A partially augmented Lagrangian method for low order H-infinity controller synthesis using rational constraints, Report no. LiTH-ISY-R-3008
نویسندگان
چکیده
When designing robust controllers, H-in nity synthesis is a common tool to use. The controllers that result from these algorithms are typically of very high order, which complicates implementation. However, if a constraint on the maximum order of the controller is set, that is lower than the order of the (augmented) system, the problem becomes nonconvex and it is relatively hard to solve. These problems become very complex, even when the order of the system is low. The approach used in this work is based on formulating the constraint on the maximum order of the controller as a polynomial (or rational) equation. This equality constraint is added to the optimization problem of minimizing an upper bound on the H-in nity norm of the closed loop system subject to linear matrix inequality (LMI) constraints. The problem is then solved by reformulating it as a partially augmented Lagrangian problem where the equality constraint is put into the objective function, but where the LMIs are kept as constraints. The proposed method is evaluated together with two well-known methods from the literature. The results indicate that the proposed method has comparable performance in most cases, especially if the synthesized controller has many parameters, which is the case if the system to be controlled has many input and output signals.
منابع مشابه
A Primal-Dual Method for Low Order H-infinity Controller Synthesis, Report no. LiTH-ISY-R-2933
When designing robust controllers, H-in nity synthesis is a common tool to use. The controllers that result from these algorithms are typically of very high order, which complicates implementation. However, if a constraint on the maximum order of the controller is set, that is lower than the order of the (augmented) system, the problem becomes nonconvex and it is relatively hard to solve. These...
متن کاملOn design of low order H-infinity controllers
When designing controllers with robust performance and stabilization requirements, H-infinity synthesis is a common tool to use. These controllers are often obtained by solving mathematical optimization problems. The controllers that result from these algorithms are typically of very high order, which complicates implementation. Low order controllers are usually desired, since they are consider...
متن کاملA Decomposition Algorithm for KYP-SDPs, Report no. LiTH-ISY-R-2919
In this paper, a structure exploiting algorithm for semidefinite programs derived from the Kalman-Yakubovich-Popov lemma, where some of the constraints appear as complicating constraints is presented. A decomposition algorithm is proposed, where the structure of the problem can be utilized. In a numerical example, where a controller that minimizes the sum of the H2-norm and the H∞-norm is desig...
متن کاملEuclidean Norm Robust Optimal Averaging Level Control, Report no. LiTH-ISY-R-3034
Using insights gained from the robust MPC design of (Rosander et al., 2011) an explicit robustly optimal controller is derived using the Euclidean norm as measure of flow smoothness. The derived controller gives a lower bound on the achievable filtering performance for any controller that mimic the behavior of the robust MPC controller.
متن کاملSuboptimal model reduction using LMIs with convex constraints, Report no. LiTH-ISY-R-2759
An approach to model reduction of LTI systems using Linear Matrix Inequalities (LMIs) in an H∞ framework is presented, where non-convex constraints are replaced with stricter convex constraints thus making it suboptimal. The presented algorithms are compared with the Optimal Hankel reduction algorithm, and are shown to achieve better results (i.e lower H∞-errors) in cases where some of the Hank...
متن کامل