Port-Hamiltonian representation for pdes with second-order derivatives in the energy density

In this contribution we consider a port-Hamiltonian setting for partial differential equations. A crucial property of this system class is the property to be able to link a power balance relation to the structure of the equations. However, one has to take into account also the effects of energy flows via the boundary. This is straightforward when the Hamiltonian depends on derivative variables of first order, e.g. by using integration by parts. If second-order derivatives appear then integration by parts cannot be used without due care, thus we suggest an approach by using the so-called Cartan-form. We visualize the derivation of a power balance relation by using the Kirchhoff plate as an example. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Group-Theoretic Approach to Parameter Identifiability of PDE Systems

The contribution is devoted to the parameter identifiability problem of (nonlinear) PDE systems. Especially, we discuss the (local) identifiability of parameters along a trajectory. The analysis relies on a coordinate-free formulation for systems, including boundary conditions, and we motivate an approach by (Lie) transformation groups, whose success for PDE systems depends on a consequent extent to the accompanying boundary conditions. The (non-)identifiability of parameters is related to the (non-)existence of group generators, wherewith (local) conditions can be derived. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Some Remarks on Distributed PCHD-Systems

Port controlled Hamiltonian systems with dissipation are a well known tool for the modeling and the controller design for plants, described by nonlinear ordinary differential equations. This contribution presents a possible extension to systems, described by partial differential equations, where the state manifold and the input space of the ODE case are replaced by new geometric structures. This approach takes dissipative effects into account and shows, how distributed ports can be introduced. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Non‐linear Control of a Hydraulic Piston Actuator without Velocity Information

The mathematical models of hydraulic actuators are known to be non‐linear. Therefore, in order to increase the dynamic performance of the closed‐loop system, we have to take into account the significant non‐linearities of the hydraulic plant in the controller design. In this contribution, we deal with so‐called valve‐controlled translational piston actuators. In general, they have the pleasing property to be exact input‐to‐state linearizable in the sense of the differential geometric control synthesis approach. However, in practical applications it often turns out that those controllers, which have to rely on the knowledge of the piston velocity, have problems in the case of noisy measurements. This is why, we propose an approach where the non‐linear controller is designed in such a way that the control law is independent of the piston velocity. It can be even proven that the closed‐loop system is globally asymptotically stable.     

Computer Algebra Algorithms for Control Related Tests of Implicit Dynamic Systems

This contribution is focused on control related tests for implicit dynamic systems, like accessibility, observability or input to output, input to state linearizability. Since the performance of these tests needs tedious symbolic calculations, computer algebra systems are the ideal tool to cope with this problem. Accessibility and observability are exemplarily used to present a new approach based on Lie groups. It is shown that non accessible or non observable systems admit Lie‐groups acting on their solutions such that distinguished parts remain unchanged. This fact allows us to apply this technique, as well as its realization by computer algebra algorithm, to several fundamental problems in control.     

Control and stability analysis of a turbocharged Diesel engine using singular perturbation methods

The control of the air path of a diesel engine with a variable geometry turbocharger and exhaust gas recirculation can be improved significantly by nonlinear methods. The control objective is to supply an amount of fresh air by the compressor and to achieve a desired pressure in the intake manifold in the neighborhood of an operating point of the engine. The mathematical model of the air path is split into a slow and a fast part. For the proposed controller, asymptotic stability of the closed loop system in the sense of Lyapunov is guaranteed by the use of singular perturbation methods. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Tracking Controller for a Certain Class of Nonlinear Systems

Controller design methods based on flatness and passivity are well established. These methods are applied to PCHD systems such that flatness is used to achieve a high tracking performance and passivity ensures disturbance rejection and robustness. Since the error system, written in displacement coordinates, is not a PCHD system in general, we present conditions, which ensures this property. Therefore, one can apply methods from passivity control to stabilize the error dynamics. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Some Remarks concerning Flatness and the Parameterization of the System Variables by a Flat Output

For flat systems, by definition the state- and input variables can be parameterized by the flat output and its time derivatives. In the present contribution, for special classes of flat outputs like e.g. flat outputs that only depend on the state, we derive upper bounds for the number of time derivatives that occur in this parameterization. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)