Conversion Between Model Types

Explicit Conversion Between Model Types

You can explicitly convert a model from one representation to another using the model-creation command for the target model type. For example, convert to state-space representation usingss, and convert to parallel-form PID usingpid. For information about converting to a particular model type, see the reference page for that model type.

In general, you can convert from any model type to any other. However, there are a few limitations. For example, you cannot convert:

frdmodels to analytic model types such asss,tf, orzpk(unless you perform system identification with System Identification Toolbox™ software).
ssmodels with internal delays totforzpk.

You can convert between Numeric LTI models and Generalized LTI models.

Converting a Generalized LTI model to a Numeric LTI model evaluates any Control Design Blocks at their current (nominal) value.
Converting a Numeric LTI model to a Generalized LTI model creates a Generalized LTI model with an emptyBlocksproperty.

Automatic Conversion Between Model Types

一些算法操作只能在一个类型的模型object. For example, the algorithm for zero-order-hold discretization withc2dcan only be performed on state-space models. Similarly, commands such astfdataorpiddataexpect a particular type of model (tforpid, respectively). For convenience, such commandsautomatically convert input models to the appropriate or required model type. For example:

sys = ss(0,1,1,0) [num,den] = tfdata(sys)

tfdataautomatically converts the state-space modelsysto transfer function form to return numerator and denominator data.

Conversions to state-space form are not uniquely defined. For this reason, automatic conversions to state space do not occur when the result depends on the choice of state coordinates. For example, theinitialandkalmancommands require state-space models.

Recommended Working Representation

You can represent numeric system components using any model type. However, Numeric LTI model types are not equally well-suited for numerical computations. In general, it is recommended that you work with state-space (ss) or frequency response data (frd) models, for the following reasons:

The accuracy of computations using high-order transfer functions (tforzpkmodels) is sometimes poor, particularly for MIMO or high-order systems. Conversions to a transfer function representation can incur a loss of accuracy.
When you converttforzpkmodels to state space usingss, the software automatically performs balancing and scaling operations. Balancing and scaling improves the numeric accuracy of computations involving the model. For more information about balancing and scaling state-space models, seeScaling State-Space Models.

In addition, converting back and forth between model types can introduce additional states or orders, or introduce numeric inaccuracies. For example, conversions to state space are not uniquely defined, and are not guaranteed to produce a minimal realization for MIMO models. For a given state-space modelsys,

ss(tf(sys))

can return a model with different state-space matrices, or even a different number of states in the MIMO case.