Thomas Meurer

Tracking control for boundary controlled parabolic PDEs with varying parameters: Combining backstepping and differential flatness

The combination of backstepping-based state-feedback control and flatness-based trajectory planning and feedforward control is considered for the design of an exponentially stabilizing tracking controller for a linear diffusion-convection-reaction system with spatially and temporally varying parameters and nonlinear boundary input. For this, in a first step the backstepping transformation is utilized to determine a state-feedback controller, which transforms the original distributed-parameter system into an appropriately chosen exponentially stable distributed-parameter target system of a significantly simpler structure. In a second step, the flatness property of the target system is exploited in order to determine the feedforward controller, which allows us to realize the tracking of suitably prescribed trajectories for the system output. This results in a systematic procedure for the design of an exponentially stabilizing tracking controller for the considered general linear diffusion-convection-reaction system with varying parameters, whose applicability and tracking performance is evaluated in simulation studies.

Flatness-based tracking control of a piezoactuated Euler–Bernoulli beam with non-collocated output feedback: theory and experiments†

This paper considers the combination of flatness-based motion planning and feedforward control with output feedback to achieve robust tracking of prescribed trajectories for the tip displacement of a multi-layered piezoelectric cantilever beam. Thereby, the flatness property of the distributed-parameter beam model is exploited to derive the infinite-dimensional tracking error system, which serves as the basis for the design of the output error feedback control. The stability of the resulting closed-loop system involving the infinite-dimensional beam model is proven in an input/output sense by utilizing a Nyquist-type stability criterion. Experimental results illustrate the high tracking performance in view of exogenous disturbances. The presented approach provides a systematic extension of the two-degrees-of-freedom control concept to distributed-parameter systems. †This paper is dedicated to Prof. Michel Fliess on the occasion of his 60th birthday.

Brief paper: Finite-time multi-agent deployment: A nonlinear PDE motion planning approach

The systematic flatness-based motion planning using formal power series and suitable summability methods is considered for the finite-time deployment of multi-agent systems into planar formation profiles along predefined spatial-temporal paths. Thereby, a distributed-parameter setting is proposed, where the collective leader-follower agent dynamics is modeled by two boundary controlled nonlinear time-varying PDEs governing the motion of an agent continuum in the plane. The discretization of the PDE model directly induces a decentralized communication and interconnection structure for the multi-agent system, which is required to achieve the desired spatial-temporal paths and deployment formations.

On the Extended Luenberger-Type Observer for Semilinear Distributed-Parameter Systems

The design of an extended Luenberger observer is considered to solve the state observation problem for semilinear distributed-parameter systems. For this, a backstepping-based technique is proposed for the design of the output injection weights by making use of the (extended) linearization of the semilinear observer error system with respect to the observer state. Stability of both the linearized and the semilinear observer error dynamics is analyzed theoretically. Moreover, an efficient sample-and-hold implementation is considered to improve the computational efficiency of the observer design. Simulation examples are provided for a bistable semilinear partial differential equation and the simplified model of a bioreactor with Monod kinetics.

Wave propagation in nonlinear and hysteretic media––a numerical study

Abstract This paper considers the problem of one dimensional wave propagation in nonlinear, hysteretic media. The constitutive law in the media is prescribed by an integral relationship based on the Duhem model of hysteresis. It is found that the well known nonlinear elastic stress–strain relationship is a special case of this integral relationship. It is also shown that the stress–strain relationship from the McCall and Guyer model of hyesteretic materials can also be derived from this integral stress–strain relationship. The first part of this paper focuses on a material with a quadratic stress–strain relationship, where the initial value problem is formulated into a system of conservation laws. Analytical solutions to the Riemann problem are obtained by solving the corresponding eigenvalue problem and serve as reference for the verification and illustration of the accuracy obtained using the applied numerical scheme proposed by Kurganov and Tadmor. The second part of this research is devoted to wave propagation in hysteretic media. Several types of initial excitations are presented in order to determine special characteristics of the wave propagation due to material nonlinearity and hysteresis. The results of this paper demonstrate the accuracy and the robustness of this numerical scheme to analyze wave propagation in nonlinear materials.

