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The Structure of the ApplicationTraditional Notations

1.3 The Control Objects

Most Control System Professional functions operate on special data types, or control objects, that contain the available information of the control system. These are TransferFunction, StateSpace, and ZeroPoleGain. The control objects are freely convertible from one to another and are easy to pass from one function to another. You can think of control objects as "active wrappers". On the one hand, they are containers, or wrappers, that conveniently combine the information about the system in one Mathematica expression. On the other hand, they work like functions when one is applied to another.

Let us create an integrator system in the transfer function form.



We find a state-space realization of the transfer function object by applying the StateSpace head to it. In this case, the resultant state-space system contains very simple matrices , , and . The percentage mark, % refers as usual to the result of the preceding computation.



Converting between control objects.

Along with the structural information about the system, control objects may contain a reference to the domain (continuous-time or discrete-time) the system is in and/or the period at which the (discrete-time) system was sampled.

This finds a discrete-time approximation to the integrator system. Notice that the result is still the TransferFunction object, in which the discrete-time domain is indicated by the option Sampled. For the convention for using internal variable in TransferFunction, refer to Section 3.1 ff.



This converts the discrete-time object back to continuous time.



By default, the system is assumed to be in the continuous-time domain if the Sampled option is not supplied. You can reverse this if you are mainly dealing with the discrete-time systems. For a detailed description of the control objects see Chapter 3.

The Structure of the ApplicationTraditional Notations