Karl Heinz Kienitz

Fractional Order Modeling of Large Three-Dimensional RC Networks

An incidence matrix analysis is used to model a three-dimensional network consisting of resistive and capacitive elements distributed across several interconnected layers. A systematic methodology for deriving a descriptor representation of the network with random allocation of the resistors and capacitors is proposed. Using a transformation of the descriptor representation into standard state-space form, amplitude and phase admittance responses of three-dimensional random RC networks are obtained. Such networks display an emergent behavior with a characteristic Jonscher-like response over a wide range of frequencies. A model approximation study of these networks is performed to infer the admittance response using integral and fractional order models. It was found that a fractional order model with only seven parameters can accurately describe the responses of networks composed of more than 70 nodes and 200 branches with 100 resistors and 100 capacitors. The proposed analysis can be used to model charge migration in amorphous materials, which may be associated to specific macroscopic or microscopic scale fractal geometrical structures in composites displaying a viscoelastic electromechanical response, as well as to model the collective responses of processes governed by random events described using statistical mechanics.

Controller design using fuzzy logic: a case study

Abstract Controller design is considered for system specifications which are not handled naturally by analytical methods. Using fuzzy sets and related theory, system specifications are translated into preference functions which are readily combined with search methods to determine adequate controller parameters. This contribution integrates the discussion of the theory and its step-by-step application to aircraft control during the flare-out phase of landing.

Multivariate analysis of the dielectric response of materials modeled using networks of resistors and capacitors

We discuss the modeling of dielectric responses of electromagnetically excited networks which are composed of a mixture of capacitors and resistors. Such networks can be employed as lumped-parameter circuits to model the response of composite materials containing conductive and insulating grains. The dynamics of the excited network systems are studied using a state space model derived from a randomized incidence matrix. Time and frequency domain responses from synthetic data sets generated from state space models are analyzed for the purpose of estimating the fraction of capacitors in the network. Good results were obtained by using either the time-domain response to a pulse excitation or impedance data at selected frequencies. A chemometric framework based on a Successive Projections Algorithm (SPA) enables the construction of multiple linear regression (MLR) models which can efficiently determine the ratio of conductive to insulating components in composite material samples. The proposed method avoids restrictions commonly associated with Archies law, the application of percolation theory or Kohlrausch-Williams-Watts models and is applicable to experimental results generated by either time domain transient spectrometers or continuous-wave instruments. Furthermore, it is quite generic and applicable to tomography, acoustics as well as other spectroscopies such as nuclear magnetic resonance, electron paramagnetic resonance and, therefore, should be of general interest across the dielectrics community.

Attitude stabilization with actuators subject to switching-time constraints using explicit MPC

This paper is concerned with the design of an explicit model predictive controller (eMPC) for attitude stabilization using on-off thrusters subject to switching-time constraints. 12In the proposed approach, the control actions are specified by a sequence of integer values in the set {−1, 0, +1}, i.e the thrusters can be fully opened in one of two possible directions (−1 or +1) or remain closed (0). Switching-time constraints are taken into account by imposing restrictions on the minimum number of consecutive equal elements in the control sequence. The explicit solution to the constrained MPC problem is computed by solving a multi-parametric mixed integer linear program (mpMILP), where the parameters are the components of the state vector. The solution to the mpMILP is a piecewise affine (PWA) function, which can be evaluated at each sampling time to obtain the optimal control law. Since the on-line computation effort is restricted to a table-lookup, the controller can be implemented using a simple computational hardware.

