Elmo HARSFEN0602 199, Second order block Block Type=15, Scheduled Double lead block Block type=22

HARSFEN0602ElmoHARmonicaSoftwareManual								PRELIMINARYDRAFT
where	p =		β − α	, q = 1− β , i.e. β = 1 − q , α = 1 −		q	.
			1 − α			1 − p
Order		Parameter			Description			Comment
1		p						Float, represented by
								2 long values
2		q						Float, represented by
								2 long values

199

15.4.1.3Second order block (Block Type=15)

The basic continuous time second order element is filter

D Es2 + As + B

⋅

B Es2 + Cs + D

Note that it can be used as a notch filter or as a low pass complex pole filter.

The equivalent discrete form is

			b z2	+ b z + b
			0	1		2
		z2 + (b + b + b − a			2	− 1)z + a	2
	0		1	2
Order	Parameter		Description				Comment
1	k1		b0 + b1 + b2				Float, represented by
							2 long values
2	k2		−(b1 + b2 )				Float, represented by
							2 long values
3	k3		−b2				Float, represented by
							2 long values
4	k4		a2				Float, represented by
							2 long values

b0 = k1 + k 2 , b1 = k3 − k 2 , b2 = −k3 , a 2 = k 4 .

15.4.1.4Scheduled Double lead block (Block type=22):

The basic continuous time double lead-lag element is

			s + a(k)		2
	b(k)	⋅		 .
 a(k)			s + b(k) 

The index k is the gain scheduler selector: it selects one set of (a,b) from the 63 possible selections (a(1),b(1)) , (a(2),b(2))....(a(63),b(63)).

The frequency a(k) /(2π) [Hz] is the lead corner frequency. The frequency b(k) /(2π) [Hz] is the lag corner frequency.

The discrete equivalent form is

		 z(1- β(k)) 2
	 G(k) + (1- G(k))			
				
			z - β(k) 
Order	Parameter	Description			Comment
1	β (k)	0< β(k) <1			Floating point
2	G(k)	0<G(k)<1			Floating point

The DC gain of this block is unity.