Areas and Topics

 

The research activities of the Chair of Automatic Control focus on state-of-the art techniques for modeling, analysis and control of complex dynamical systems and the development of novel solution approaches for industrial control tasks. The main research areas comprise control and observer design for nonlinear as well as distributed-parameter systems governed by partial differential equations. The developed techniques are applied and evaluated for smart and intelligent structures  such as adaptive and morphing flexible structures with piezoelectric actuation, reheating, thermal and forming processes, flow control, cooperative interacting systems, as well as production processes. Selected research activities in the directions 

are further detailed in the following.


 

Distributed-parameter systems and control theory

Distributed-parameter systems are characterized by state variables depending on both time and space such that the modeling leads to a mathematical description in terms of partial differential equations (PDEs). Well known examples include elastomechanic or thermomechanic structures in mechatronics or aeronautics, fixed-bed and tubular reactors in chemical and process engineering, reheating and cooling processes in steel industry and forming, heat exchangers, fluid flow and fluid-structure interactions but also collective dynamics of robots, crowds and flocks. The research activities in particular addresses systematic techniques for

  • Motion planning
  • Feedback stabilization
  • Observer design
  • Semi-analytic design techniques

for linear and nonlinear distributed-parameter systems with single and higher-dimensional spatial domains. Herein, so-called late lumping approaches are considered which directly exploit the underlying mathematical PDE structure to develop novel flatness-, backstepping- and passivity-based design techniques. In addition, it is shown that the combination of the determined approaches yields sophisticated tracking control concepts to realize prescribed spatial-temporal paths. Stability (exponential or asymptotic) of the feedback and tracking control schemes is analyzed using operator and semigroup theory. 

dps_blockdiag

Figure: Model-based control and system design concept for distributed-parameter systems.

In order to address the complexity arising in many applications, e.g., due to complex shaped geometries or the number of depended state variables, semi-analytical design techniques are deduced by combining the developed analytical approaches with numerical discretization and approximation schemes such as finite difference, finite volume or finite element methods. Recent application areas concern smart adaptive structures, multi-agent systems, chemical and bio-chemical processes, and material processing.

Funding:
Research is financially supported by the Deutsche Forschungsgemeinschaft (DFG) in the project ME-3231/3-1 Model predictive PDE control for energy efficient building operation (starting 2015) in terms of a joint research project with Lars Grüne (University Bayreuth) and Stefan Volkwein (University Konstanz).

 

Smart adaptive structures

Smart structures with integrated actuator and sensor elements are nowadays in particular used for active vibration suppression. However, apart from these stabilization tasks novel applications, e.g., in flow control and adaptive optics, require the realization of highly dynamical desired motion trajectories for lightweight flexible structures. Due to the inherent spatio-temporal system dynamics sophisticated design approaches are developed combining

  • Flatness-based motion planning
  • Passivity-based (non-collocated) feedback stabilization and observer design
  • Semi-analytic designs using finite element formulations

For the mathematical modeling of smart material structures the spatial extension of the structure and the distribution of actors and sensors has to be considered and leads to a description in terms of partial differential equations (PDE). This PDE formulation can be exploited for motion planning, stabilization and observer design. 

 
For piezo-actuated beam and plate structures systematic flatness-based motion planning techniques have been developed to realize the desired transient behavior by an open-loop controller. Taking into account passivity-based feedback control within the so-called two-degree-of-freedom (2DOF) control concept yields an asymptotically stable tracking error dynamics. Herein, the research activities address non-collocated feedback control design, which results in a dynamic output feedback scheme involving a distributed-parameter state observer. The asymptotic stability of the closed-loop control can be verified in a rather general setting by making use of operator and semigroup theory. State-of-the-art experimental benchmark examples confirm the high tracking accuracy of the proposed motion planning and 2DOF control concept. Selected examples are shown below (click figures for movies). 
 

Current research addresses interconnected structures of coupled elements, optimal actuator and sensor placement as well as applications in active flow control for maritime structures.





Funding:
Research was financially supported by the Deutsche Forschungsgemeinschaft (DFG) in the project ME-3231/1-1 Flatness-based tracking control of distributed-parameter systems with higher-dimensional domains (2007-2009).

 

Multi-agent systems

In the past decades, extensive research has been conducted on the cooperative formation control of multi-agent systems with possible applications ranging from UAVs over transportation systems to micro-satellite clusters. Besides the discrete analysis of the interconnected individual agents, continuous models based on PDEs have been used to represent and control traffic flow or large vehicular platoons. 

Our research considers the development and the application of PDE-based motion planning and feedback control strategies to achieve consensus, formation control and synchronization of multi-agent systems. For this flatness-based techniques are considered and combined, e.g., with backstepping-based state feedback control and observer design for the tracking error dynamics. The transfer from the agent continuum to the discrete formulation is finally achieved by discretization which imposes the communication topology. Selected examples for agent formation control are shown below (click on figure to start animation).

Funding:
Research is financially supported by the Deutsche Forschungsgemeinschaft (DFG) in the project ME-3231/2-1 Formation Control of Multi-Agent Systems using Continuum Models (onging 2015). 

