Joachim Deutscher

Continuous Curvature Trajectory Design and Feedforward Control for Parking a Car

In this paper, a two-step trajectory planning algorithm from robotics literature is applied to generate suitable trajectories for an autonomous parking maneuver of a car. First, a collision-free curve between a given start and a desired goal configuration within the parking space is planned ignoring the kinematic restrictions on the movement of the car. Second, the collision-free curve is converted into a feasible collision-free trajectory, which can be exactly followed by the car. It is shown how this general planning scheme must be adapted to meet the requirements of the automotive industry

Brief paper: Output regulation for linear distributed-parameter systems using finite-dimensional dual observers

In this article, the solution of the output regulation problem is considered for linear infinite-dimensional systems where the outputs to be controlled cannot be measured. It is shown that this problem can be solved by a finite-dimensional dual observer that is directly implementable so that the separation principle can be applied for the stabilization as in finite dimensions. A parametric design of these dual observers is proposed for Riesz-spectral systems that allows to achieve a low controller order and a desired control performance for the closed-loop system. The presented results are illustrated by determining a finite-dimensional regulator for an Euler-Bernoulli beam with Kelvin-Voigt damping that achieves tracking for steplike reference inputs and that asymptotically rejects sinusoidal disturbances.

A backstepping approach to the output regulation of boundary controlled parabolic PDEs

In this article the output regulation problem for boundary controlled parabolic systems with spatially varying coefficients is solved by applying the backstepping approach. Thereby, the outputs to be controlled are not required to be measurable and can be pointwise, distributed or boundary quantities, whereas the measurement is located at the boundary. By solving the state feedback regulator problem in the backstepping coordinates regulator equations with a simple structure result, so that their analysis and solution is facilitated. The output feedback regulator design is completed by determining a finite-dimensional reference observer and an infinite-dimensional disturbance observer. For the latter a backstepping approach is presented that consists of a triangular decoupling in the backstepping coordinates. This allows a systematic design and the explicit derivation of directly verifiable existence conditions for the disturbance observer. It is shown that for the resulting compensator the separation principle holds implying output regulation for the exponentially stable closed-loop system with a prescribed stability margin. The output regulation results of the article are illustrated by means of a parabolic system with an in-domain pointwise controlled output.

Backstepping Design of Robust Output Feedback Regulators for Boundary Controlled Parabolic PDEs

In this article a backstepping-based solution of the robust output regulation problem for boundary controlled parabolic PDEs with spatially varying parameters is presented. This is achieved by stabilizing the plant extended with a finite-dimensional internal model of the exogenous signals. For the resulting PDE-ODE system with spatially varying parameters a systematic backstepping-based compensator design method is developed. The robustness of the achieved output regulation is verified for non-destabilizing model uncertainties. An uncertain parabolic system illustrates the results of the article.

A linear differential operator approach to flatness based tracking for linear and non-linear systems

This contribution presents a flatness based solution to the tracking for linear systems in differential operator representation. Since the differential operator representation is a flat system representation, tracking controllers can easily be designed using dynamic output feedback. Then, the differential operator approach for flatness based tracking of linear systems is extended to non-linear systems. The design of the resulting linear time varying dynamic output feedback controller is based on a linearization about the trajectory, which directly yields the differential operator representation. Different from the non-linear flatness based controller design the new approach uses linear methods, both in stabilizing the tracking and in computing the output feedback controller. The proposed design procedure assures exact tracking in the steady state when no disturbances are present. A simple example demonstrates the design of a dynamic output feedback controller for the tracking of a non-linear system.

Krylov Subspace Methods for Linear Infinite-Dimensional Systems

The well-known Krylov subspace methods for model order reduction of large-scale lumped parameter systems are generalized such that they can be applied directly to a large class of linear infinite-dimensional systems including distributed parameter systems as well as delay systems. The proposed approach allows to derive finite-dimensional approximations of these infinite-dimensional systems without recourse to a large-scale lumped parameter approximation. The resulting finite-dimensional model has the usual property that prescribed moments of its transfer function coincide with the moments of the infinite-dimensional system. As in the finite-dimensional case the approach allows for a numerical efficient implementation. The results of the article are demonstrated by means of a simple example.

Trajectory generation and feedforward control for parking a car

In this paper a two-step trajectory planning algorithm is applied to generate suitable trajectories for an autonomous parking maneuver of a car. It is shown how important requirements of the automotive industry can be met with the proposed approach. Furthermore, some details on the implementation of the algorithm are given, which are essential to obtain reasonable computation times

Tracking control for nonlinear flat systems by linear dynamic output feedback

Abstract In this contribution linear dynamic output feedback is used to achieve stable tracking for nonlinear flat systems. To this end a time varying differential operator representation resulting from a linearization of the plant about the reference trajectory is used. The control scheme is illustrated for a uniaxial vehicle model.

Finite-time output regulation for linear 2×2 hyperbolic systems using backstepping

This contribution presents the backstepping design of output feedback regulators for boundary controlled linear 2×2 hyperbolic systems, that achieve regulation in finite time. It is assumed that the disturbances can act in-domain, at both boundaries and at the output to be controlled. The latter need not be available for measurement and consists of in-domain pointwise, distributed or boundary outputs. Firstly, a solution of the finite-time state feedback regulator problem is given on the basis of the regulator equations. They are formulated in backstepping coordinates so that a solution is attainable in closed-form. This leads to a very straightforward regulator design for 2×2 hyperbolic systems with a general class of outputs. Then, a finite-dimensional reference observer that converges in finite-time is introduced, which consists of two observers and a delay. This result is extended to the backstepping design of finite-time disturbance observers for 2×2 hyperbolic systems with a collocated measurement. In particular, two backstepping disturbance observers are determined so that after introducing a delay the disturbance model and plant states can be estimated in finite-time. Hence, by combining the state feedback regulator with these observers a finite-time output feedback regulator is obtained. For the state feedback regulator and the disturbance observer existence conditions are derived in terms of the plant transfer behaviour. A simple example with an in-domain pointwise and distributed output illustrates the theoretical results.

Parametric state feedback design of linear distributed-parameter systems

The parametric approach for the design of state feedback controllers has been formulated so far only for linear lumped-parameter systems. It yields an explicit parametric expression for the state feedback gain given the closed-loop eigenvalues and the set of corresponding parameter vectors. This contribution presents a parameterisation of state feedback controllers for linear distributed-parameter systems with scalar state and distributed control. By introducing the closed-loop eigenvalues and the parameter vectors as design parameters, an explicit expression for the state feedback is obtained. In contrast to the pure eigenvalue assignment, the parameterisation allows the assignment not only of the closed-loop eigenvalues but also of the closed-loop eigenfunctions. The usefulness of the proposed parametric approach is demonstrated by decoupling the transfer behaviour of a MIMO diffusion system with respect to its dominant modes.