Modelling

class hilo_mpc.Model(id=None, name=None, discrete=False, solver=None, solver_options=None, time_unit='h', plot_backend=None)

Class representing the dynamic model of a system over time

Parameters:

• id (str, optional) – The identifier of the model object. If no identifier is given, a random one will be generated.

• name (str, optional) – The name of the model object. By default the model object has no name.

• discrete (bool, optional) – Whether or not the dynamics of the model are discrete, defaults to False (i.e. the model has continuous-time dynamics)

• solver (str, optional) – Name of the solver to be used for continuous-time integration, defaults to ‘cvodes’ if discrete is set to False. If discrete is set to True the argument solver will not be used.

• solver_options (dict, optional) – Options to be passed to the selected solver. Only used when the model has continuous-time dynamics. By default no options will be set.

• time_unit (str) – The time unit of the model. Common time units are seconds (‘s’), hours (‘h’) or days (‘d’). Will only be used for plotting and as an information storage. Defaults to ‘h’.

• plot_backend (str, optional) – Plotting library that is used to visualize simulated data. At the moment only Matplotlib and Bokeh are supported. By default no plotting library is selected, i.e. no plots can be generated.

add_algebraic_equations(equations, position=None, check_properties=False)

Parameters:

• equations –

• position –

• check_properties –

Returns:

add_algebraic_states(states, position=None)

Parameters:

• states –

• position –

Returns:

add_dynamical_equations(equations, position=None, check_properties=False)

Parameters:

• equations –

• position –

• check_properties –

Returns:

add_dynamical_states(states, position=None)

Parameters:

• states –

• position –

Returns:

add_equations(equations=None, **kwargs)

Parameters:

• equations –

• kwargs –

Returns:

add_inputs(inputs, position=None)

Parameters:

• inputs –

• position –

Returns:

add_measurement_equations(equations, position=None, check_properties=False)

Parameters:

• equations –

• position –

• check_properties –

Returns:

add_measurements(measurements, position=None)

Parameters:

• measurements –

• position –

Returns:

add_options(opts=None, keys=None, values=None)

Parameters:

• opts –

• keys –

• values –

Returns:

add_parameters(parameters, position=None, **kwargs)

Parameters:

• parameters –

• position –

• kwargs –

Returns:

check_consistency()

Returns:

check_solver(solver)

Parameters:

solver –

Returns:

copy(name=None, setup=False, **kwargs)

Parameters:

• name –

• setup –

• kwargs –

Returns:

discretize(method, order=None, butcher_tableau=None, degree=None, polynomial_type=None, inplace=False)

Discretize a continuous-time model. Implemented discretization methods are explicit Runge-Kutta and collocation schemes.

Note:

The discretize() method doesn’t require a numerical sampling time ‘dt’, since the discretization is executed symbolically.

Note:

If the model is already discrete, an according message will be displayed and the discretization attempt will be aborted.

Parameters:

• method (str) – The method used for discretization. At the moment only explicit Runge-Kutta methods and collocation schemes are supported. Accepted values are ‘rk4’ for the most widely known 4th order Runge-Kutta method, ‘erk’ for general order explicit Runge-Kutta methods and ‘collocation’ for the implicit collocation methods.

• order (int, optional) – Order of the explicit Runge-Kutta method ‘erk’. Supported orders are 1 to 4. Will be ignored if ‘rk4’ or ‘collocation’ is selected. Defaults to 1 for ‘erk’.

• butcher_tableau (str, optional) – The Butcher tableau used in the discretization with the explicit Runge-Kutta method ‘erk’. Will be ignored if ‘rk4’ or ‘collocation’ is selected. The default value of the Butcher tableau depends on the order of the explicit Runge-Kutta method. For more information on the Butcher tableau refer to the Modules section.

• degree (int, optional) – Degree of the interpolating polynomial used in the collocation method. Will be ignored if ‘erk’ or ‘rk4’ is selected. Defaults to 2 for ‘collocation’.

• polynomial_type (str, optional) – Polynomial used for calculating the collocation points, i.e. the roots of the polynomial. At the moment only Gauss-Legendre polynomials and Gauss-Radau polynomials are supported. Set polynomial_type to ‘legendre’ for Gauss-Legendre polynomials and to ‘radau’ for Gauss-Radau polynomials. Will be ignored if ‘erk’ or ‘rk4’ is selected. Defaults to ‘radau’ for ‘collocation’.

• inplace (bool) – If True, do discretization on the current Model instance and return None, otherwise a new discretized Model instance will be returned. Defaults to False.

