Getting Started

Interconnecting Linear Models

You can perform simple operations on LTI models, such as addition, multiplication, or concatenation. Addition performs a parallel interconnection. For example, typing

• tf(1,[1 0]) + tf([1 1],[1 2])   % 1/s + (s+1)/(s+2)
  

produces this transfer function.

• Transfer function:
  s^2 + 2 s + 2
  -------------
    s^2 + 2 s
  

Multiplication performs a series interconnection. For example, typing

• 2 * tf(1,[1 0])*tf([1 1],[1 2])   % 2*1/s*(s+1)/(s+2)
  

produces this cascaded transfer function.

• Transfer function:
  2 s + 2
  ---------
  s^2 + 2 s
  

If the operands are models of different types, the resulting model type is determined by precedence rules; see Precedence Rules under "Creating and Manipulating Models" online for more information. State-space models have the highest precedence while transfer functions have the lowest precedence. Hence the sum of a transfer function and a state-space model is always a state-space model.

Other available operations include system inversion, transposition, and pertransposition; see Arithmetic Operations online under "Creating and Manipulating Models." The Control System Toolbox also supports matrix-like indexing for extracting subsystems; see Extracting and Modifying Subsystems online in "Operations on LTI Models" (also under "Creating and Manipulating Models") for more information.

You can also use the series and parallel functions as substitutes for multiplication and addition, respectively.

Table 2-2: Equivalent Ways to Interconnect Systems

Operator	Function	Resulting Transfer Function
sys1 + sys2	parallel(sys1,sys2)	Systems in parallel
sys1 * sys2	series(sys2,sys1)	Cascaded systems

Model Characteristics

Feedback Interconnection