Symbolic Math Toolbox

The proposed matrix-based approach is illustrated by manual derivation of results for small, well-known examples. For more complex system models, software such as CAMP-G/MATLAB together with the Symbolic Math Toolbox can be used. 

Performing these operations by hand is practically hardly feasible even for small systems. However, software programs such as CAMP-G, MATLAB , and the Symbolic Math Toolbox can set up the matrices of the state space models, perform multiplications of matrix entries, and build the sum of terms. 

Existing software such as CAMP-G/MATLAB supported by the Symbolic Math Toolbox can derive equations from the bond graph and from its associated incremental bond graph and can build the matrices of the state space equations and the output equations for both bond graphs in symbolic form. 

In the case of linear system models, the combination of CAMP-G, MATLAB, and the Symbolic Math Toolbox can generate state space matrices as well as transfer functions in symbolic form from a bond graph. MATLAB in conjunction with the Symbolic Math Toolbox can also be used for the incremental bond graph approach presented in Chapter 4. 

Using MATLAB s Symbolic Math Toolbox, you can carry out algebraic or symbolic calculations such as factoring polynomials or solving algebraic equations. Type help symbolic to make sure that the Symbolic Math Toolbox is installed on your system. 

We use MATLAB R201 lb and the Symbolic Math Toolbox V5.7 for the calculation of the average delays as described in Sect. 4.1. Figures 4.1a and b show Fw, for a node moving in a left direction with r = 0 and t = oo respectively. The main difference... 

Mathematical modeling. SIMULINK for simulating nonlinear dynamic systems. Toolboxes for symbolic math, neural networks, statistics, spline analysis, signal processing, and image processing. PCs (Windows) and Macintosh. 

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