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focont package

Submodules

focont.foc module

  • focont.foc.get_closed_loop_system(pdata, i=- 1, j=- 1)[source]
    Returns the closed loop system in SciPy discrete LTI system form.

    • Parameters:

      • dict (pdata) – Problem data structure.

      • int (i) – Controller output index for the MIMO controller.

      • int (j) – Controller input index for the MIMO controller.

    • Return scipy.signal.lti:
      SciPy (discrete) LTI system representation.

    Returns an m by r Python array when i or j is not provided. The ith row and jth column of the return value gives the discrete LTI system from jth input to the ith output.

  • focont.foc.get_controller(pdata, i=- 1, j=- 1)[source]
    Returns the controller in SciPy discrete LTI system form.

    • Parameters:

      • dict (pdata) – Problem data structure.

      • int (i) – Controller output index for the MIMO controller.

      • int (j) – Controller input index for the MIMO controller.

    Returns an m by r Python array when i or j is not provided. The ith row and jth column of the return value gives the discrete LTI system from jth input to the ith output.

  • focont.foc.norm(pdata, cl=True)[source]
    Calculates 2-norm of the impulse response of closed or open loop MIMO system.

    • Parameters:

      • dict (pdata) – Problem data structure.

      • [TODO:type] (cl) – Calculate closed loop norm if it is True.

    • Return float:
      2-norm.

    Proposed algorithm is supposed to minimize quadratic cost function of the system states.

  • focont.foc.response_improvement(pdata)[source]
    Compares the 2-norms of the impulse responses of the closed loop system obtained by the algortihm and the open loop system if the open loop system is also stable.

    • Parameters:
      dict (pdata) – Problem data structure.

    • Return float:
      Ratio of the closed and open loop 2-norms.

  • focont.foc.solve(pdata)[source]
    Solves the SOF (static output feedback) or FOC (fixed order controller) problem for the given LTI (discrete or continous) system by applying the proposed solution method [1-2].

    [1]: Demir, O. and Özbay, H., 2020. Static output feedback stabilization of discrete time linear time invariant systems based on approximate dynamic programming. Transactions of the Institute of Measurement and Control, 42(16), pp.3168-3182.

    [2]: Demir, O., 2020. Optimality based structured control of distributed parameter systems (Doctoral dissertation, Bilkent University).

    • Parameters:
      dict (pdata) – Python dictionary of problem parameters obtained from

    system.load function of focont library.

    Controller is calculated by performing the following steps;

    1. Find an appropriate realization of the LTI system.

    2. Apply the approximate dyanmic programming (ADP) iterations to calculate the stabilizing controller which minimize a quadratic cost function similart to the well-known linear quadratic regulator (LQR) problem.

    NOTE: Solution is appended to the input argument pdata.

focont.system module

  • focont.system.load(input_data)[source]
    Load Fixed Order Controller problem paramters from a Python data structure or from a json, or mat file.

    • Parameters:
      dict_or_str (input_data) – The source from which the problem parameters will be loaded.

    input_data can be json or mat filepath. In this case, file will be read and problem parameters data structre will be created from the json or mat file.

    NOTE: Matrices must be Python array of array of floats with appropriate row and column sizes (They are not numpy arrays!). Some matrices can be defined as a string for ease of use. E.g:

    C = ‘I’ or Q = ‘1e-2I’

    They will be translated to numpy identity matrices, np.eye(n) and 1e-2 * np.eye(n), where n is the dimension of LTI systems state vector.

    • focont expects the following paramters:

      • A: System matrix of the LTI sytem ($A \in R_{n \times n}$).

      • B: Input matrix ($B \in R_{n \times m}$).

      • C: Output matrix (can be defined as a string, see the note above.) ($C \in R_{r \times n}$).

      • Q (optional): Cost function weight for LTI system states (can be defined as a string.)

      Q must have the same dimension as A and must be symmetric and semi-positive definite. If it is not provided, its default value is ‘I’.

      • R (optional): Cost function weight for LTI system’s input. (can be a string.) R must be square and have the same number of columns as B. It must be symmetric and positive definite. Its default value is ‘I’.

      • Q0’ (optional): It has the same properties as `Q, but it is used for calculating an appropriate realization of the LTI system as an intermediary step of the algorithm. Its default value is ‘I’.

      • type (optional): It can be ‘D’ if the LTI system is discrete and ‘C’ if it is continuous. Its default value is ‘D’.

      • Ts (optional): It is the sampling period used for ZOH discretization of the LTI system. Its default value is ‘0.01’.

      • max_iter (optional): Dynamic programming iterations limit. Its default value is ‘1e6’.

      • eps_conv (optional): Condition for convergence. If change in the cost-to-go function is smaller than this value, iterations will be terminated. Its default value is ‘1e-12’.

      • zoh_calc_step (optional): Max number of iterations used in ZOH discretization. Its default value is ‘256’.

      • structure (optional): It is ‘SOF’, if a static output feedback is wanted to be calculated. It is ‘FO’ if controller is dynamic.

      • If controller structre is dynamic, then the paramters below can be provided.

        • Ccont (optional): Output matrix of the proposed dynamic controller.

        Its default value is ‘$I_{m \times m}$’.

        • Dcont (optional): Input to output gain of the controller. Its default value is ‘$0_{m \times r}$’.
        • Qcont (optional): Cost function weight on controller’s state vector. Its default value is ‘I’.
        • Q0cont (optional)
        • Rcont (optional): Cost function weight on controller’s input vector. Its default value is ‘I’.
  • focont.system.load_from_json_file(json_filename)[source]
  • focont.system.load_from_mat_file(filename)[source]

Module contents