Simulink Reference

Zero-Pole

Implement a transfer function specified in terms of poles and zeros

Library

Continuous

Description

The Zero-Pole block implements a system with the specified zeros, poles, and gain in terms of the Laplace operator s.

A transfer function can be expressed in factored or zero-pole-gain form, which, for a single-input single-output system in MATLAB, is

where Z represents the zeros vector, P the poles vector, and K the gain. Z can be a vector or matrix, P must be a vector, K can be a scalar or vector whose length equals the number of rows in Z. The number of poles must be greater than or equal to the number of zeros. If the poles and zeros are complex, they must be complex conjugate pairs.

Block input and output widths are equal to the number of rows in the zeros matrix.

The Zero-Pole Block Icon

The Zero-Pole block displays the transfer function in its icon depending on how the parameters are specified:

• If each is specified as an expression or a vector, the icon shows the transfer function with the specified zeros, poles, and gain. If you specify a variable in parentheses, the variable is evaluated.

• For example, if you specify Zeros as [3,2,1], Poles as (poles), where poles is defined in the workspace as [7,5,3,1], and Gain as gain, the icon looks like this:

• If each is specified as a variable, the icon shows the variable name followed by (s) if appropriate. For example, if you specify Zeros as zeros, Poles as poles, and Gain as gain, the icon looks like this.

Specifying the Absolute Tolerance for the Block's States

By default, Simulink uses the absolute tolerance value specified in the Simulation Parameters dialog box (see Error Tolerances) to solve the states of the Zero-Pole block. If this value does not provide sufficient error control, specify a more appropriate value in the Absolute tolerance field of the Zero-Pole block's dialog box. The value that you specify is used to solve all the block's states.

Data Type Support

A Zero-Pole block accepts real signals of type double.

Parameters and Dialog Box

Zeros

The matrix of zeros. The default is [1].

Poles

The vector of poles. The default is [0 -1].

Gain

The vector of gains. The default is [1].

Absolute tolerance

Absolute tolerance used to solve the block's states. You can enter auto or a numeric value. If you enter auto, Simulink determines the absolute tolerance (see Error Tolerances). If you enter a numeric value, Simulink uses the specified value to solve the block's states. Note that a numeric value overrides the setting for the absolute tolerance in the Simulation Parameters dialog box.

Characteristics

Direct Feedthrough	Only if the lengths of the Poles and Zeros parameters are equal
Sample Time	Continuous
Scalar Expansion	No
States	Length of Poles vector
Dimensionalized	No
Zero Crossing	No

Zero-Order Hold

Linearization and Trimming Commands