Peter J. Seiler

Sanjana Vijayshankar, Victor Purba, Peter J. Seiler et al.

This paper presents an aggregate reduced-order model for a wind farm composed of identical parallel-connected Type-3 wind turbines. The model for individual turbines includes mechanical dynamics (arising from the turbine and doubly fed induction generator) and electrical dynamics (arising from the rotor-side and grid-side converters and associated filters). The proposed aggregate wind-farm model is structure preserving, in the sense that the parameters of the model are derived by scaling corresponding ones from the individual turbines. The aggregate model hence maps to an equivalent--albeit fictitious--wind turbine that captures the dynamics corresponding to the entire wind farm. The reduced-order model has obvious computational advantages, but more importantly, the presented analysis rigorously formalizes parametric scalings for aggregate wind-turbine models that have been applied with limited justification in prior works. Exhaustive numerical simulations validate the accuracy and computational benefits of the proposed reduced-order model.

Tamas Peni, Peter J. Seiler

Determining the induced L2 norm of a linear, parameter-varying (LPV) system is an integral part of many analysis and robust control design procedures. Most prior work has focused on efficiently computing upper bounds for the induced L2 norm. The conditions for upper bounds are typically based on scaled small-gain theorems with dynamic multipliers or dissipation inequalities with parameter dependent Lyapunov functions. This paper presents a complementary algorithm to compute lower bounds for the induced L2 norm. The proposed approach computes a lower bound on the gain by restricting the parameter trajectory to be a periodic signal. This restriction enables the use of recent results for exact calculation of the L2 norm for a periodic linear time varying system. The proposed lower bound algorithm has two benefits. First, the lower bound complements standard upper bound techniques. Specifically, a small gap between the bounds indicates that further computation, e.g. upper bounds with more complex Lyapunov functions, is unnecessary. Second, the lower bound algorithm returns a bad parameter trajectory for the LPV system that can be further analyzed to provide insight into the system performance.

Diganta Bhattacharjee, Shih-Chi Liao, Peter J. Seiler et al.

A trapping region is a compact set that is forward invariant with respect to the dynamics. Existence of a trapping region certifies boundedness of trajectories, and the size of the set provides an estimate of the ultimate bound. Prior work on trapping region analysis has focused on quadratic systems with energy-preserving (lossless) nonlinearities. In this work, we focus on a generalization of the lossless property and present an efficient parameterization that enables optimal trapping region computation for a broader class of quadratic systems than afforded by existing methods. We also formulate conditions for ellipsoidal trapping regions, whereas spherical regions have been the focus of prior works. Three numerical examples are used to demonstrate the proposed framework: (1) a four dimensional system for which the prior state-of-the art is incapable of identifying a trapping region; (2) a low-order unsteady aerodynamics model for which the proposed approach yields trapping regions approximately an order of magnitude smaller than prevailing methods; and (3) a two-state academic example in which the proposed approach correctly identifies a globally asymptotically stable equilibrium point.

Harish K. Venkataraman, Peter J. Seiler

Reinforcement learning (RL) is used to directly design a control policy using data collected from the system. This paper considers the robustness of controllers trained via model-free RL. The discussion focuses on the standard model-based linear quadratic Gaussian (LQG) problem as a special instance of RL. A simple example, originally formulated for LQG problems, is used to demonstrate that RL with partial observations can lead to poor robustness margins. It is proposed to recover robustness by introducing random perturbations at the system input during the RL training. The perturbation magnitude can be used to trade off performance for robustness. Two simple examples are presented to demonstrate the proposed method for enhancing robustness during RL training.