Modeling and Control in State Space

The behavior of dynamic systems is mathematically modeled by differential equations or partial differential equations. In the case of linear equations, a widespread type of model is the transfer function, for which numerous tools for analysis and synthesis of control laws exist, for example :

• Calculating system response to different inputs
• Study of the poles to conclude on stability
• Frequency synthesis of controllers
• ...

However, this type of model does have its limitations, so a more powerful tool is also often used: state representation.

• There are also numerous tools for analyzing and synthesizing control laws based on state representations
• In particular, these tools make it possible to study the structural properties of dynamic systems in greater depth.

This course focuses on the state representation introduced in the first year. The objectives are to introduce tools for analyzing the structural and control properties of dynamic systems based on linear state representation modeling.

Skills to be acquired :

• Study the stability of a dynamic system using a state representation
• Study the controllability and stabilizability of a dynamic system
• Study the observability and detectability of a dynamic system
• Design a static feedback control law using the quadratic criterion optimization pole placement method (LQ control)
• Design a state observer by adjusting the observation dynamics through pole placement

• Linearizing dynamic systems around equilibrium points
• Analyze and control linear dynamic systems using transfer functions
• Basic matrix calculation: matrix multiplication, matrix inversion, eigenvalue/vector calculation

Available on Moodle :

• Updated PDF version of course slides
• Two uncorrected yearbook subjects