Basic research on design analysis methods for rotorcraft vibrations

The objective of the present work was to develop a method for identifying physically plausible finite element system models of airframe structures from test data. The assumed models were based on linear elastic behavior with general (nonproportional) damping. Physical plausibility of the identified system matrices was insured by restricting the identification process to designated physical parameters only and not simply to the elements of the system matrices themselves. For example, in a large finite element model the identified parameters might be restricted to the moduli for each of the different materials used in the structure. In the case of damping, a restricted set of damping values might be assigned to finite elements based on the material type and on the fabrication processes used. In this case, different damping values might be associated with riveted, bolted and bonded elements. The method itself is developed first, and several approaches are outlined for computing the identified parameter values. The method is applied first to a simple structure for which the 'measured' response is actually synthesized from an assumed model. Both stiffness and damping parameter values are accurately identified. The true test, however, is the application to a full-scale airframe structure. In this case, a NASTRAN model and actual measured modal parameters formed the basis for the identification of a restricted set of physically plausible stiffness and damping parameters

Use of system identification techniques for improving airframe finite element models using test data

A method for using system identification techniques to improve airframe finite element models using test data was developed and demonstrated. The method uses linear sensitivity matrices to relate changes in selected physical parameters to changes in the total system matrices. The values for these physical parameters were determined using constrained optimization with singular value decomposition. The method was confirmed using both simple and complex finite element models for which pseudo-experimental data was synthesized directly from the finite element model. The method was then applied to a real airframe model which incorporated all of the complexities and details of a large finite element model and for which extensive test data was available. The method was shown to work, and the differences between the identified model and the measured results were considered satisfactory

Fuzzy System Identification Based Upon a Novel Approach to Nonlinear Optimization

Fuzzy systems are often used to model the behavior of nonlinear dynamical systems in process control industries because the model is linguistic in nature, uses a natural-language rule set, and because they can be included in control laws that meet the design goals. However, because the rigorous study of fuzzy logic is relatively recent, there is a shortage of well-defined and understood mechanisms for the design of a fuzzy system. One of the greatest challenges in fuzzy modeling is to determine a suitable structure, parameters, and rules that minimize an appropriately chosen error between the fuzzy system, a mathematical model, and the target system. Numerous methods for establishing a suitable fuzzy system have been proposed, however, none are able to demonstrate the existence of a structure, parameters, or rule base that will minimize the error between the fuzzy and the target system. The piecewise linear approximator (PLA) is a mathematical construct that can be used to approximate an input-output data set with a series of connected line segments. The number of segments in the PLA is generally selected by the designer to meet a given error criteria. Increasing the number of segments will generally improve the approximation. If the location of the breakpoints between segments is known, it is a straightforward process to select the PLA parameters to minimize the error. However, if the location of the breakpoints is not known, a mechanism is required to determine their locations. While algorithms exist that will determine the location of the breakpoints, they do not minimize the error between data and the model. This work will develop theory that shows that an optimal solution to this nonlinear optimization problem exists and demonstrates how it can be applied to fuzzy modeling. This work also demonstrates that a fuzzy system restricted to a particular class of input membership functions, output membership functions, conjunction operator, and defuzzification technique is equivalent to a piecewise linear approximator (PLA). Furthermore, this work develops a new nonlinear optimization technique that minimizes the error between a PLA and an arbitrary one-dimensional set of input-output data and solves the optimal breakpoint problem. This nonlinear optimization technique minimizes the approximation error of several classes of nonlinear functions leading up to the generalized PLA. While direct application of this technique is computationally intensive, several paths are available for investigation that may ease this limitation. An algorithm is developed based on this optimization theory that is significantly more computationally tractable. Several potential applications of this work are discussed including the ability to model the nonlinear portions of Hammerstein and Wiener systems

Practical Nonlinear Model Predictive Control with Hammerstein Model Applied to a Test Rig of Refrigeration Compressors

This paper discusses the implementation and presents the results of a suboptimal nonlinear model predictive controller used to control the suction and discharge pressures of compressors under test in a rig. The objective of this rig is to emulate operational conditions to which refrigeration compressors can be subjected when applied in a refrigeration system, such as household refrigerators and freezers, and allow quick measurements of some of the compressor characteristics under those conditions. There is a coupling between suction and discharge pressures and the behavior of such variables is nonlinear with respect to the valve openings, thus the plant to be controlled can be characterized as multivariable and nonlinear. Even though in industry it is common to use linear controllers to control nonlinear plants, the use of nonlinear controllers can bring advantages in terms of performance and robustness. The controller implemented in this paper is the practical nonlinear model predictive control algorithm, which is a general framework that can be used for the implementation of nonlinear model predictive controllers considering almost any class of nonlinear model. Even though model predictive control is harder to be implemented than classical controllers, such as PID, it poses the process control problem in the time domain, so the concepts involved are intuitive and at the same time the tuning is relatively easy, even for the multivariable case. In addition, model predictive control allows constraints, such as valve opening limitations and pressure limits, to be handled during the design phase. This paper considers a specific nonlinear model architecture, the nonlinear Hammerstein model, which is composed of a static nonlinear element in series with a linear dynamic part. Since this model is conceptually simple and presents good results in most of the practical situations, it is widely used in practice when a nonlinear model is desired. The dynamics of the real test rig were identified using this nonlinear model structure and the identification results are discussed. The practical nonlinear model predictive controller was implemented in the real test rig, being tested in a variety of operating conditions. The results of the controller are compared with the ones obtained with a classical PID controller. The modeling approach presented good results and the results obtained in this study show that it is possible to use nonlinear model predictive control algorithms in refrigeration test rigs, and that this use can contribute to increasing the productivity and operational efficiency of compressor tests

Advances in nonlinear process modeling using block-oriented exact solution techniques

Application of the Hammerstein Block-oriented Exact Solution Technique (H-BEST) to a real industrial process is presented. The methodology is extended to processes with a Wiener structure, and named the Wiener block-Oriented Exact Solution Technique (W-BEST). The W-BEST methodology is presented in detail and applied to a simulated continuous-stirred tank reactor with complex dynamic behavior. W-BEST is then compared to another continuous-time Wiener-based model found in the literature and applied to an example process. The results of the two methods are compared using a test input sequence applied to the example process

Nonparametric nonlinear model predictive control

Model Predictive Control (MPC) has recently found wide acceptance in industrial applications, but its potential has been much impeded by linear models due to the lack of a similarly accepted nonlinear modeling or databased technique. Aimed at solving this problem, the paper addresses three issues: (i) extending second-order Volterra nonlinear MPC (NMPC) to higher-order for improved prediction and control; (ii) formulating NMPC directly with plant data without needing for parametric modeling, which has hindered the progress of NMPC; and (iii) incorporating an error estimator directly in the formulation and hence eliminating the need for a nonlinear state observer. Following analysis of NMPC objectives and existing solutions, nonparametric NMPC is derived in discrete-time using multidimensional convolution between plant data and Volterra kernel measurements. This approach is validated against the benchmark van de Vusse nonlinear process control problem and is applied to an industrial polymerization process by using Volterra kernels of up to the third order. Results show that the nonparametric approach is very efficient and effective and considerably outperforms existing methods, while retaining the original data-based spirit and characteristics of linear MPC