1. Juraj Oravec Avatar Juraj Oravec
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wiki201617.1

There is a newer version of MUP toolbox available at HomeWiki. We recommend to use the up-to-date version.

Warning:

Bug included: when handle PDLF robust MPC, the feasibility check returnes information that the feasibility check failed also in case, when the feasibility check is in fact valid. You are recommendet to use the newer version, where the bux is fixed.

MUP Description:

MUP is the MATLAB-Simulink toolbox for uncertain systems handling. It is recommended to use the software for educational purposes. MUP is distributed in the hope that it will be useful, but without any warranty. Required dependences are YALMIP and recommended solver is SeDuMi. They are not included in the toolbox. If you use the MUP toolbox, we would be happy to hear about it. Please let us know at juraj.oravec@stuba.sk.

MUP Localization:

The software is recently localized into following languages:

  • English

MUP Compatibility:

The toolbox has been created in MATLAB-Simulink programming environment. It can be run in MATLAB v7 - Simulink v7 and newer.

MUP Installation:

To install the toolbox in successful way, go through the following seven steps:

  1. Download the software package from the link: https://bitbucket.org/oravec/mup/downloads/mup_v20130717.zip
  2. Unzip the package into the required home-folder (e.g.: MATLAB/toolbox/mup)
  3. Run MATLAB
  4. In the MATLAB menu use File/Set Path...
  5. Use button [Add with Subfolders...]
  6. Find out the chosen home-folder
  7. Use button [Save] to save the changes.

RMPC BLOCK

RMPC_BLOCK Description:

MATLAB-Simulink RMPC_BLOCK enables to compute on-line robust MPC control input for a given system state. The controller is designed based on the two approaches. One uses a single Lyapunov function (SLF) and the other uses the parameter-dependent Lyapunov functions (PDLF). The robust MPC with SLF strategy is based on the theory described in the paper: M. V. Kothare, V. Balakrishnan, M. Morari (1996): Robust constrained model predictive control using linear matrix inequalities, Automatica 32, 10, 1361-1379. And the robust MPC with PDLF strategy is based on the theory described in the paper: F. A. Cuzzola, J. C. Geromel, M. Morari (2002): An improved approach for constrained robust model predictive control, Automatica 38, 7, 2002, 1183-1189. The control inputs are computed using the matrix of state-feedback controller. This matrix is designed solving the convex optimization problem. The problem is formulated using the linear matrix inequalities (LMI). The infinity prediction horizon is evaluated based on the uncertain linear time-invariant (LTI) state-space model of controlled system. It is assumed, the controlled system is influenced by interval polytopic uncertainties.

RMPC_BLOCK Initialization:

The MATLAB-Simulink block RMPC_BLOCK can be obtained by typing "mup_rmpc_block" in MATLAB COMMAND-WINDOW.

Function Block Parameters of RMPC_BLOCK:

Robust MPC Configuration:

  • Lyapunov function type: SLF/PDLF - enables to determine the robust MPC design approach (see subsection "RMPC_BLOCK Description")
  • Feasibility Check: disable/enable - serves to evaluate the feasibility check of solved convex optimization problem of controller design.
  • Feasibility Tolerance: [real number is requires] - this parameter is relevant just in the case, when "Feasibility Check" is set to the choice "enable". The value of parameter serves to determine whether the found solution is feasible or not.
  • Initial Conditions of System States: x0: [real-valued vector is required] - vector of initial conditions of the controlled system.
  • System State Matrix: A: [real-valued square matrix of MATLAB-class "cell-array" is required] - the linear state-space model state matrix A of MATLAB-class "cell-array", where each cell represent the uncertain system vertex.
  • System Input Matrix: B: [real-valued matrix of MATLAB-class "cell-array" is required] - the linear state-space model input matrix B of MATLAB-class "cell-array", where each cell represent the uncertain system vertex.
  • Cost Function Weight of Inputs: Wu: [positively-semidefinite real-valued square matrix is required] - the weight matrix of system inputs of quadratic cost function.
  • Cost Function Weight of States: Wx: [positively-defined real-valued square matrix is required] - the weight matrix of system states of quadratic cost function.
  • Symmetric Constraints on Control Input: u_max: [real-valued vector is required] - symmetric constraints on the control inputs.
  • Symmetric Constraints on System States: x_max: [real-valued vector is required] - symmetric constraints on the system states.

Setup:

  • Verbose Mode: Normal/Silent/Loud - mode of information messages shown in MATLAB COMMAND-WINDOW.
  • SDP Solver: SeDuMi/SDPA/SDPLR/SDPT3/VSDP - enables to choose the solver to be used for solving the semidefinite optimization problem.
  • YALMIP Verbose Mode: Normal/Silent/Loud - mode of information messages generated by YALMIP toolbox and solver shown in MATLAB COMMAND-WINDOW.

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