def __init__(self,
Kp=1,
Ti=0,
Td=0,
dt=1,
N=float('inf'),
alpha=None,
beta=None,
**opt):
"""
Arguments:
----------
Kp : `float`
Proportional gain.
Default ``Kp``=1.
Ti : `float`
Integral time constant.
Default ``Ti``=0.
Td : `float`
Derivative time constant.
Default ``Td``=0.
dt : `float`
Sampling period.
Default ``dt``=1
N : `float`
Derivative filter coefficient
Default ``N``=float('inf')
alpha : `float`
Alpha coefficient for two-degree of freedom controller.
Default ``alpha``=None
beta : `float`
Alpha coefficient for two-degree of freedom controller.
Default ``alpha``=None
"""
self.P_block = Models.Gain(Kp=Kp, dt=dt, **opt) if Kp else None
self.I_block = Models.Integral(Ki=Kp /
Ti, dt=dt, **opt) if Ti else None
self.D_block = None
self.P2_block = None
self.D2_block = None
if Td:
self.D_block = Models.Derivative(Kd=Td * Kp, dt=dt, **opt) if N == float('inf') \
else Models.StateSpace(ABCD=[[[-N / Td]], [[1]], [[- N ** 2 / Td]], [[N]]], dt=dt, K=Kp, **opt)
if alpha: self.P2_block = Models.Gain(Kp=Kp * alpha, **opt)
if beta:
self.D2_block = Models.Derivative(Kd=Kp * Td * beta, dt=dt, **opt) if N == float('inf') \
else Models.StateSpace(ABCD=[[[-N / Td]], [[1]], [[- N ** 2 / Td]], [[N]]], dt=dt, K=Kp * beta, **opt)
super().__init__(in_len=1, name='PID_Parallel', **opt)
def __init__(self, Kp=0, Ti=0, Td=0, dt=1, N=float('inf'), **opt):
"""
Arguments:
----------
Kp : `float`
Proportional gain.
Default ``Kp``=1.
Ti : `float`
Integral time constant.
Default ``Ti``=0.
Td : `float`
Derivative time constant.
Default ``Td``=0.
dt : `float`
Sampling period.
Default ``dt``=1
N : `float`
Derivative filter coefficient
Default ``N``=float('inf')
"""
self.P_block = Models.Gain(Kp=Kp, dt=dt, **opt) if Kp else None
self.I_block = Models.Integral(Ki=1 / Ti, dt=dt, **opt) if Ti else None
self.D_block = None
if Td:
self.D_block = Models.Derivative(Kd=Td, dt=dt, **opt) if N == float('inf') \
else Models.StateSpace(ABCD=[[[-N / Td]], [[1]], [[- N ** 2 / Td]], [[N]]], dt=dt, **opt)
super().__init__(in_len=1, name='PID_Serial', **opt)
import matplotlib.pyplot as plt
from smacontrol import PID, Models
"""Simulation parameters"""
N = 100 # Simulation time's end
dt = 0.01 # Sampling time
max_len = int(N / dt) # Simulation's vectors' length
time = np.arange(0, N, dt) # Time vector
u = np.ones((1, max_len)) # Input vector u=1
input_on_time = 10 # Start time of input
u[0, :int(input_on_time / dt)] = 0 # Input u = 0 if t < input_on_time
"""State-Space model of inertia P(s) = 2/(50s+1)"""
A = [[-1 / 50]]
B = [[1]]
C = [[2 / 50]]
D = [[0]]
Plant_parallel = Models.StateSpace(ABCD=[A, B, C, D], dt=dt, len=max_len)
Plant_serial = Models.StateSpace(ABCD=[A, B, C, D], dt=dt, len=max_len)
