API Reference¶

pyadrc.pyadrc¶

Active Disturbance Rejection Control for Python

It is highly recommended to check the documentation first before attempting to use the package. Although it is simple in nature, ADRC requires some basic knowledge about PID control, observers and state-feedback.

class pyadrc.pyadrc.FeedbackTF(order, delta, b0, w_cl, k_eso, x_init=False, r_lim=(None, None), m_lim=(None, None))[source]¶

Minimal footprint ADRC implemented with transfer functions in feedback path

Parameters

orderint: first- or second-order ADRC
deltafloat: sampling time in seconds
b0float: gain parameter b0
w_clfloat: desired closed-loop bandwidth [rad/s], 4 / w_cl and 6 / w_cl is the corresponding settling time in seconds for first- and second-order ADRC respectively
k_esofloat: relational observer bandwidth
x_inittuple, optional: initial state for the storage variables, by default False
r_limtuple, optional: rate limits of the controller, by default (None, None)
m_limtuple, optional: magnitude limits of the controller, by default (None, None)

References

3: G. Herbst, “A Minimum-Footprint Implementation of Discrete-Time ADRC”, https://arxiv.org/abs/2104.01943

__call__(y, r, zoh=False)[source]¶

Returns value of the control signal depending on current measurements and reference signal.

Parameters

yfloat: Current measurement y[k] of the process
rfloat: Current reference signal r[k]
zohbool, optional: Only update every delta seconds, by default False

Returns

float: Current control signal u[k]

property limiter¶

Returns the value of both limiters of the controller

Returns

tuple of tuples: Returns (magnitude_limits, rate_limits)

property x_states¶

Returns the storage variables

Returns

tuple: Storage variables

class pyadrc.pyadrc.StateSpace(order, delta, b0, w_cl, k_eso, inc_form=False, eso_init=False, r_lim=(None, None), m_lim=(None, None), half_gain=(False, False))[source]¶

Discrete linear time-invariant state space implementation of ADRC

Parameters

orderint: first- or second-order ADRC
deltafloat: sampling time in seconds
b0float: gain parameter b0
w_clfloat: desired closed-loop bandwidth [rad/s], 4 / w_cl and 6 / w_cl is the corresponding settling time in seconds for first- and second-order ADRC respectively
k_esofloat: relational observer bandwidth
inc_formfloat: toggle incremental form of ADRC, by default False. If the incremental form is toggled, the controller will return the incrementation to the current control signal. This value needs to be accumulated by the user. Functionally identical to the non-incremental (normal) form.
eso_inittuple, optional: initial state for the extended state observer, by default False
r_limtuple, optional: rate limits for the control signal, by default (None, None)
m_limtuple, optional: magnitude limits for the control signal, by default (None, None)
half_gaintuple, optional: half gain tuning for controller/observer gains, by default (False, False)

References

1: G. Herbst, “Practical active disturbance rejection control: Bumpless transfer, rate limitation, and incremental algorithm”, https://arxiv.org/abs/1908.04610
2: G. Herbst, “Half-Gain Tuning for Active Disturbance Rejection Control”, https://arxiv.org/abs/2003.03986

__call__(y, u, r, zoh=False)[source]¶

Returns value of the control signal depending on current measurements, previous control action, reference signal.

Parameters

yfloat: Current measurement y[k] of the process
ufloat: Previous control signal u[k-1]
rfloat: Current reference signal r[k]
zohbool, optional: Only update every delta seconds, by default False

Returns

float: Current control signal u[k]

property eso_states¶

Returns the states of the linear extended state observer

Returns

tuple: States of the linear extended state observer

property limiter¶

Returns the value of both limiters of the controller

Returns

tuple of tuples: Returns (magnitude_limits, rate_limits)

reset(x0=None)[source]¶

Resets the extended state observer

Parameters

x0np.array, optional: new initial state vector for the extended state observer, by default None, i.e. resets to zero

class pyadrc.pyadrc.TransferFunction(order, delta, b0, w_cl, k_eso, eso_init=None, r_lim=(None, None), m_lim=(None, None), half_gain=(False, False), method='general_terms')[source]¶

Discrete time linear active disturbance rejection control in transfer function representation

Parameters

orderint: first- or second-order ADRC TF
deltafloat: sampling time in seconds
b0float: modelling parameter b0
w_clfloat: desired closed-loop bandwidth [rad/s], 4 / w_cl and 6 / w_cl is the corresponding settling time in seconds for first- and second-order ADRC respectively
k_esofloat: observer bandwidth is parametrized as k_eso-multiple faster than w_cl
eso_initnp.array, optional: initial state for the extended state observer, by default None
r_limtuple, optional: rate limits for the control output, by default (None, None)
m_limtuple, optional: magnitude limits for the control output, by default (None, None)
half_gaintuple, optional: half gain tuning for controller/observer gains, by default (False, False)
methodstr, optional, ‘general_terms’ or ‘bandwidth’: method with which the transfer function parameters are calculated, functionally identical, but general_terms is used to implement half gain tuning

References

4: G. Herbst, Transfer Function Analysis and Implementation of Active Disturbance Rejection Control https://arxiv.org/abs/2011.01044

__call__(y, r)[source]¶

Control loop call

Parameters

yfloat: current output signal
rfloat: current reference signal

Returns

float: control signal to the plant (accumulator output)

property accumulator¶

Get accumulator

Returns

float: accumulator output

property parameters¶

Get parameters

Returns

dict: calculated paramaters

pyadrc.pyadrc.saturation(_limits, _val)[source]¶

Saturation function

Parameters

_limitstuple: saturation limits (low, high)
_valfloat: sat(_val)

Returns

float: saturated signal

pyadrc.models¶

class pyadrc.models.QuadAltitude(dt=0.001, m=0.028, g=9.807)[source]¶

Discrete-time model of altitude of a quadcopter

Parameters

dtfloat, optional: Discretization time (zero-order hold), by default 0.001
mfloat, optional: Mass of the quadcopter, by default 0.028
gfloat, optional: Gravitational acceleration, by default 9.807

__call__(u)[source]¶

Input port to the quadcopter

Parameters

ufloat: Thrust of the rotors

Returns

float:: Current altitude of quadcopter

reset()[source]¶: Reset position and velocity to zero

property states¶: Return the state of the quadcopter

class pyadrc.models.RandomSystem(states=1)[source]¶

__call__(u)[source]¶: Call self as a function.

class pyadrc.models.System(K=1.0, T=1.0, D=None, delta=0.001)[source]¶

Python class to generate a first-or second-order process for simulation and verification purposes

Parameters

Kfloat, optional: system gain, by default 1.0
Tfloat, optional: time constant, by default 1.0
Dfloat, optional: damping factor, by default None
deltafloat, optional: discretization time in seconds, by default 0.001

__call__(u)[source]¶

System response w.r.t. control signal u

Parameters

ufloat: control signal u

Returns

float: system response y