Converting TF to SS

[csianglim]

Control System Plant Simulator: A Framework for Hardware-In-The-Loop Simulation

By David Chandler

Masters thesis on CSPS (Control System Plant Simulator), a similar project written as a Win32 console app.

http://www.se.rit.edu/~se463/ResearchProject/CSPS/Control%20System%20Plant%20Simulator%20Thesis.pdf

Some sections of interest for improving this PDE project.

3.2.3 Plant Definition Types Supported

The Control System Plant Simulator package provided offers six different ways to define a plant, each of which, with the exception of the state space method, must be converted to a set of state space equations. The plant may be defined as a set of State Space matrices, as a transfer function defined by a numerator and denominator, as a transfer function defined by a set of poles and zeros, as a matrix of transfer functions defined either way, or as a set of nonlinear equations. Transfer functions are converted to state space equations as per the controller algorithm defined in Section 2.1.4. Matrices of transfer functions are converted to state space equations by converting each transfer function and placing the resultant state space matrix as a submatrix within the overall system matrix. Conversion of a set of nonlinear equations is performed as described in Section 2.1.7. New plant definition types may be added by modifying the PlantConfigurationManager class, and adding to the options available to the user when setting the plant.

2.1.3 State Space Equations

As noted earlier, defining systems with multiple inputs and multiple outputs (MIMO) in terms of transfer functions is cumbersome, as the number of transfer functions required is equal to the number of inputs multiplied by the number of outputs. More common is the use of a set of state space matrices. Ogata defines the term state to be “the smallest set of variables (called state variables) such that the knowledge of these variables at t = t0, together with the knowledge of the input for t ≥ t0, completely determines the behavior of the system for any time t ≥ t0” [28]. That is, the current output can be determined as a function of the current states and the current set of inputs. Additionally, the next state can be determined as a function of the current state and current set of inputs as well.

• See Figure 3