Flatness-based trajectory planning for diffusion-reaction systems in a parallelepipedon-A spectral approach

Spectral analysis is considered for the flatness-based solution of the trajectory planning problem for a boundary controlled diffusion-reaction system defined on a 1@?r-dimensional parallelepipedon. By exploiting the Riesz spectral properties of the system operator, it is shown that a suitable reformulation of the resolvent operator allows a systematic introduction of a basic output, which yields a parametrization of both the system state and the boundary input in terms of differential operators of infinite order. Their convergence is verified for both infinite-dimensional and finite-dimensional actuator configurations by restricting the basic output to certain Gevrey classes involving non-analytic functions. With this, a systematic approach is introduced for basic output trajectory assignment and feedforward tracking control towards the realization of finite-time transitions between stationary profiles.

Trajectory Planning for Boundary Controlled Parabolic PDEs With Varying Parameters on Higher-Dimensional Spatial Domains

The flatness-based design of a feedforward tracking control is considered for the solution of the trajectory planning problem for a boundary controlled diffusion-convection-reaction system with spatially and temporally varying parameters defined on a 1 les m-dimensional parallelepipedon with the nonlinear input being restricted to a (m-1) -dimensional hyperplane. For this, an implicit state and input parametrization in terms of a basic output is determined via a Volterra-type integral equation with operator kernel. By recursively computing successive series coefficients, a series solution of the integral equation is obtained, whose absolute and uniform convergence is verified by restricting the system parameters and the basic output to a certain but broad Gevrey class. Hence, prescribing an admissible desired trajectory for the basic output directly yields the feedforward control by evaluating the input parametrization. This results in a systematic procedure for trajectory planning and feedforward control design for boundary controlled parabolic distributed-parameter systems defined on higher-dimensional domains.

Modelling and experimental model validation for a pusher-type reheating furnace

The slab reheating process turns out to play a key role in dealing with the steadily increasing demands on the quality of hot rolled steel plates. Improvements both in the throughput of the furnace as well as the accurate realization of reheating paths for the slabs require to incorporate modern model-based control design techniques into the furnace automation. For this, suitable mathematical models with manageable dimension and complexity have to be determined for the furnace and slab dynamics. In this contribution, first principles are applied for the derivation of a physics-based model of the reheating process in a so-called pusher-type reheating furnace. Thereby, a discontinuous mode of furnace operation is considered, which is characterized by a varying number of slabs with variable geometry being discontinuously moved through the furnace. This, in particular, results in a hybrid structure of the mathematical model. The accuracy of the mathematical model is validated by a comparison with experimental data obtained from a measurement campaign with a test slab performed at an industrial pusher-type reheating furnace.

Two-degree-of-freedom tracking control design for boundary controlled distributed parameter systems using formal power series

A two-degree-of-freedom design approach is proposed for boundary controlled distributed parameter systems using formal power series, advanced summation methods, and output feedback. The approach is illustrated for the tracking control of a tubular bioreactor with nonlinear reaction rate.

Towards ontology-based automated disassembly systems

The disassembly of products is a key process in the treatment of Waste Electrical and Electronic Equipment. When performed efficiently, it enables the maximization of resources re-usage and a minimization of pollution. However, currently employed automation solutions are mainly custom-oriented and not quite suited to cope with the dynamic nature of the disassembly environment resulting from the wide variety of products to be disassembled as well as their general shape at their disposal (e.g., scratches and fractions). To overcome these limitations we present an ontology-based automated disassembly system that integrates distributed multiagent based machine control as well as vision-based real-time path planning and robot automation. On the one side, the usage of ontologies in combination with intelligent agents provides the system with agility and the ability to autonomously perform soft-and hardware modifications in order to perform a particular activity (e.g., by selecting a specific tool). On the other side, the flexible semantic coupling of the ontology with the vision system supports the “understanding” of the captured image and enables an automated and robust realization of the individual disassembly operations as well as their coordination.