Linear and nonlinear optimal controller design for a 3 DOF helicopter

An Extension Algorithm of Regional Eigenvalue Assignment Controller Design for Nonlinear Systems

“…The difference of this approach from the linear approach is that in the linear case, the locations of the eigenvalues in the disc are fixed, whereas in the nonlinear case, the locations of the pointwise eigenvalues can move inside the disc at each time instant because of the changing dynamics of the system. In this section, we will first describe the methodology of the state-dependent regional eigenvalue assignment (SDREA) introduced in our previous studies [31,32]. Then, we will define two different update algorithms to update the disc parameters at each time instant, and we will complete the section with a simulation study to verify the effectiveness of the proposed algorithms.…”

“…The state-dependent Riccati equation (SDRE) can be also used to design the rEA controller for nonlinear systems. In [31], a state-dependent regional pole assignment controller design was proposed for a class of nonlinear systems. The SDRE was modified using the given disc parameters to ensure that eigenvalues located into the desired disc using the modified optimal control law.…”

“…In our previous studies [31,32], all pointwise eigenvalues of the "frozen" closed-loop system of the nonlinear systems were located in the desired fixed disc region at each time step by using the state-dependent rEA. In this study, we propose two new algorithms that are used to update the disc parameters depending on the locations of the pointwise eigenvalues at the current time for improving the stability and response characteristics according to the design criteria.…”