Tuning Natural Frequencies by Output Feedback

Any linear control system, including those with complex structure and dynamic compensation can systematically be formulated as a static output feedback problem where the control system parameters are contained in the output feedback matrix. For this reason, many numerical techniques have been developed specifically to solve the 7/2 optimal ouput feedback problem posed in static output feedback form. Current numerical techniques for computing the output feedback gain matrix recast the problem as a coupled set of Lyapunov equations. Various numerical techniques effectively solve the Lyapunov equations differently. Here, we propose a new numerical method for solving the output feedback gain matrix by direct solution of the cost function using Fade approximation. Using this technique, analytic expressions for cost function derivatives can be written compactly, allowing for efficient solution using second order optimiztion methods. Using a flight control system example, the new method is compared to existing optimal output feedback algorithms.

This paper will research the problem of static output feedback (SOF) stabilization of state-constrained switched linear systems via an improved average dwell time method (ADT). Firstly, an improved ADT method is adopted to establish sufficient conditions for SOF of the state-constrained switched linear systems in the form of matrix inequality. It has been shown that this method is less conservative than traditional ADT, which in view of different decay rates of a Lyapunov function related to an active subsystem on the basis of whether the saturations occur or not. Then, a new iterative algorithm is designed to solve the matrix inequality and a SOF controller can be added. In the iterative linear matrix inequality (ILMI) algorithm, it is important not only to overcome the typical bilinear matrix inequality (BMI) problem of SOF, but also to solve the non-convex problem caused by state constraints. Finally, the availability and the applicability of the proposed method is shown by the application of a boost converter.

This paper considers the problem of static output feedback (SOF) control for discrete-time switched linear systems under arbitrary switching. By the aid of switched quadratic Lyapunov functions combined with Finsler’s lemma, new sufficient conditions for SOF stabilization are obtained which guarantee a γ-performance of the closed-loop switched systems subject to input disturbances. The proposed method can work successfully in situations where the existing ones fail. Three examples are given to illustrate its effectiveness.

This paper deals with the problem of static output feedback (SOF) control design for a class of diffusion partial differential equation (PDE) and ordinary differential equation (ODE) cascades, where the ODE model is used to describe the dynamics of the multi-input and multi-output (MIMO) plant and the diffusion PDE model is employed to represent the dynamics of actuators. The objective of this paper is to develop a simple as well as effective SOF controller via the Lyapunov's direct method such that the resulting closed-loop system is globally exponentially stable. By constructing a quadratic Lyapunov function, the sufficient condition on the globally exponential stability of the closed-loop cascaded system is presented in terms of linear matrix inequality (LMI). Then, an LMI-based design method of the SOF controller is developed on the basis of the obtained stability analysis result. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed design method.

Robust static output feedback infinite horizon RMPC for linear uncertain systems

this paper investigates the problem of robust gain-scheduled static output feedback (SOF) controller for a class of uncertain linear parameter varying systems (LPVSs). An uncertain LPVS is described by an interconnection of a nominal LPVS which is solely dependent on the measurable parameters, and a block structured uncertainty. For designing a H∞ gain-scheduled SOF controller as well as performing the stability analysis, the proposed method uses integral quadratic constraints (IQCs) to derive the linear matrix inequalities (LMIs) without any constraints on nominal system matrices. The performance and effectiveness of the proposed method are demonstrated based on an example.

This paper studies the robust static output feedback (SOF) problem considering pole placement constraints for linear systems with polytopic uncertainty as well as linear parameter varying (LPV) systems. New linear matrix inequality (LMI) approaches are proposed for the SOF controller design while the pole placement, H2, and H∞ constraints are guaranteed. In addition, the gain-scheduled SOF controller will be designed for LPV systems if system parameters are measured. The proposed methods can be applied to general linear systems without imposing any constraints on system matrices. The performance and effectiveness of the proposed methods are shown using two examples.

A Nonsmooth, Nonconvex Optimization Approach to Robust Stabilization by Static Output Feedback and Low-Order Controllers

The problem of fuzzy static output feedback H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> control is investigated for a class of nonlinear systems with time-varying delay. Specifically, the considered system is approximated by a Takagi-Sugeno (T-S) fuzzy model. By using linear matrix inequality (LMI) methods, we design a fuzzy static output feedback H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> controller, which guarantees asymptotic stability and a prescribed H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> index for the resulting closed-loop system. In contrast to the existing results, the gains of controller are obtained by solving a set of LMIs. The proposed method is easy to implement and can be applied to linear systems. A numerical example is provided to illustrate the effectiveness of the developed method.

In this paper we propose a novel distributed algorithm for cooperative output regulation in networks of agents with identical dynamics. Namely, each agent utilizes local and relative output information in order to synchronize its output to the reference trajectory provided by a single node in the network. Stability analysis is carried out by the means of small-gain theorem, and it is shown that control synthesis comes down to a <tex>$\mathcal{H}_{\infty}$</tex> static output feedback problem. Simulation results that verify the effectiveness of the proposed algorithm are provided.

Minimal-norm static feedbacks using dissipative Hamiltonian matrices

Rbust control of linear systems with real parametric uncertainty

Considering the Linear Parameter Varying (LPV) systems of discrete time, in this paper an approach for the synthesis of robust Proporcional+Integral Observers (PIO) is presented. From LPV systems characterized with polytopical uncertainties, the method of design is based on considering a dynamics extended of the typical PIO, in order to transform the design of the matrices of the dynamics of the observer, as a design of the gain of Static Output Feedback (SOF) of a problem of robust control. Under these conditions and from the norms H2=H1 described as Linear Matrix Inequalities (LMI), the criteria to obtain the gain in the SOF problem are established; taking into account performance indices in H2 and H1, under the presence of uncertainties and disturbances.

Iterative redesign techniques are proposed to integrate the design of the structural parameters and the active control parameters for vector second-order lumped-parameter structural systems. The objective is to minimize the required active control effort to satisfy given output variance constraints and robust performance constraints. The problem is formulated as an iterative sequential control design followed by control/structure redesign. Each step of the iterative algorithm is formulated as a linear matrix inequality (LMI) optimization problem that can be solved effectively using available LMI solvers. Convergence of the proposed algorithm to a solution that provides improved control effort and robust stability compared to the single-step structural and control design is guaranteed. Both static state-feedback and dynamic output feedback problems are considered.

A technique is discussed for the selection of the closed loop poles in the output (or state) feedback problem. Each closed loop pole is placed on a circular arc whose radius corresponds to that pole's open loop natural frequency. It is shown that the damping value is the only parameter which can be changed so that the eigenvalues remain on the defined circle. The required gain matrix for pole placement can then be formulated as an unconstrained optimization problem. The Powell method and a heuristic search technique, called a genetic algorithm, are used in the optimization. A 6-DOF continuous time structural model with low damping and two closely spaced modes is used to obtain the required pole placement gain matrix. It is shown that the genetic algorithm gave overall better results than Powell's method in terms of minimizing the norm of the state and output pole placement gain. In addition, an eigenparameter sensitivity calculation was successful only in further reducing the norm in the state feedback case. Furthermore, it is shown that only velocity feedback terms need be considered. This has the advantage of a 50-percent reduction in the design space. (Author)