Johan Sjöberg

Computing the controllability function for nonlinear descriptor systems

The computation of the controllability function for nonlinear descriptor systems is considered. Three different methods are derived. The first method is based on the necessary conditions for optimality from the Hamilton-Jacobi-Bellman theory for descriptor systems. The second method uses completion of squares to find the solution. The third method gives a series expansion solution, which with a finite number of terms can serve as an approximate solution

Nonlinear Stochastic Differential-Algebraic Equations with Application to Particle Filtering

Differential-algebraic equation (DAE) models naturally arise when modeling physical systems from first principles. To be able to use such models for state estimation procedures such as particle filtering, it is desirable to include a noise model. This paper discusses well-posedness of differential-algebraic equations with noise models, here denoted stochastic differential-algebraic equations. Since the exact conditions are rather involved, approximate implementation methods are also discussed. It is also discussed how a particle filter can be implemented for DAE models, and how the approximate implementation methods can be used for particle filtering. Finally, the particle filtering methods are exemplified by implementation of a particle filter for a DAE model

MODEL REDUCTION OF NONLINEAR DIFFERENTIAL-ALGEBRAIC EQUATIONS

In this work, a computational method to compute balanced realizations for nonlinear differential-algebraic equation systems is derived. The work is a generalization of an earlier work for nonlinear control-affine systems, and is based on analysis of the controllability and observability functions.

Power Series Solution of the Hamilton-Jacobi-Bellman Equation for Descriptor Systems

Optimal control problems for a class of nonlinear descriptor systems are considered. It is shown that they possess a well-defined analytical feedback solution in a neighborhood of the origin, provided stabilizability and some other regularity conditions are satisfied. Explicit formulas for the series expansions of the cost function and control law are given.

Identifiability of physical parameters in systems with limited sensors

In this paper, a method for estimating physical parameters using limited sensors is investigated. As a case study, measurements from an IMU are used for estimating the change in mass and the change in center of mass of a ship. The roll motion is studied and an instrumental variable method estimating the parameters of a transfer function from the tangential acceleration to the angular velocity is presented. It is shown that only a subset of the unknown parameters are identifiable simultaneously. A multi-stage identification approach is presented as a remedy for this. A limited simulation study is also presented to show the properties of the estimator. This shows that the method is indeed promising but that more work is needed to reduce the variance of the estimator.

Power Series Solution of the Hamilton-Jacobi-Bellman Equation for Time-varying Differential-Algebraic Equations

Optimal control problems for a class of nonlinear time-varying differential-algebraic equations are considered. It is shown that they possess a well-defined feedback solution in a neighborhood of the origin. Explicit formulas for the series expansions of the cost function and control law are given

Hamilton-Jacobi equations for nonlinear descriptor systems

Optimal control problems for nonlinear descriptor systems are considered. An approach where the descriptor system is conceptually reduced to a state space form is compared to an approach where the Hamilton-Jacobi equation is directly formulated for the descriptor system. The two approaches are shown to give essentially the same systems of equations to be solved. A certain unknown function is present only in the second approach but is shown to be computable from the quantities common to both approaches

Optimization-based radial active magnetic bearing controller design and verification for flexible rotors

Engineering costs, especially cost for controller design, are substantial and obstruct active magnetic bearings for broader industrial applications. An optimization-based active magnetic bearing controller design method is developed to solve this problem. Optimization criteria are selected to describe active magnetic bearing practical performance. Controller components are chosen considering that the parameters can be manually interpreted and modified on-site for commissioning. A multi-objective optimization toolbox can be used to tune the controller parameters automatically by minimizing the optimization criteria. The method has been verified within a controller design process for an active magnetic bearing levitated machine. With this method, engineering effort for controller design can be reduced significantly.

System identification of Active Magnetic Bearing for commissioning

System identification is a prerequisite for the operation of Active Magnetic Bearings (AMB). An identified model is required for synthesizing high performance model based controllers. However, from a commissioning point of view, certain parameters such as AMB stiffness constants and in the case of a flexible rotor, the flexible mode natural frequency (and damping ratio) of the rotor have to be explicitly identified. In this work, system identification of AMB is approached within the context of commissioning. A procedure for identification is developed and applied to experimental data from a prototype AMB system. A linear state-space model, along with the required parameters, is identified.

Rational Approximation of Nonlinear Optimal Control Problems

In this paper rational approximation of solutions to nonlinear optimal control problems is considered. A computational procedure is presented that makes it possible to compute a rational function that approximates the true optimal cost function. It is shown that the rational function has the same series expansion around the origin as the true solution. Finally, two examples are given that compares the new method with the power series approximation, which is a rather well-known method to find approximative solutions.