Gz Georgo Angelis

Grey-box Modeling of Friction: An Experimental Case-study

Grey-box modeling covers the domain where we want to use a balanced amount of first principles and empiricism. The two generic grey-box models presented, i.e., a Neural Network model and a Polytopic model are capable of identifying friction characteristics that are left unexplained by first principles modeling. In an experimental case study, both grey-box models are applied to identify a rotating arm subjected to friction. An augmented state extended Kalman filter is used iteratively and off-line for the estimation of unknown parameters. For the studied example and defined black-box topologies, little difference is observed between the two models.

Stability and causality constraints on frequency response coefficients applied for non-parametric H 2 and H ∞ control synthesis

The value of norm-based control synthesis methodologies heavily depends on the quality of the model at hand. The acquisition of low-order control oriented models however is often a non-trivial task. This paper pursuits the non-parametric synthesis of optimal controllers while omitting parametrization of the plant. As a result, the actual parametrization is performed on the controller such that no data-reduction is performed without knowledge of closed-loop relevant behavior. The synthesis of frequency response coefficients of an optimal controller for a sampled version of the mixed-sensitivity problem is considered. To convexify the problem, the actual optimization is performed over the frequency response coefficients of the Youla parameter Qi. Using the Youla parameter, the set of stabilizing controllers is mapped onto the set of stable transfer functions. The main contribution of this paper is the derivation of algebraic constraints over Qi that guarantee the existence of a rational stable interpolant over the points Qi. Simulations shows that the frequency response coefficients found via the proposed approach show similar behavior as model based methods.

Frequency response based multivariable control design for motion systems

In this paper, we discuss the design of multivariable motion controllers exploiting crosscouplings in the controller for open loop decoupling, disturbance rejection and feedforward decoupling. Using specific properties of motion systems, we illustrate that frequency response design methods can be extended to handle several multivariable control problems. Application to high performance motion systems shows significant improvement

Frequency response data based optimal control using the data based symmetric root locus

This paper describes a data-based frequency domain optimal control synthesis method. Plant frequency response data is used to compute the frequency response of the controller using a spectral decomposition of the optimal return difference. The underlying cost function is selected from a databased symmetric root-locus, which gives insight in the closed-loop pole locations that will be achieved by the controller. A simulation study shows the abilities of the proposed method.

A practical loop-shaping approach for pole-placement in mechatronic systems

Manual design of feedback-controllers based on frequency-domain data is often used in industry to design low-order SISO controllers based on experimental data. Such design approaches are often either based on a data representation in the pole-zero plane, i.e. root-locus approaches, or a representation of the open-loop frequency response function (FRF), i.e. shaping of the sensitivity function. Both data representations however are not explicitly coupled during tuning to combine the advantages of both design methods. A new approach is proposed which combines both data representations into one controller design method such that loop-shaping in an extended form can be used to place closed-loop poles. By means of generalized stability, performance demands given in the pole-zero plane can be linked to phase and gain specification of the open-loop transfer-function. As a result, this method generalizes and refines the well known loop-shaping approach. Simulations and experiments with a two-mass-spring system show that transient behavior can be improved significantly compared to controllers that are designed on FRF data only

Non-parametric H-infinity control synthesis with suboptimal controller sets

Abstract The effectiveness of norm-based control methodologies heavily relies on the quality of the model that describes the dynamic behavior of the plant. In practical applications, the requirement to accurately describe the system at hand often results in high-order plant-models. On the other hand, low-order models are desired to end-up with low-order controllers that reduce implementational costs. The resulting trade-off between dynamical order and closed-loop performance can not be handled in a straightforward manner since the closed-loop behavior is unknown at the moment of plant-parametrization. This paper proposes a method to overcome this trade-off via non-parametric H ∞ control-synthesis, i.e. omitting parametrization of the plant. As a result, no data-reduction or data-interpolation is performed before synthesis. The resulting controller is represented as Frequency Response Sets for a given frequency grid. This data can be used as input for controller parametrization with explicit trade-off between closed-loop performance and controller order. This is achieved by considering the mixed-sensitivity problem as a model-matching problem based on Youla-parametrization. Via a specific conceptual choice of the coprime-factorization for the Youla parametrization, it is proved that the SISO H ∞ control synthesis problem can be solved in a non-parametric way based on the plant zeros and frequency response coefficients of the system solely. A simulation study is performed on a fourth-order system to illustrate the main steps in the approach.