Maple Toolbox for Switched Stabilizing Controller

This paper is celebrating the increment of interest in the application of  computer algebra in control system analysis. A Maple toolbox for stabilizing state feedback controllers for a class of switched system is presented. The attention is focused on finding the existence of common Lyapunov function  (CLFs), as this ensures stability for arbitrary switching sequences between several subsystems. The system considered here are restricted to second order linear  systems. In order to find the common Lyapunov function and the ability of the Maple software, the toolbox is proved to be less computational demanding compared to a lot of methods that has been solved by Linear Matrix Inequalities (LMI)

Superstabilizing Control of Discrete-Time ARX Models under Error in Variables

This paper applies a polynomial optimization based framework towards the superstabilizing control of an Autoregressive with Exogenous Input (ARX) model given noisy data observations. The recorded input and output values are corrupted with L-infinity bounded noise where the bounds are known. This is an instance of Error in Variables (EIV) in which true internal state of the ARX system remains unknown. The consistency set of ARX models compatible with noisy data has a bilinearity between unknown plant parameters and unknown noise terms. The requirement for a dynamic compensator to superstabilize all consistent plants is expressed using polynomial nonnegativity constraints, and solved using sum-of-squares (SOS) methods in a converging hierarchy of semidefinite programs in increasing size. The computational complexity of this method may be reduced by applying a Theorem of Alternatives to eliminate the noise terms. Effectiveness of this method is demonstrated on control of example ARX models.Comment: 12 pages, 0 figures, 5 table

Data-Driven Stabilizing and Robust Control of Discrete-Time Linear Systems with Error in Variables

This work presents a sum-of-squares (SOS) based framework to perform data-driven stabilization and robust control tasks on discrete-time linear systems where the full-state observations are corrupted by L-infinity bounded input, measurement, and process noise (error in variable setting). Certificates of state-feedback superstability or quadratic stability of all plants in a consistency set are provided by solving a feasibility program formed by polynomial nonnegativity constraints. Under mild compactness and data-collection assumptions, SOS tightenings in rising degree will converge to recover the true superstabilizing controller, with slight conservatism introduced for quadratic stabilizability. The performance of this SOS method is improved through the application of a theorem of alternatives while retaining tightness, in which the unknown noise variables are eliminated from the consistency set description. This SOS feasibility method is extended to provide worst-case-optimal robust controllers under H2 control costs. The consistency set description may be broadened to include cases where the data and process are affected by a combination of L-infinity bounded measurement, process, and input noise. Further generalizations include varying noise sets, non-uniform sampling, and switched systems stabilization.Comment: 27 pages, 1 figure, 9 table

Analysis and robust decentralized control of power systems using FACTS devices

Today\u27s changing electric power systems create a growing need for flexible, reliable, fast responding, and accurate answers to questions of analysis, simulation, and design in the fields of electric power generation, transmission, distribution, and consumption. The Flexible Alternating Current Transmission Systems (FACTS) technology program utilizes power electronics components to replace conventional mechanical elements yielding increased flexibility in controlling the electric power system. Benefits include decreased response times and improved overall dynamic system behavior. FACTS devices allow the design of new control strategies, e.g., independent control of active and reactive power flows, which were not realizable a decade ago. However, FACTS components also create uncertainties. Besides the choice of the FACTS devices available, decisions concerning the location, rating, and operating scheme must be made. All of them require reliable numerical tools with appropriate stability, accuracy, and validity of results. This dissertation develops methods to model and control electric power systems including FACTS devices on the transmission level as well as the application of the software tools created to simulate, analyze, and improve the transient stability of electric power systems.;The Power Analysis Toolbox (PAT) developed is embedded in the MATLAB/Simulink environment. The toolbox provides numerous models for the different components of a power system and utilizes an advanced data structure that not only increases data organization and transparency but also simplifies the efforts necessary to incorporate new elements. The functions provided facilitate the computation of steady-state solutions and perform steady-state voltage stability analysis, nonlinear dynamic studies, as well as linearization around a chosen operating point.;Applying intelligent control design in the form of a fuzzy power system damping scheme applied to the Unified Power Flow Controller (UPFC) is proposed. Supplementary damping signals are generated based on local active power flow measurements guaranteeing feasibility. The effectiveness of this controller for longitudinal power systems under dynamic conditions is shown using a Two Area - Four Machine system. When large disturbances are applied, simulation results show that this design can enhance power system operation and damping characteristics. Investigations of meshed power systems such as the New England - New York power system are performed to gain further insight into adverse controller effects

Stability of hybrid model predictive control

In this paper we investigate the stability of hybrid systems in closed-loop with Model Predictive Controllers (MPC) and we derive a priori sufficient conditions for Lyapunov asymptotic stability and exponential stability. A general theory is presented which proves that Lyapunov stability is achieved for both terminal cost and constraint set and terminal equality constraint hybrid MPC, even though the considered Lyapunov function and the system dynamics may be discontinuous. For particular choices of MPC criteria and constrained Piecewise Affine (PWA) systems as the prediction models we develop novel algorithms for computing the terminal cost and the terminal constraint set. For a quadratic MPC cost, the stabilization conditions translate into a linear matrix inequality while, for an 1-norm based MPC cost, they are obtained as 1-norm inequalities. It is shown that by using 1-norms, the terminal constraint set is automatically obtained as a polyhedron or a finite union of polyhedra by taking a sublevel set of the calculated terminal cost function. New algorithms are developed for calculating polyhedral or piecewise polyhedral positively invariant sets for PWA systems. In this manner, the on-line optimization problem leads to a mixed integer quadratic programming problem or to a mixed integer linear programming problem, which can be solved by standard optimization tools. Several examples illustrate the effectiveness of the developed methodology