Ulf Jönsson

Comparison of Hybrid Control Techniques for Buck and Boost DC-DC Converters

Five recent techniques from hybrid and optimal control are evaluated on two power electronics benchmark problems. The benchmarks involve a number of practically interesting operating scenarios for fixed-frequency synchronous dc-dc converters. The specifications are defined such that good performance can only be obtained if the switched and nonlinear nature of the problem is accounted for during the design phase. A nonlinear action is featured in all methods either intrinsically or as external logic. The designs are evaluated and compared on the same experimental platform. Experiments show that the proposed methods display high performances, while respecting circuit constraints, thus protecting the semiconductor devices. Moreover, the complexity of the controllers is compatible with the high-frequency requirements of the considered application.

Brief New results for analysis of systems with repeated nonlinearities

This work presents new results for analysis of systems with repeated monotonic or slope restricted nonlinearities. We first give new integral quadratic constraints (IQCs) that are satisfied by the inputs and outputs of diagonal operators with equal, monotonic or slope restricted, diagonal entries. Then, we present new analysis results for systems with repeated nonlinearities, obtained using the new IQCs. For the type of nonlinearities considered in this work, the new results are less conservative than previously known results. The computation of the new conditions is discussed. The results in this paper apply also to problems with nonrepeated nonlinearities whenever these are representable as the interconnection of multiple repeated nonlinearities and a constant matrix.

Averaging of nonsmooth systems using dither

It was shown by Zames and Shneydor and later by Mossaheb that a high-frequency dither signal of a quite arbitrary shape can be used to narrow the effective nonlinear sector of Lipschitz continuous feedback systems. In this paper, it is shown that also discontinuous nonlinearities of feedback systems can be narrowed using dither, as long as the amplitude distribution function of the dither is absolutely continuous and has bounded derivative. The averaged system is proven to approximate the dithered system with an error of the order of dither period.

Dither for smoothing relay feedback systems

Dither signals provide an effective way to compensate for nonlinearities in control systems. The seminal works by Zames and Shneydor, and more recently, by Mossaheb, present rigorous tools for systematic design of dithered systems. Their results rely, however, on a Lipschitz assumption relating to nonlinearity, and thus, do not cover important applications with discontinuities. This paper presents initial results on how to analyze and design dither in nonsmooth systems. In particular, it is shown that a dithered relay feedback system can be approximated by a smoothed system. Guidelines are given for tuning the amplitude and the period time of the dither signal, in order to stabilize the nonsmooth system.

Fast-Lipschitz optimization with wireless sensor networks applications

Motivated by the need for fast computations demanded by wireless sensor networks, the new F-Lipschitz optimization theory is introduced for a novel class of optimization problems. These problems are defined by simple qualifying properties specified in terms of increasing objective function and contractive constraints. It is shown that feasible F-Lipschitz problems have always a unique optimal solution that satisfies the constraints at equality. The solution is obtained quickly by asynchronous algorithms of certified convergence. F-Lipschitz optimization can be applied to both centralized and distributed optimization. Compared to traditional Lagrangian methods, which often converge linearly, the convergence time of centralized F-Lipschitz problems is at least superlinear. Distributed F-Lipschitz algorithms converge fast, as opposed to traditional Lagrangian decomposition and parallelization methods, which generally converge slowly and at the price of many message passings. In both cases, the computational complexity is much lower than traditional Lagrangian methods. Examples of application of the new optimization method are given for distributed detection and radio power control in wireless sensor networks. The drawback of the F-Lipschitz optimization is that it might be difficult to check the qualifying properties. For more general optimization problems, it is suggested that it is convenient to have conditions ensuring that the solution satisfies the constraints at equality.

A Popov criterion for networked systems

Abstract We consider robustness analysis of heterogeneous and homogeneous networked systems based on integral quadratic constraints (IQCs). First, we show how the analysis decomposes into lower dimensional problems if the interconnection structure is exploited. This generally leads to a significant reduction of the computational complexity. Secondly, by considering a set of IQCs that characterizes the eigenvalues of the interconnection matrices of symmetrically networked systems, we derive a Popov-like criterion for such systems. In particular, when the nodes of the networked system are single-input–single-output linear time-invariant operators, the criterion can be illustrated using a generalized Popov plot. In such cases, the Popov criterion is also a necessary condition in the sense that if the criterion is violated then a destabilizing network with the specified eigenvalue distribution can be constructed.

Specialized fast algorithms for IQC feasibility and optimization problems

The conventional way to treat integral quadratic constraint (IQC) problems is to transform them into semi-definite programs (SDPs). SDPs can then be solved using interior point methods which have been proven efficient. This approach, however, is not always the most efficient since it introduces additional decision variables to the SDP, and the additional decision variables sometimes largely increase the complexity of the problem. In this paper, we demonstrate how to solve IQC problems by other alternatives. More specifically, we consider two cutting plane algorithms. We will show that in certain cases these cutting plane algorithms can solve IQC problems much faster than the conventional approach. Numerical examples, as well as some explanations from the point of view of computational complexity, are provided to support our point.

Stability analysis with Popov multipliers and integral quadratic constraints

It is shown that a general form of Popov multipliers can be used in stability analysis based on integral quadratic constraints (IQC). The Popov multiplier is nonproper and a condition that the nominal plant is strictly proper will be imposed in order to ensure boundedness of the IQC corresponding to the Popov multiplier. A consequence of our main result is that the classical Popov criterion can be combined with a stability criterion for slope restricted nonlinearities developed by Zames and Falb. An example shows that the combination of these two criteria is useful in applications.

Hybrid Control Techniques for Switched-Mode DC-DC Converters Part I: The Step-Down Topology

Several recent techniques from hybrid and optimal control are evaluated on a power electronics benchmark problem. The benchmark involves a number of practically interesting operating scenarios for a fixed-frequency synchronous step-down DC-DC converter. The specifications are defined such that good performance only can be obtained if the switched and nonlinear nature of the problem is respected during the design phase.

A cutting plane algorithm for robustness analysis of periodically time-varying systems

An algorithm for robustness analysis of periodic systems is derived. The system under consideration consists of a linear periodically time-varying plant in feedback interconnection with a structured uncertainty. Conditions for robust stability and robust performance can be formulated in terms of periodic integral quadratic constraints (IQCs). In this way, the robustness analysis becomes a problem of optimizing the parameters of the IQC. A cutting plane algorithm is suggested for solving this infinite-dimensional optimization problem.