Johann Reger

Load Torque Estimation and Passivity-Based Control of a Boost-Converter/DC-Motor Combination

An algebraic approach is presented for the fast feed-forward adaptation of the angular velocity trajectory tracking task in a Boost-converter driven dc-motor system. For the adaptation, the load torque perturbations are assumed piecewise constant and are, nonasymptotically, online estimated using the available noisy measurements of the state variables. The controller is a linear controller based on the exact tracking error dynamics passive output feedback (ETEDPOF) controller design methodology including suitable adaptive feed-forward precompensation depending explicitly on the precisely estimated torque. The performance of the adaptation, which is achieved by means of the algebraic online-estimation of the current unknown load torque, is successfully validated in an experimental laboratory setup.

On non-asymptotic observation of nonlinear systems

In this contribution, we use the so-called algebraic derivative method for a non-asymptotic state observation of nonlinear SISO systems. We derive a general formula of a time-varying filter that allows a non-model-based, quasiinstantaneous estimation of time derivatives of arbitrary analog time signals. The estimates are based on integrals of measured signals alone. For preserving accuracy, the estimation process has to be re-initialized after some period of time. Besides resetting the estimation time-interval equidistantly, estimated absolute error bounds and integral error bounds are also used for improving the efficiency of the estimation process. As an example, we use Chen’s chaotic oscillator to illustrate the velocity and the robustness of our observation method with respect to uncertainty of initial values and uniformly distributed measurement noise.

Flatness based control of a buck-converter driven DC motor

Abstract The aim of this contribution is to give a detailed account on the circuit and control design of a buck converter driven DC motor. The steps of design, as for example the choice of the coil, the switching devices employed are discussed at length, all in view of the control objective: tracking control of the DC motors shaft angular velocity. The dynamic system composed from converter/motor is shown to be differentially flat viewed from the angular velocity, which is a flat output. It is thus possible to derive a flatness-based tracking controller which achieves favorable properties like a smooth starting trajectory for the angular velocity.

On algebraic time-derivative estimation and deadbeat state reconstruction

This paper places into perspective the so-called algebraic time-derivative estimation method recently introduced by Fliess and co-authors with standard results from linear state-space theory for control systems. In particular, it is shown that the algebraic method can essentially be seen as a special case of deadbeat state estimation based on the reconstructibility Gramian of the considered system.

An algebraic perspective to single-transponder underwater navigation

This paper studies the position estimation of an underwater vehicle using a single acoustic transponder. The chosen estimation approach is based on nonlinear differential algebraic methods which allow to express very simply conditions for observability. These are then used in combination with an integrator-based time-derivative estimation technique to design an algebraic estimator, which, contrary to asymptotic observers, does not require sometimes tedious convergence verification. Simple simulation results are presented to illustrate the approach.

A Derivative Estimation Toolbox based on Algebraic Methods - Theory and Practice

In this paper, the implementation and usage of a so-called Derivative Estimation Toolbox is demonstrated. By means of this toolbox, time derivatives of sampled, noisy time signals may be determined in realtime, all based on a recently presented algebraic derivative estimation method. The main contribution is a possible implementation on a prototyping control unit. The performance of the Derivative Estimation Toolbox is experimentally validated on a brake-testbench. In particular, the friction force and the drive torque are estimated in realtime.

A TIME-VARYING LINEAR STATE FEEDBACK TRACKING CONTROLLER FOR A BOOST-CONVERTER DRIVEN DC MOTOR

Abstract This article deals with the trajectory tracking problem for the angular velocity of a dc-motor shaft using a Boost-converter as the switch regulated electronic drive. The main result of our proposed control scheme is that measuring of the angular velocity is not really necessary and the control law is synthesized using only a linear time-varying combination of the converter current and voltage variables. The voltage reference trajectory for the converter is generated exploiting a partial differential flatness property of the combined system. The reference trajectories of the average control and the input current are calculated via stored energy considerations and planning for the initial and final stationary regimes. The discrete switching control realization of the designed continuous feedback control law is accomplished by means of a traditional PWM-modulation scheme. Experimental results are provided.

An exact tracking error dynamics passive output feedback controller for a Buck-Boost-converter driven DC motor

This article deals with the trajectory tracking problem for the angular velocity of a DC-motor shaft using a buck-boost-converter as the switch regulated electronic drive. The main result of our proposed control scheme is that a linear time-varying controller results from the consideration of the exact tracking error dynamics and static passive output feedback controller design. The measuring of the angular velocity is not really necessary and the control law is synthesized using only a linear time-varying combination of the converter current and voltage variables. The voltage reference trajectory for the converter is generated exploiting a partial differential flatness property of the combined system. The reference trajectories of the average control and the input current are calculated via stored energy considerations and planning for the initial and final stationary regimes. The discrete switching control realization of the designed continuous feedback control law is accomplished by means of a traditional PWM-modulation scheme. Experimental results are provided

Robust algebraic state estimation of chaotic systems

We propose an improvement of a recently introduced algebraic approach for the non-asymptotic state and parameter estimation of nonlinear systems. In particular, we increase the robustness of the estimation method with respect to zero mean, high frequency, measurement noises by introducing a so-called invariant filtering technique. In order to reduce an already fast transient to the convergence, when subject to measurement noise, we devise an estimation policy consisting of two overlapping estimators with appropriate switchings between their results. These are two identical time-shifted estimators running in parallel with an overlapping estimation period. The benefits of our method are demonstrated on the state observation of a chaotic system of the R¿ssler type.

Constructing predictive models of human running

Running is an essential mode of human locomotion, during which ballistic aerial phases alternate with phases when a single foot contacts the ground. The spring-loaded inverted pendulum (SLIP) provides a starting point for modelling running, and generates ground reaction forces that resemble those of the centre of mass (CoM) of a human runner. Here, we show that while SLIP reproduces within-step kinematics of the CoM in three dimensions, it fails to reproduce stability and predict future motions. We construct SLIP control models using data-driven Floquet analysis, and show how these models may be used to obtain predictive models of human running with six additional states comprising the position and velocity of the swing-leg ankle. Our methods are general, and may be applied to any rhythmic physical system. We provide an approach for identifying an event-driven linear controller that approximates an observed stabilization strategy, and for producing a reduced-state model which closely recovers the observed dynamics.