Plant_open = Models.StateSpace(ABCD=[A, B, C, D], dt=dt, len=max_len)
"""Parallel and serial PID objects"""
Kp = 10
Ti = 2
Td = 0.2
Reg_PID_parallel = PID.PID(Kp=Kp, Ti=Ti, Td=Td, dt=dt, len=max_len)
Kps = Kp / 2 * np.sqrt(1 + 4 * Td / Ti)
Tis = Ti / 2 * np.sqrt(1 + 4 * Td / Ti)
Tds = Ti / 2 * np.sqrt(1 - 4 * Td / Ti)
Reg_PID_serial = PID.SerialPID(Kp=Kps, Ti=Tis, Td=Tds, dt=dt, len=max_len)
"""Simulation"""
for it in range(0, max_len):
t = time[it]
import matplotlib.pyplot as plt """Simulation parameters""" N = 100 # Simulation time's end dt = 0.01 # Sampling time max_len = int(N / dt) # Simulation's vectors' length time = np.arange(0, N, dt) # Time vector u = np.ones((1, max_len)) # Input vector u=1 input_on_time = 20 # Start time of input u[0, 0:int(input_on_time / dt)] = 0 # Input u = 0 if t < input_on_time """ Open loop - step response """ # Process P(s) = 12/(12s+1)e^-2 to state-space A, B, C, D = [[-1 / 12]], [[1]], [[1]], [[0]] d = int(2 / dt) Plant_openloop0 = Models.StateSpace(ABCD=[A, B, C, D], dt=dt, len=max_len) Delay_openloop0 = Models.Delay(d=d, dt=dt, len=max_len) """ ****** *** IMC 1 - model with delay ****** """ # Process P(s) = 12/(12s+1)e^-2s to state-space Plant1 = Models.StateSpace(ABCD=[A, B, C, D], dt=dt, len=max_len) Delay1 = Models.Delay(d=d, dt=dt, len=max_len) # Model Pm(s) = 12/(12s+1)e^-2s Plant_model1 = Models.StateSpace(ABCD=[A, B, C, D], dt=dt, len=max_len) # Regulator Q(s) = 12s+1/6s+12 Ar1, Br1, Cr1, Dr1 = [[-2]], [[1]], [[-23 / 6]], [[2]] Reg1 = Models.StateSpace(ABCD=[Ar1, Br1, Cr1, Dr1], dt=dt, len=max_len)
"""Simulation parameters""" N = 50 # Simulation time's end dt = 0.1 # Sampling time max_len = int(N / dt) # Simulation's vectors' length time = np.arange(0, N, dt) # Time vector u = np.ones((1, max_len)) # Input vector u=1 v = -1*np.ones((1, max_len)) # Disturbance vector v=-1, for t>=20 v_start = int(20 / dt) v[0, :v_start] = 0 """Open loop - step response""" # Process model P(s) = 1/(1s+1)e^-5 to state-space A, B, C, D = [[-1]], [[1]], [[1]], [[0]] d = int(5 / dt) Plant_openloop = Models.StateSpace(ABCD=[A, B, C, D], dt=dt, len=max_len) Delay_openloop = Models.Delay(d=d, dt=dt, len=max_len) """Smith Predictor""" # Process model P(s) = 1/(1s+1)e^-5 to state-space Plant = Models.StateSpace(ABCD=[A, B, C, D], dt=dt, len=max_len) Delay = Models.Delay(d=d, dt=dt, len=max_len) # Model Pmo(s) = 1/(1s+1) Model = Models.StateSpace(ABCD=[A, B, C, D], dt=dt, len=max_len) # Regulator C(s) = (1s + 1)/(0.5s) Ar, Br, Cr, Dr = [[0]], [[1]], [[2]], [[2]] Reg = Models.StateSpace(ABCD=[Ar, Br, Cr, Dr], dt=dt, len=max_len) # Output memory Mem = Models.Memory(in_len=1, dt=dt, len=max_len) # SmithPredictor structure SmithPred = SP.SmithPredictor(reg=Reg, model=Model, delay=d, len=max_len)