A New Approach to Stabilization in SISO Plants

In this paper, we explore the role of compensators in stabilizing nonlinear systems with feedback control. The authors present a new approach to designing compensators that ensures stability and offers several advantages over existing methods. They demonstrate their technique through examples and illustrate how it can be used to solve real-world problems.
The authors begin by explaining that compensators are essential for ensuring stability in nonlinear systems with feedback control. They introduce the concept of a suitable "Up(s)" matrix, which represents the inverse of the plant and is crucial for stability. However, finding an Up(s) matrix can be challenging, especially for plants with high relative degree. This is where compensators come into play.
The authors propose using adjustment of fractional powers (AFP) to design compensators for plants with relative degree less than 3. AFP involves adjusting the power spectrum of the plant to make it stable and then adding a compensator that ensures stability. The authors show that this approach guarantees the existence of a suitable Up(s) matrix, making it easier to stabilize the system.
The authors also highlight the importance of Cs(s), which is the compensator used in parallel with the plant. They explain that Cs(s) plays a critical role in ensuring stability and can be thought of as a "filter" that moves the zeros of Cp(s) + P (s) to the left half plane.
The authors provide several examples to illustrate their technique, including the use of AFP for plants with relative degree less than 3. They show how this approach can be used to solve real-world problems and demonstrate its effectiveness through simulations.
Overall, the authors’ proposed architecture is designed to simplify the process of stabilizing nonlinear systems with feedback control. By using compensators in combination with AFP, they have made it possible to guarantee stability and overcome some of the challenges associated with traditional methods. Their approach offers several advantages, including increased flexibility and adaptability, and can be used to solve a wide range of problems in engineering and other fields.