In-Situ Component-Based TPA for Time-Variant Dynamic Systems: A State-Space Formulation

In this chapter, a methodology to calculate equivalent forces by taking into account the possible time-varying dynamic behavior of the components under analysis is presented. This methodology is based on the use of the state-space realization of the in-situ component-based TPA method. To take into account possible time-varying dynamic behavior of the systems under study, a local linear parameter varying (LPV) model identification approach is used. This approach enables the computation of state-space models representative of the components at each time instant by interpolating a given set of linear time-invariant (LTI) state-space models representative of the dynamics of the components under study for fixed operating conditions. By exploiting a numerical example, it is found that when dealing with structures presenting time-varying behavior, accurate equivalent forces can be computed in time domain by using the approaches presented in this chapter. Furthermore, it is clearly demonstrated that ignoring the time dependency of the dynamic behavior of mechanical systems can lead to an important deterioration of the results

Reverse Engineering Biological Control Systems for Applications in Process Control.

The main emphasis of this dissertation is the development of nonlinear control strategies based on biological control systems. Commonly utilized biological control schemes have been studied in order to reverse engineer the important concepts for applications in process control. This approach has led to the development of a nonlinear habituating control strategy and nonlinear model reference adaptive control schemes. Habituating control is a controller design strategy for nonlinear systems with more manipulated inputs than controlled outputs. Nonlinear control laws that provide input-output linearization while simultaneously minimizing the cost of affecting control are derived. Local stability analysis shows the controller can provide a simple solution to singularity and non-minimum phase problems. A direct adaptive control strategy for a class of single-input, single-output non-linear systems is presented. The major advantage is that a detailed dynamic non-linear model is not required for controller design. Unknown controller functions in the associated input-output linearizing control law are approximated using locally supported radial basis functions. Lyapunov stability analysis is used to derive parameter update laws which ensure the state vector remains bounded and the plant output asymptotically tracks the output of a linear reference model. A nonlinear model reference adaptive control strategy in which a linear model (or multiple linear models) is embedded within the nonlinear controller is presented. The nonlinear control law is constructed by embedding linear controller gains derived from models obtained using standard linear system identification techniques within the associated input-output linearizing control law. Higher-order controller functions are approximated with radial basis functions. Lyapunov stability analysis is used to derive stable parameter update laws. The major disadvantage of the previous techniques is computational expense. Two modifications have been developed. First, the effective dimension is reduced by applying nonlinear principal component analysis to the state variable data obtained from open-loop tests. This allows basis functions to be placed in a lower dimensional space than the original state space. Second, the total number of basis functions is fixed a priori and an algorithm which adds/prunes basis function centers to surround the current operating point on-line is utilized

State-Space realization of LPV Input-Output models: practical methods for the user

Identification of Linear Parameter-Varying (LPV) systems is often accomplished via Input-Output (IO) model structures in discrete-time. This approach is common because of its simplicity and the possibility to extend identification methods for Linear Time-Invariant (LTI) systems. However, a realization of LPV-IO models as State-Space (SS) representations, often required for control synthesis, is complicated due to the phenomenon of dynamic dependence (dependence of the resulting representation on time-shifted versions of the scheduling signal). This conversion problem is revisited and practically applicable approaches are suggested which result in SS representations that have only static dependence (dependence on the instantaneous value of the scheduling signal). To reduce complexity, a criterion is established to decide when an LTI type of realization can be used without introducing significant error. To reduce the order of the resulting SS realization, a LPV Ho-Kalman type of model reduction approach is introduced, which is capable of reducing even unstable models. The proposed methods are illustrated by application oriented examples

Evolutionary-based sparse regression for the experimental identification of duffing oscillator

In this paper, an evolutionary-based sparse regression algorithm is proposed and applied onto experimental data collected from a Duffing oscillator setup and numerical simulation data. Our purpose is to identify the Coulomb friction terms as part of the ordinary differential equation of the system. Correct identification of this nonlinear system using sparse identification is hugely dependent on selecting the correct form of nonlinearity included in the function library. Consequently, in this work, the evolutionary-based sparse identification is replacing the need for user knowledge when constructing the library in sparse identification. Constructing the library based on the data-driven evolutionary approach is an effective way to extend the space of nonlinear functions, allowing for the sparse regression to be applied on an extensive space of functions. The results show that the method provides an effective algorithm for the purpose of unveiling the physical nature of the Duffing oscillator. In addition, the robustness of the identification algorithm is investigated for various levels of noise in simulation. The proposed method has possible applications to other nonlinear dynamic systems in mechatronics, robotics, and electronics

System identification, time series analysis and forecasting:The Captain Toolbox handbook.

CAPTAIN is a MATLAB compatible toolbox for non stationary time series analysis, system identification, signal processing and forecasting, using unobserved components models, time variable parameter models, state dependent parameter models and multiple input transfer function models. CAPTAIN also includes functions for true digital control

Parametric Macromodels of Digital I/O Ports

This paper addresses the development of macromodels for input and output ports of a digital device. The proposed macromodels consist of parametric representations that can be obtained from port transient waveforms at the device ports via a well established procedure. The models are implementable as SPICE subcircuits and their accuracy and efficiency are verified by applying the approach to the characterization of transistor-level models of commercial devices