Model system by zero-pole-gain transfer function

Continuous

The Zero-Pole block models a system that you define with the zeros, poles, and gain of a Laplace-domain transfer function. This block can model single-input single output (SISO) and single-input multiple-output (SIMO) systems.

The Zero-Pole block assumes the following conditions:

The transfer function has the form

$$H(s)=K\frac{Z(s)}{P(s)}=K\frac{(s-Z(1))(s-Z(2))\dots (s-Z(m))}{(s-P(1))(s-P(2))\dots (s-P(n))},$$

where

*Z*represents the zeros,*P*the poles, and*K*the gain of the transfer function.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.

For a multiple-output system, all transfer functions must have the same poles. The zeros can differ in value, but the number of zeros for each transfer function must be the same.

You cannot use a Zero-Pole block to model a multiple-output system when the transfer functions have a differing number of zeros or a single zero each. Use multiple Zero-Pole blocks to model such systems.

For a single-output system, the input and the output of the block are scalar time-domain signals. To model this system:

Enter a vector for the zeros of the transfer function in the

**Zeros**field.Enter a vector for the poles of the transfer function in the

**Poles**field.Enter a 1-by-1 vector for the gain of the transfer function in the

**Gain**field.

For a multiple-output system, the block input is a scalar and the output is a vector, where each element is an output of the system. To model this system:

Enter a matrix of zeros in the

**Zeros**field.Each

*column*of this matrix contains the zeros of a transfer function that relates the system input to one of the outputs.Enter a vector for the poles common to all transfer functions of the system in the

**Poles**field.Enter a vector of gains in the

**Gain**field.Each element is the gain of the corresponding transfer function in

**Zeros**.

Each element of the output vector corresponds to a column in **Zeros**.

The Zero-Pole block displays the transfer function depending on how you specify the zero, pole, and gain parameters.

If you specify each parameter as an expression or a vector, the block shows the transfer function with the specified zeros, poles, and gain. If you specify a variable in parentheses, the block evaluates the variable.

For example, if you specify

**Zeros**as`[3,2,1]`

,**Poles**as`(poles)`

, where`poles`

is`[7,5,3,1]`

, and**Gain**as`gain`

, the block looks like this:If you specify each parameter as a variable, the block 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 block looks like this:

The Zero-Pole block accepts real signals of type `double`

.
For more information, see Data Types Supported by Simulink in
the Simulink^{®} documentation.

Define the matrix of zeros.

**Default:** `[1]`

For a single-output system, enter a vector for the zeros of the transfer function.

For a multiple-output system, enter a matrix. Each

*column*of this matrix contains the zeros of a transfer function that relates the system input to one of the outputs.

Parameter: `Zeros` |

Type: vector |

Value: `'[1]'` |

Default: `'[1]'` |

Define the vector of poles.

**Default:** `[0 -1]`

For a single-output system, enter a vector for the poles of the transfer function.

For a multiple-output system, enter a vector for the poles common to all transfer functions of the system.

Parameter: `Poles` |

Type: vector |

Value: `'[0 -1]'` |

Default: `'[0 -1]'` |

Define the vector of gains.

**Default:** `[1]`

For a single-output system, enter a 1-by-1 vector for the gain of the transfer function.

For a multiple-output system, enter a vector of gains. Each element is the gain of the corresponding transfer function in

**Zeros**.

Parameter: `Gain` |

Type: vector |

Value: `'[1]'` |

Default: `'[1]'` |

Specify the absolute tolerance for computing block states.

**Default:** `auto`

You can enter

`auto`

, –1, a positive real scalar or vector.If you enter

`auto`

or –1, then Simulink uses the absolute tolerance value in the Configuration Parameters dialog box (see Solver Pane) to compute block states.If you enter a real scalar, then that value overrides the absolute tolerance in the Configuration Parameters dialog box for computing all block states.

If you enter a real vector, then the dimension of that vector must match the dimension of the continuous states in the block. These values override the absolute tolerance in the Configuration Parameters dialog box.

Parameter: ` AbsoluteTolerance` |

Type: character vector,
scalar, or vector |

Value: `'auto'` | `'-1'` |
any positive real scalar or vector |

Default: ` 'auto'` |

Assign a unique name to each state.

**Default:** `' '`

If this field is blank, no name assignment occurs.

To assign a name to a single state, enter the name between quotes, for example,

`'velocity'`

.To assign names to multiple states, enter a comma-delimited list surrounded by braces, for example,

`{'a', 'b', 'c'}`

. Each name must be unique.The state names apply only to the selected block.

The number of states must divide evenly among the number of state names.

You can specify fewer names than states, but you cannot specify more names than states.

For example, you can specify two names in a system with four states. The first name applies to the first two states and the second name to the last two states.

To assign state names with a variable in the MATLAB

^{®}workspace, enter the variable without quotes. A variable can be a character vector, cell array, or structure.

Parameter: `ContinuousStateAttributes` |

Type: character vector |

Value: `' '` |
user-defined |

Default: `' '` |

Data Types | Double |

Sample Time | Continuous |

Direct Feedthrough | Only if the lengths of the |

Multidimensional Signals | No |

Variable-Size Signals | No |

Zero-Crossing Detection | No |

Code Generation | Yes |

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