# Model Feedback Control Systems

## Generating Linearized Plant Models

- Matrices A, B, C, and D are written in the Matlab format in four separate files with extensions .a, .b, .c, and .d, respectively.
- The state space form linear system is written in the Simulink format in an MDL file. This is the Simulink MDL format, which is different from the MotionView MDL format.
- States selected for linearization are written to a TAG file.
- Eigenvalues are written to the EIG file.
- Eigenvectors and Eigenvalues are written in tabular format to the TAB file.
- One MRF file is written per eigenvector. It is used for mode shape animation in conjunction with the MotionView model MDL file.

## SISO and MIMO Systems Modeling

**Item****Description**- Control_SISO - Single Input Single Output (SISO) Control Element
- The Control_SISO element defines a transfer function in the Laplace
domain.
(2) $$G(s)=\frac{Y(s)}{U(s)}=\frac{{b}_{0}+{b}_{1}s+\cdots +{b}_{m}{s}^{m}}{{a}_{0}+{a}_{1}s+\cdots +{a}_{n}{s}^{n}},m\le n$$It is used for modeling linear, time invariant systems arising in diverse fields, such as aerodynamics, hydraulics, and electrical systems. It can also be used to fit experimentally measured transfer functions. The curve fitting must be done using other software, such as MATLAB.

- Control_StateEqn - Multiple Input Multiple Output (MIMO) System Element
- This element is used for time domain representation of general multiple
input multiple output (MIMO) systems and controllers. Control_StateEqn
element can be of two types:
- Type LINEAR
- Defines a multi-dimensional, linear time invariant system of
differential equations in the state space form.
(3) $$\begin{array}{l}\dot{x}=Ax+Bu\\ y=Cx+Du\end{array}$$ - Type USERSUB
- Defines a multi-dimensional, nonlinear time varying system
of differential equations in the state space form.
(4) $$\begin{array}{l}\dot{x}=f(x,u,t),x({t}_{0})={x}_{0}\\ y=g\left(x,u,t\right)\end{array}$$