Nonlinear pressure control of self-supplied variable displacement axial piston pumps

The present paper deals with the pressure control of self-supplied variable displacement axial piston pumps subject to fast changing, unknown loads. First, the setup of the system and the mathematical model are described. As the pump is self-supplied, the mathematical model exhibits a switching right-hand side which makes the control design a challenging task. A nonlinear two degrees-of-freedom control strategy, comprising a feedforward and a feedback control, in combination with a load estimator is proposed for the pressure control. The proof of the stability of the overall closed-loop system is based on Lyapunov's theory. The performance of the control concept is verified by means of experiments. The results show that the proposed control concept has an excellent and robust behavior.     

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.     

A dynamical envelope model for vibratory gyroscopes

In this contribution, a method will be presented to derive an envelope model for vibratory gyroscopes capturing the essential “slow” dynamics (envelope) of the system. The methodology will be exemplarily carried out for a capacitive gyroscope with electrostatic actuators and sensors. The resulting envelope model can be utilized for both transient and steady state simulations with the advantage of a significantly increased simulation speed. Especially for the sensor design and optimization, where usually very complex mathematical models are used, efficient steady state simulations are of certain interest. Another great advantage of this approach is that the steady state solutions in terms of the envelope model are constant. Thus, for the controller design, a linearization of the nonlinear envelope model around the steady state solution yields a linear time-invariant system allowing for the application of the powerful methods known from linear control theory.     

Nichtlineare Trajektorienfolgeregelung für einen Laborhelikopter

This contribution is devoted to the nonlinear tracking control problem of the laboratory experiment helicopter 3DOF distributed by Quanser. The laboratory experiment belongs to the class of mechanical systems with three degrees-of-freedom and two control inputs. It is well known that the systematic design of nonlinear controllers for underactuated mechanical systems is a challenge compared to fully actuated systems. On certain simplifying assumptions, which very well apply to the operating range of practical interest, we can show that the mathematical model is configuration flat. Thereby, a mechanical system is said to be configuration flat if it is differential flat and the flat outputs solely depend on the generalized coordinates of the mechanical system. The controller design is based on a formulation of the mechanical system on a Riemannian manifold where the kinetic energy serves as a natural Riemannian metric. In a first step a nonlinear tracking controller including an integral part in the linear error system is designed by means of a quasi-static state feedback. In a second step the design of the tracking controller is based on the theory of exact linearization utilizing the so-called dynamic extension algorithm. The experimental results of both controllers are compared and discussed in detail. In particular, the quasi-static state feedback controller shows an excellent tracking behavior. The performance as being obtained by the nonlinear controlled cannot be achieved by conventional linear control strategies.     

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.