MOBY-DIC TOOLBOX

Model-based synthesis of digital electronic circuits for embedded control

Contents

MOBY-DIC toolbox has been developed within MOBY-DIC European project www.mobydic-project.eu.

Control systems

The aim of the toolbox is to provide an automated design flow, which allows to implement embedded digital controllers starting from the definition of the system to control and of the constraints to be fulfilled. The resulting circuit, described in VHDL language, can implement an exact or approximate Model Predictive Control (MPC) law. The toolbox also provides tools for the closed-loop system simulation and for the stability analysis. The flow of the toolbox is described in the picture below.

The first step is the creation of two objects, linearSystem and constraints, defining the linear system to control and the constraints you want to fulfill, respectively. The generateMPC function computes, by interfacing with external toolboxes such as Hybrid Toolbox or Multi Parametric Toolbox, an MPC control law, which results in a Piecewise Affine (PWA) function of the system states and parameters. Such function is represented, in MOBY-DIC toolbox, as a pwag object. The stability properties of the closed-loop system, controlled with the pwag function, can be studied by resorting to function stabilityTest. Eventually the VHDL files describing an architecture (pwag_ser, pwag_par) or implementing such control law can be automatically generated with method synthesize. A Simulink model for the simulation of the closed-loop system by taking into account the effects of sata quantization and circuit delays can be generated with method generateSimulinkModel.

If the circuit implementing the exact MPC controller (pwag function) is too complex or slow, it is possible to approximate such controller with a simpler one, more suitable for a digital circuit implementation. The pwag function can be approximated with another PWA function defined over a simplicial partition (pwas function) or over a hyper-rectangular partition (pwar function). The two approximations techniques are realized by resorting to functions pwasApproximation and pwarApproximation. The maximum approximation error can be computed with function suboptimalityAnalysis. The obtained pwas and pwar objects can be used exactly as the pwag one, i.e. a stability analysis can be performed, digital architectures can be generated (pwas_ser, pwas_par, pwar_par, pwar_par) and a Simulink model is available for closed-loop simulations.

Virtual sensors

Moby-dic toolbox also allows to implement Piecewise Affine Simplicial (PWAS) virtual sensors, for the estimation of a unmeasurable output of a dynamical system. The flow of the toolbox is shown in the picture below.

The first step is the creation of a virtualsensor object. The virtual sensor is then identified with method identify starting by measures of the dynamical system inputs (u), measurable outputs (y) and outputs measurable only for a finite amount of time (z). All these measures are possibly corrupted by noise. Then, a validation of the virtual sensor can be performed with method validate, starting from a different set of measures (test set). Once the virtual sensor has been identified and validated it can be implemented on a circuit with method synthesize by obtaining vs_ser or vs_par architecture. A pwas object can be estracted from the virtualsensor object with method getFunction.

Requirements

Installation

Read file INSTALL.TXT

Launch script installMOBYDIC and follow instructions.

Classes

linearSystem - Linear discrete-time system

constraints - Linear inequality constraints on state and input variables

pwaFunction - Piece-Wise Affine function object

pwag - Piece-Wise Affine Generic function object

pwas - Piece-Wise Affine Simplicial function object

pwar - Piece-Wise Affine Hyper-Rectangular function object

pwaSystem - Piecewise affine discrete-time dynamical system object.

virtualsensor - Piece-Wise Affine Simplicial virtual sensor object

Functions

generateMPC - Generates an MPC control law.

pwasApproximation - Performs a PWAS constrained approximation of an MPC controller.

pwarApproximation - Performs a PWAR constrained approximation of an MPC controller.

suboptimalityAnalysis - Find the maximum approximation error between a pwag and a pwas function

stabilityTest - Provides a sufficent condition to verify stability and invariance of the closed-loop system resulting from the application of a piecewise-affine control law of any kind (pwag, pwas, pwar).

all functions...

Circuits

pwag_ser - Circuit for the implementation of pwag controllers - serial architecture

pwag_par - Circuit for the implementation of pwag controllers - parallel architecture

pwas_ser - Circuit for the implementation of pwas controllers - serial architecture

pwas_par - Circuit for the implementation of pwas controllers - parallel architecture

pwar_ser - Circuit for the implementation of pwar controllers - serial architecture

pwar_par - Circuit for the implementation of pwar controllers - parallel architecture

vs_ser - Circuit for the implementation of pwas virtual sensors - serial architecture

vs_par - Circuit for the implementation of pwas virtual sensors - parallel architecture

References

The algorithms, techniques and circuits employed in the toolbox are described in the following publications:

Acknowledgments

Developers

Published with MATLAB® 7.13