- L: the observer gain matrix.. 61 - 0 T T J=∫∞ x Ix+ λu udt: To account for the expenditure of the energy of the control signal, we will use this performance index.
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CONTROL SYSTEM DESIGN
Lecture Notes The Design of State Variable Feedback Systems
4 - ˆx : the estimate value of x
- xɺ : the time – derivative of x
- K: the full – state matrix
- L: the observer gain matrix
8 - n = 3
14 - det( λI− (A BK− )) = 0: the characteristic equation
( λ + 2 ζω λ ω λ ζωn + n)( + n) = 0: the desired characteristic equation
18 - For SISO systems
0 0 0 1 c−q( )
=
21 - det( λI− (A−LC)) = 0: the characteristic equation
30 - Design procedure
39 - K: the feedback gain matrix
44 - L: the observer gain matrix
51 -
0 ( , , )
f
t
J=∫ g x ut dt: the performance index
- t f: the final time
52 -
0
f
t T
J=∫ x xdt: the specific form of the performance index
- ( ) 3 21
1
T s
= + + + : the normalized, third-order, closed-loop transfer
function
53 - H PT +PH= −I: an assumption
54 - xT( ) ∞ Px( ) ∞ = 0: if the system is stable
58
- (0) 1
1
=
x : initial conditions
61 -
0 ( T T )
J=∫∞ x Ix+ λu udt: To account for the expenditure of the energy of the
control signal, we will use this performance index
- λ: a scalar weighting factor
- Q: define such a matrix
67
- r r r
r r
r
=
=
d x
ɺ
: + consider a reference input to be generated by a linear system of this form
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+ initial conditions are unknown
- r=x r, xɺr = 0: a step reference input with zero steady – state error