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Figure: Flatness-based planar formation control into a Z-shape for a multi-agent network using continuous flow models (time-varying Burgers-type PDEs).

 

Nonlinear control and observer design

Research in nonlinear control and observer design covers modern model-based approaches for complex nonlinear systems. At a methodic level this includes differential geometric techniques such as 

  • Differential flatness
  • Energy-based approaches, e.g., dissipativity and passitivity
  • Optimal and predictive control
  • Nonlinear filters and observers.
Many control problems include unknown (time-varying) perturbations, parameter errors and state disturbances, which can be modeled by so called unknown inputs. Most of the common control design techniques lack to achieve robust stability in presence of unknown inputs, and thus explicit adaptive control techniques have to be developed for this purpose. For the particular class of differentially flat single-input-single-ouptput systems with identical relative degree of the control and the unknown input, recently a particularly simple adaptive two-degree-of-freedom control structure has been proposed and the robust stability properties have been demonstrated in simulation scenarios. It is shown that due to the inherent strong observability and controllability properties of these systems a flatness-based state and (quasi-) unknown input estimator can be designed and combined with a flatness-based trajectory tracking algorithm. The design and controller performance have been illustrated for a system with double saddle-node bifurcation, steady-state bistability and the associated typical hysteretic behavior. 
 
Recent application examples concern model-based state estimation for pusher-type re-heating furnaces, modeling and control of gas engines for robust efficiency optimization and soft-sensors for bio-pharmazeutical processes. One of the main distinctions herein concerns the completion of the methodic work by the experimental evaluation of the developed techniques together with partners from university and industry.
 
 

Process systems engineering and control in biotechnology 

Research in biotechnology addresses fermentation and growth processes of micro-organisms. In particular, microalgae growth processes in photo-bioreactors have been analyzed recently. Microalgae are important primary resources for the biotechnology industry, especially the food, cosmetics and pharma industries. Due to the high complexity of this process different semi-empirical models are known, which the group has began to analyze in view of process control and process optimization. The most simple and widely used microalgae model is the Droop model which describes the dynamics of extra- and intracellular substrate (nitrogen, phosphorus) and biomass (cell) concentration. The associated dynamics includes multiple steady-states and a transcritical bifurcation in dependence of the dilution rate (i.e., the ratio of volumetric flow rate and actual reactor volume). For the Droop model an inversion-based trajectory planning and feedforward control has been addressed evaluated in simulation studies. This approach shows good performance and robustness properties against perturbations in the feed concentration. For the simultaneous estimation of the state and the unmeasured feed concentration a quasi-unknown input observer has been developed.

bio_reactor_large

Figure: Experimental fermentation facility at the biolab of the Chair of Automatic Control.

In addition, the control of anaerobic digestion problems has been considered leading to a complete description of the process dynamics in terms of steady-state multiplicity, structural instabilities (bifurcations) and associated robustness properties, as well as the design of a robust output-feedback control scheme for the stabilization of the steady-state of maximum volatile fatty acid production. The results were obtained in collaboration with Prof. Jesus Alvarez (Metropolitan University, Mexico City), Prof. Juan Paulo Garcia Sandoval and Prof. Victor Gonzalez-Alvarez (University of Guadalajara, Mexico).

Funding:
Research is financially supported by the Cluster of Excellence "Future Ocean" in the mini-proposal Mathematical modeling and model-based optimal control and estimation of microalgae growth processes (starting 2015) in terms of a joint research project with Rüdiger Schulz (University Kiel) and Andreas Oschlies (GEOMAR Kiel).

 

Thermal and fluiddynamical systems 

Thermal and fluid-dynamical systems comprise a large class of challenging control problems. Examples include heat-up of metal slabs in reheating furnaces or the prevention of flow separation in aeroelastic structures. Herein, the distributed-parameter nature of the system dynamics has to explicitly taken into account for the control and observer design. Since typically complex geometries arise methods of approximation and model order reduction techniques have to be integrated for the explicit evaluation. 
 
The groups research activities address, e.g., heat-up processes in smart forming tools, where heating cartridges are embedded into the tool to realize a desired temperature distribution in selected parts of the tool. For this, a flatness-based design technique has been developed that makes use of the spectral properties of the corresponding system operator. This enables to systematically design an open-loop controller to achieve finite time transitions between stationary temperature profiles within the forming tool. Extensions to tracking control using the two-degree-of-freedom control concept have been considered and analyzed. Besides simulation results our research is distinct by the experimental validation of the control concept with industrial partners. 
 
Research in fluiddynamical systems focuses on motion planning, i.e., the determination of an open-loop control to achieve a desired prescribed flow velocity profile. Based on the Stokes equations for this a flatness-based design technique has been developed, which enables to systematically solve the control problem. Simulation results confirm both the applicability and the control performance.

 stokes_image

Figure: Flatness-based motion planning for Stokes flow. Actuator configuration (left) and transfer into velocity eigenmode from zero initial state (right).

Research