βˆ’
    π‘Ž
    𝑏
    π‘₯ π‘₯3 π‘₯2 π‘₯1
    Μ‡3 π‘₯Μ‡2
Our customer support team is here to answer your questions. Ask us anything!
WeCreativez WhatsApp Support
Support Supervisor
Brian
Available