Returns:

If argument inplace was set to True a new Model instance will be returned, otherwise None

is_linear()

Returns:

is_linearized()

Returns:

is_time_variant()

Returns:

linearize(name=None, trajectory=None)

Parameters:

• name –

• trajectory –

Returns:

remove_algebraic_equations(indices, check_properties=False)

Parameters:

• indices –

• check_properties –

Returns:

remove_algebraic_states(indices_or_names)

Parameters:

indices_or_names –

Returns:

remove_dynamical_equations(indices, check_properties=False)

Parameters:

• indices –

• check_properties –

Returns:

remove_dynamical_states(indices_or_names)

Parameters:

indices_or_names –

Returns:

remove_equations(ode=None, alg=None, quad=None, meas=None)

Parameters:

• ode –

• alg –

• quad –

• meas –

Returns:

remove_inputs(indices_or_names)

Parameters:

indices_or_names –

Returns:

remove_measurement_equations(indices, check_properties=False)

Parameters:

• indices –

• check_properties –

Returns:

remove_measurements(indices_or_names)

Parameters:

indices_or_names –

Returns:

remove_options(keys)

Parameters:

keys –

Returns:

remove_parameters(indices_or_names)

Parameters:

indices_or_names –

Returns:

reset()

Returns:

reset_solution(keep_initial_conditions=True, keep_equilibrium_point=True)

Parameters:

• keep_initial_conditions –

• keep_equilibrium_point –

Returns:

scale(value, id=None, name=None)

Parameters:

• value –

• id –

• name –

Returns:

set_algebraic_equations(arg, delimiter=None, check_properties=False)

Parameters:

• arg –

• delimiter –

• check_properties –

Returns:

set_algebraic_states(*args, **kwargs)

Parameters:

• args –

• kwargs –

Returns:

set_dynamical_equations(arg, delimiter=None, check_properties=False)

Parameters:

• arg –

• delimiter –

• check_properties –

Returns:

set_dynamical_states(*args, description=None, labels=None, units=None, **kwargs)

Sets the dynamical state vector of the model

Parameters:

• args – Possible combinations of how to supply arguments to this method can be taken from the table

• description (str, sequence of str, optional) – Description of the single elements of the dynamical state vector. If only a single description is supplied, but the vector has a dimension higher than 1, it is assumed that all the elements of the vector have the same description. This is just for convenience, since the information stored in the description will not be used anywhere else.

• labels (str, sequence of str, optional) – Labels of the single elements of the dynamical state vector. If only a single label is supplied, but the vector has a dimension higher than 1, it is assumed that all the elements of the vector have the same label. At the moment the label information is only used for automatically generating the y-axis labels for the plotting functionality.

• units (str, sequence of str, optional) – Units of the single elements of the dynamical state vector. If only a single unit is supplied, but the vector has a dimension higher than 1, it is assumed that all the elements of the vector have the same unit. At the moment the unit information is only used for automatically generating the y-axis labels for the plotting functionality.

• kwargs (str, optional) – Additional keyword arguments, see table

Returns:

Differential state vector of the model as a symbolic expression

Return type:

casadi.casadi.SX | casadi.casadi.MX

args	kwargs
list of each state variable (sequence of str)	–
dimension of state vector (int)	name of state vector (str)

set_equations(equations=None, **kwargs)

Parameters:

• equations –

• kwargs –

Returns:

set_initial_conditions(x0, t0=0.0, z0=None)

Parameters:

• x0 –

• t0 –

• z0 –

Returns:

set_initial_parameter_values(p)

Parameters:

p –

Returns:

set_inputs(*args, **kwargs)

Parameters:

• args –

• kwargs –

Returns:

set_measurement_equations(arg, delimiter=None, check_properties=False)

Parameters:

• arg –

• delimiter –

• check_properties –

Returns:

set_measurements(*args, **kwargs)

Parameters:

• args –

• kwargs –

Returns:

set_parameters(*args, **kwargs)

Parameters:

• args –

• kwargs –

Returns:

setup(**kwargs)

Parameters:

kwargs –

Returns:

simulate(*args, **kwargs)

Parameters:

• args –

• kwargs –

Returns:

substitute(*args, **kwargs)

Parameters:

• args –

• kwargs –

Returns:

substitute_from(obj)

Parameters:

obj –

Returns:

property algebraic_equations

Returns:

property algebraic_state_description

Returns:

property algebraic_state_names

Returns:

property algebraic_state_units

Returns:

property algebraic_states

Returns:

property continuous

Returns:

property discrete

Returns:

property dynamical_equations

Returns:

property dynamical_state_description

Returns:

property dynamical_state_names

Returns:

property dynamical_state_units

Returns:

property dynamical_states

Differential state vector of the model

Returns:

Differential state vector of the model as a symbolic expression

Return type:

casadi.casadi.SX | casadi.casadi.MX

Alias:

x

property feedthrough_matrix

Returns:

property initial_algebraic_states

Returns:

property initial_dynamical_states

Returns:

property initial_time

Returns:

Return type:

DM

property input_description

Returns:

property input_matrix

Returns:

property input_names

Returns:

property input_units

Returns:

property inputs

Returns:

property measurement_description

Returns:

property measurement_equations

Returns:

property measurement_names

Returns:

property measurement_units

Returns:

property measurements

Returns:

property n_p

Returns:

property n_u

Returns:

property n_x

Returns:

property n_y

Returns:

property n_z

Returns:

property options

Returns:

property output_matrix

Returns:

property parameter_description

Returns:

property parameter_names

Returns:

property parameter_units

Returns:

property parameters

Returns:

property sampling_time

Sampling time variable of the model

Returns:

Sampling time variable of the model as a symbolic expression

Return type:

casadi.casadi.SX | casadi.casadi.MX

Alias:

dt

property solution

Returns:

property solver

Returns:

property state_matrix

Returns:

property time

Time variable of the model

Returns:

Time variable of the model as a symbolic expression

Return type:

casadi.casadi.SX | casadi.casadi.MX

Alias:

t