David Hajdu

The effect of non-symmetric FRF on machining: A case study

Stability prediction of machining operations is often not reliable due to the inaccurate mechanical modeling. A major source of this inaccuracy is the uncertainties in the dynamic parameters of the machining center at different spindle speeds. The so-called tip-to-tip measurement is the fastest and most convenient method to determine the frequency response of the machine. This concept consists of the measurement of the tool tip’s frequency response function (FRF) usually in two perpendicular directions including cross terms. Although the cross FRFs are often neglected in practical applications, they may affect the system’s dynamics. In this paper, the stability diagrams are analyzed for milling operations in case of diagonal, symmetric and non-symmetric FRF matrices. First a time-domain model is derived by fitting a multiple-degrees-of-freedom model to the FRF matrix, then the semi-discretization method is used to determine stability diagrams. The results show that the omission of the non-symmetry of the FRF matrix may lead to inaccurate stability diagram.Copyright

To Delay or Not to Delay—Stability of Connected Cruise Control

The dynamics of connected vehicle systems are investigated where vehicles exchange information via wireless vehicle-to-vehicle (V2V) communication. In particular, connected cruise control (CCC) strategies are considered when using different delay configurations. Disturbance attenuation (string stability) along open chains is compared to the linear stability results using ring configuration. The results are summarized using stability diagrams that allow one to design the control gains for different delay values. Critical delay values are calculated and trade-offs between the different strategies are pointed out.

Extension of Stability Radius to Neuromechanical Systems With Structured Real Perturbations

The ability of humans to maintain balance about an unstable position in a continuously changing environment attests to the robustness of their balance control mechanisms to perturbations. A mathematical tool to analyze robust stabilization of unstable equilibria is the stability radius. Based on the pseudo-spectra, the stability radius gives a measure to the maximum change of the system parameters without resulting in a loss of stability. Here, we compare stability radii for a model for human frontal plane balance controlled by a delayed proportional-derivative feedback to two types of perturbations: unstructured complex and weighted structured real. It is shown that: 1) narrow stance widths are more robust to parameter variation; 2) stability is maintained for larger structured real perturbations than for unstructured complex perturbations; and 3) the most robust derivative gain to weighted structured real perturbations is located near the stability boundary. It is argued that stability radii can effectively be used to compare different control concepts associated with human motor control.

Time domain analysis of the smith predictor in case of parameter uncertainties: A case study

Time domain representation of the original Smith Predictor is presented for systems with feedback delays. It is shown that if the parameters in the internal model of the predictor are not equal to the parameters of the real system, then the dimension of the closed loop system is double of the dimension of the open-loop system. Furthermore, the time-domain representation of the corresponding control law involves terms of integrals with respect to the past similarly to the Finite Spectrum Assignment control technique. The results are demonstrated for a second order system (pendulum) subjected to the Smith Predictor. It is demonstrated that stability diagrams can be constructed using the D-subdivision method and Stepan’s formulas. The sensitivity of the stability properties with respect to the parameter uncertainties in the predictor’s internal model is analyzed. It is shown that the original Smith Predictor can stabilize unstable plants for some extremely detuned internal model parameters. Thus the general concept that the Smith Predictor is not capable to stabilize unstable systems is technically not true.Copyright