In addition to Control System Professional's control objects, StateSpace, TransferFunction, and ZeroPoleGain, which represent, correspondingly, the state-space, transfer function matrix, and zero-pole-gain models of a control system, Polynomial Control Systems provides the SystemMatrix, LeftMatrixFraction, and RightMatrixFraction objects that represent the system matrix and the left and right matrix-fraction models. All the control objects can be consistently converted from one to another and supplied to the relevant Control System Professional and Polynomial Control Systems functions as input. They can also display in Mathematica's traditional form using the same conventions and can be similarly edited. Make sure the application is loaded. Here is a transfer function of a system that consists of an integrator and a first-order element with a simple pole. This guide typically uses the control format from Control System Professional (see Section 1.5) to display results. | Out[3]= |  |
This is the left matrix-fraction form of the system. It consists of a set of matrices "D" and "N" (see Section 3.4.1). The percent symbol, %, customarily refers to the result of the preceding computation. | Out[5]= |  |
 | As usual in Control System Professional, to find another representation of a control object, apply the desired head to the object. |
Converting between control objects. The familiar Control System Professional functions continue to operate on the new polynomial control objects. Similarly, the new functions from Polynomial Control Systems work on control objects from Control System Professional. This is the discrete-time representation of the left matrix-fraction model system, sampled with a period  . The result is a discrete-time left matrix-fraction model, which is obtained using the function ToDiscreteTime from Control System Professional. | Out[7]= |  |
The McMillan degree of the transfer-function system can be obtained using the new function McMillanDegree (see Section 4.1.3). It gives the degree of a minimal state-space realization of the system. | Out[9]= |  |
Polynomial Control Systems also provides different methods to functions in Control System Professional. These are accessible through options. In particular, the default value of the option TargetForm for the StateSpace object is set to the new option value Controllable, which frequently gives state-space realizations that are smaller than the ones provided with the option ControllableCompanion. This is a controllable realization of the transfer function. The realization is also observable and therefore minimal. The order of the realization is 2, in accordance with the McMillan degree of the system. | Out[11]= |  |
The controllable companion realization, provided by Control System Professional, is also available. | Out[13]= |  |
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