Tracking control design for a wave equation with dynamic boundary conditions modeling a piezoelectric stack actuator

This paper is concerned with the design of an asymptotically stabilizing tracking controller for an undamped wave equation modeling a piezoelectric stack actuator. For this, flatness‐based methods for trajectory planning and feedforward control are combined with dynamic feedback control involving a Luenberger‐type observer within the two degrees‐of‐freedom control concept. The asymptotic stability of the closed‐loop system is verified using Lyapunov's stability theory and LaSalle's invariance principle. Thereby, a separation theorem is introduced for bounded perturbations of infinitesimal generators of asymptotically stable C₀‐semigroups. Finally, the tracking performance is illustrated in simulation scenarios. Copyright © 2010 John Wiley & Sons, Ltd.     

Nonlinear model predictive control of a continuous slab reheating furnace

A nonlinear model predictive controller is designed for a continuous reheating furnace for steel slabs. Based on a first-principles mathematical model, the controller defines local furnace temperatures so that the slabs reach their desired final temperatures. The controller is suitable for non-steady-state operating situations and reaching user-defined desired slab temperature profiles. In the control algorithm, a nonlinear unconstrained dynamic optimization problem is solved by the quasi-Newton method. The design of the controller exploits the fact that the considered slab reheating furnace is a continuous production process. Long-term measurement results from an industrial application of the controller demonstrate its reliability and accuracy.     

Compensation of parasitic effects for a silicon tuning fork gyroscope

This paper refers to a silicon micromachined tuning fork gyroscope, which is driven via two piezoelectric thin film actuators. The device responds to an external angular rate by a torsional motion about its sensitive axis due to the Coriolis effect. The shear stress in the upper torsional stem, which is proportional to the angular rate, is detected via a piezoresistive readout structure. In addition to the wanted signal corresponding to the angular rate, there are unwanted contributions from the drive motion, e.g., from mechanical unbalances and from asymmetries of the piezoelectric excitation induced by fabrication tolerances. These effects, which disturb the sensor signal with varying contributions in amplitude and phase, have already been examined for capacitive surface micromachined sensors. In this paper, they are identified for a piezoelectrically driven, bulk-micromachined gyro and compared to results of FEM simulations. System-level simulations are performed and show possibilities to compensate the main parasitic effects. Results of eliminating the mechanical unbalance by femtosecond laser trimming are presented and compared with the simulations.     

Extended Kalman filter and adaptive backstepping for mean temperature control of a three‐way catalytic converter

This contribution is concerned with an adaptive control strategy for the mean temperature of an automotive three‐way catalytic converter. Tailored finite‐dimensional approximations of the complex infinite‐dimensional mathematical model of the catalytic converter serve as a basis for the design of an extended Kalman filter for state profile estimation and of an adaptive backstepping controller for the mean temperature. Although the model used for observer design relies on (semi‐)discretising the infinite‐dimensional model, a simple model for the mean temperature employing a phenomenological approach to describe the reaction heat is used for control design. The observer/controller is tested in simulation scenarios using a validated model of the three‐way catalytic converter. Copyright © 2013 John Wiley & Sons, Ltd.     

Active compensation of roll eccentricity in rolling mills

This paper is concerned with the active compensation of the roll-eccentricity-induced periodic disturbances in the strip exit thickness of hot and cold rolling mills. The roll eccentricity may be caused by different reasons, e.g., inexact roll grinding or nonuniform thermal expansion of the rolls. The increasing demands on the thickness tolerances require new methods for the active compensation of the contribution of the roll eccentricity to the final thickness deviation. The presented method is based on the factorization approach over the set of stable transfer functions in combination with an adaptive least-mean-squares algorithm derived from the projection theorem. Here, the authors take advantage of the fact that the eccentricity-caused disturbance is periodic with a frequency proportional to the measured angular velocity of the rolls. Furthermore, it turns out that the presented concept fits the conventional control circuit of automatic gauge control in an optimal way. Simulation results for a cold rolling mill and measurement results for a hot strip mill demonstrate the feasibility and the excellent performance of the design     

Mathematical Modeling and Nonlinear Controller Design for a Novel Electrohydraulic Power-Steering System

This paper is concerned with the mathematical modeling and nonlinear controller design of a novel electrohydraulic closed-center power-steering system. After a short introduction to the requirements of modern power-steering systems, the construction of the power-steering system under consideration will be described. The main advantage of this construction is the enhancement of the overall energetic efficiency of the steering system and the possibility of a variable steering assistance while keeping the good steering feeling of traditional hydraulic steering systems. Based on a detailed mathematical model of the essential components of the system, it is shown how some of the parameters of the system can be chosen to achieve an optimal dynamic behavior of the closed-loop system. The controller design proceeds in two steps: first, a nonlinear controller for the assistance force based on the differential flatness property of the system is designed, and afterwards, a steering torque controller using an impedance matching design is derived. Finally, measurement results of a test stand show the good performance and the robust behavior of the proposed control strategy     

Aktiver Erdbebenschutz für mehrstöckige Gebäude

A multi-storey building is fit with an actor and a base isolation system for the purpose of active earthquake protection. The whole system is described by a nonlinear mechanical model, that takes hysteresis into account. The active damping is provided by a nonlinear control law, which is designed following the theory of Liapunov. The principle of invariance is used to prove the stability of the control loop. Simulations for an artificial earthquake show, that the proposed protection is applicable for real buildings.