Reference required

[kasheex]

Please provide the reference to convert transfer function $\frac{y}{u} = K \frac{1+sT_1}{1+sT_2}$ into the implementable equations $$T_2 \dot{x}^\prime = (u - x^\prime)$$
$$T_2 y = KT_1(u-x^\prime) + KT_2x^\prime +E_2$$

[jinningwang]

The LeadLag block should be ready to use

andes/andes/core/block.py

Lines 1410 to 1494 in 5ab784b

	class LeadLag(Block):
	r"""
	Lead-Lag transfer function block in series implementation.
	::
	┌───────────┐
	│ 1 + sT1 │
	u -> │ K ─────── │ -> y
	│ 1 + sT2 │
	└───────────┘
	Exports two variables: internal state `x` and output algebraic variable `y`.
	Notes
	-----
	To allow zeroing out lead-lag as a pure gain, set ``zero_out`` to `True`.
	Parameters
	----------
	T1 : BaseParam
	Time constant 1
	T2 : BaseParam
	Time constant 2
	zero_out : bool
	True to allow zeroing out lead-lag as a pass through (when T1=T2=0)
	"""
	def __init__(self, u, T1, T2, K=1, zero_out=True, name=None, tex_name=None, info=None):
	super().__init__(name=name, tex_name=tex_name, info=info)
	self.u = dummify(u)
	self.T1 = dummify(T1)
	self.T2 = dummify(T2)
	self.K = dummify(K)
	self.zero_out = zero_out
	self.enforce_tex_name((self.T1, self.T2))
	self.x = State(info='State in lead-lag', tex_name="x'", t_const=self.T2)
	self.y = Algeb(info='Output of lead-lag', tex_name=r'y', diag_eps=True)
	self.vars = {'x': self.x, 'y': self.y}
	if self.zero_out is True:
	self.LT1 = LessThan(T1, dummify(0), equal=True, enable=zero_out, tex_name='LT',
	cache=True, z0=1, z1=0)
	self.LT2 = LessThan(T2, dummify(0), equal=True, enable=zero_out, tex_name='LT',
	cache=True, z0=1, z1=0)
	self.x.discrete = (self.LT1, self.LT2)
	self.vars['LT1'] = self.LT1
	self.vars['LT2'] = self.LT2
	def define(self):
	r"""
	Notes
	-----
	Implemented equations and initial values
	.. math ::
	T_2 \dot{x'} &= (u - x') \\
	T_2 y &= K T_1 (u - x') + K T_2 x' + E_2 \, , \text{where} \\
	E_2 = &
	\left\{\begin{matrix}
	(y - K x') &\text{ if } T_1 = T_2 = 0 \& zero\_out=True \\
	0& \text{ otherwise }
	\end{matrix}\right. \\
	x'^{(0)} & = u\\
	y^{(0)} & = Ku\\
	"""
	self.x.v_str = f'{self.u.name}'
	self.y.v_str = f'{self.u.name}'
	self.x.e_str = f'({self.u.name} - {self.name}_x)'
	self.y.e_str = f'{self.K.name} * {self.T1.name} * ({self.u.name} - {self.name}_x) + ' \
	f'{self.K.name} * {self.name}_x * {self.T2.name} - ' \
	f'{self.name}_y * {self.T2.name}'
	# when T1=T2=0, use equation `0 = y - Kx`
	if self.zero_out is True:
	self.y.e_str += f'+ {self.name}_LT1_z1 * {self.name}_LT2_z1 * ' \
	f'({self.name}_y - {self.K.name} * {self.name}_x)'