A describing function approach to limit cycle controller design

The design of robust limit cycle controllers introduced here can be used for autonomous systems with separable single-input-single-output nonlinearities. Considering a system with unavoidable limit cycle and an uncertain linear subsystem, the objective is to design a controller such that the variation in limit cycle amplitude and frequency due the uncertainty is as small as possible in the controlled system for the worst uncertainty considered. The method consists of quasi-linearization of the nonlinear element via a describing function (DF) approach and then shaping the loop to reach desired limit cycle characteristics. As the DF method is used, loop shaping takes place in the Nyquist plot

Development of a complete UAV system using COTS equipment

This paper describes the development of a complete Unmanned Aerial Vehicle (UAV) system (navigation software + ground station + specific aircraft) using Commercial Off-the-Shelf (COTS) equipment. This development includes conceptual design and tests, as well as hardware and software development. The UAV can be remotely piloted from a ground station equipped with a laptop computer, real-time video, telemetry, interface devices, flight controls (joystick), virtual reality glasses (VRG) and dedicated software. The software installed on the ground station laptop, monitors flight information, captures/updates video and telemetry data in real time, and processes the Head-Up-Display imagery. Using a Synthetic Vision Navigation System (software under development) a 3D path route is created as a second navigation reference. This reference can be used to aid the pilot in navigation. All interfaces between pilot and ground station equipment are user friendly and are shown on the laptop screen and/or on the VRG. The VRG allow for complete pilot immersion into the navigation system.

Robust limit cycle control in an attitude control system with switching-constrained actuators

In this paper the robust behavior in some piecewise affine systems with minimally spaced transition times is studied. Such systems are found e.g. in satellites and satellite launchers. On-off thrusters are frequently used as actuators for attitude control and are typically subject to switching constraints. In these systems, persistent motions of different nature may occur, such as limit cycles, quasi-periodic-like and chaotic motions. Thus, in the presence of model uncertainties, the emergence of bifurcations can seriously affect performance. In this contribution, we use Tsypkin¿s method in order to investigate the robustness of the condition for the existence of limit cycles. Robustness frontiers in the space of control parameters are identified. These frontiers are verified via simulation and compared to those given by the describing function method, revealing the difficulties of this latter method to address the robustness analysis in this system. Moreover, we present a design method for robust controllers based on the Hamel locus. An evaluation of performance requirements such as fuel consumption, limit cycle amplitude and transient response is carried out in the identified regions of robust behavior.

An algebraic approach to the design of robust limit cycle controllers

The design of robust limit cycle controllers introduced here can be used for autonomous systems with separable single-input-single-output nonlinearities and unavoidable limit cycles. The objective is to design a controller to secure specified oscillation amplitude and frequency. The method consists of quasi-linearization of the nonlinear element via a describing function (DF) approach and then shaping the loop to reach desired limit cycle characteristics. As the DF method is used, loop shaping takes place in the Nyquist plot.

Design of gain-scheduled controllers based on parametric H ∞ loop shaping

Synthesis conditions for the design of gain-scheduled controllers based on a parametric H ∞ loop shaping approach are presented for linear parameter-varying (LPV) systems. The main procedures to find such robust controllers are given. The design problem has been formulated via static H ∞ output feedback control, considering the uncertainty as normalised coprime factors of the shaped plant. The shaped plant must be chosen appropriately to satisfy the robustness requirements of the closed-loop system. The design procedure features free parameters to increase the flexibility of the design ensuring robust stabilisation of the LPV system. For the existence of a gain-scheduled parametric H ∞ loop shaping controller, a set of sufficient conditions has been derived in an LMI framework. Numerical examples illustrate the use of the proposed control design with applications to two physical systems: a two-mass-spring system and a hover system.

Predictive control with trajectory planning in the presence of obstacles

In this work, a trajectory planning technique for an autonomous vehicle is proposed. A Predictive Control formulation is used both to plan a trajectory and control the vehicle in the presence of obstacles and dynamic constraints. However, some particularities of this sort of missions may make the time required for solution of the associated optimization problem prohibitive for a given sampling period. In this context, the possibility of using smaller prediction and control horizons is important to obtain a suitable control sequence within each sampling time. For this purpose, a trajectory planner which distributes waypoints along a previously established path is employed in the present paper. Each waypoint is determined so that it can be reached in a horizon which is smaller than the one necessary to reach the target set from the initial position, thus reducing the computational burden during the control phase. Moreover, during the planning phase the waypoints are chosen under the restriction that the target set should be reached within finite time so that the mission can be accomplished.