DYNAST - a Modeling Toolbox for MATLAB

MATLAB is, of course, a very useful software package for control design thanks to its wide variety of computational options and control-design toolboxes. However, using MATLAB to represent physical models of the controlled plants is rather laborious and cumbersome unless the models are sufficiently idealized and simple.

Efficient use of a computer in control design means using the computer not only for control synthesis and analysis, but also for **automated forming the equations** underlying the plant model. Note please that when using software like SIMULINK to model a plant, manual derivation of the underlying equations and, in addition, manual conversion of the equations into a block diagram, is required. A block-diagram structure is only a graphical representation of a set of equations, it has nothing in common with the real structure of the system the equations represent.

To make physical modeling easier, we have developed many years ago a simulation package DYNAST. It can now be easily used as a physical modeling toolbox for MATLAB, you can even use it across the Internet. DYNAST allows for setting up models of engineering systems from system parts in a kit-like fashion based on a mere inspection of the real systems in the same way in which the systems are assembled from real components without forming any equations or graphs. DYNAST formulates all the equations respecting the physical laws governing mutual energetic interactions between the components automatically.

The **unified modeling and simulation of mixed energy-domain systems** in DYNAST is based on the multipole approach. The multipole model of a real system is a mapping of the system geometric structure onto its topological structure. Each multipole models the energetic interactions between a system component and the rest of the system assuming that the interactions take place just in a limited number of energy entries like electrical terminals, pipe inlets, mechanical or thermal contacts, shafts, etc. The energy flow through each such entrance is represented by a product of two complementary physical quantities - a through variable and an across variable: force - velocity, torque - angular velocity, volume flow - pressure, current - voltage, entropy flow - temperature, etc. (No bond graphs need to be constructed, however.)

DYNAST is accompanied by a **library of ** multipole **submodels** of many typical components. The library is open in the sense that the users can add their own models or model modifications. The component models can be characterized by sets of algebro-differential equations, by tables of measured data, by multipole and/or block configurations, or by a mixture of these. Using DYNCAD -- the DYNAST companion for **submitting models** to DYNAST in a **graphical form** –- you can also design your own graphical symbols for the submodels.

DYNAST **simulates nonlinear systems**, i.e., it computes transient as well as steady-state responses, either static or periodic. The static steady-states can be computed for a system- or ambient-parameter sweeps through an interval. Fourrier analysis of periodic responses is also available. The transient responses can start either from initial conditions specified by the user, or from initial conditions corresponding to a static or periodic steady-state. DYNAST provides **also automatically linearized system models** that can be subjected to small-excitation analysis in the vicinity of the user-specified or computed quiescent operating point. This analysis yields operator functions representing either system transfer functions or transforms of system initial-state responses. These **operator functions** are available **in a semisymbolic form** with the Laplace operator *s *as a symbol, and with the polynomial roots (poles and zeroes) and coefficients as numbers. For such operator functions, DYNAST can compute **semisymbolic- and numeric-form time-and frequency-domain characteristics**.

To solve the resulting nonlinear algebro-differential equations, DYNAST uses a **stiff-stable backward-differentiation formula**. The length of the integration steps and, at the same time, the order of the method are varied during the integration to minimize the computation time while respecting the admissible computational error. The equation jacobians are evaluated using a symbolic differentiation procedure. Considerable savings of computational time and memory are achieved also by exploiting the **jacobian sparsity**. Thanks to the implicit form of the equations and to their simultaneous solving, DYNAST imposes **no restrictions on the system structure**. There is no need for equation sorting to solve the causality or algebraic loop problem.

DYNAST runs under MS Windows and Unix. Besides using it freely in the Web-based mode you can download it if you like. User's Manual, a collection of solved examples, and a Web-based course on multipole modeling is here.