Sliding mode and shaped input vibration control of flexible systems

Copyright [2008] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, the vibration reduction problem is investigated for a flexible spacecraft during attitude maneuvering. A new control strategy is proposed, which integrates both the command input shaping and the sliding mode output feedback control (SMOFC) techniques. Specifically, the input shaper is designed for the reference model and implemented outside of the feedback loop in order to achieve the exact elimination of the residual vibration by modifying the existing command. The feedback controller, on the other hand, is designed based on the SMOFC such that the closed-loop system behaves like the reference model with input shaper, where the residual vibrations are eliminated in the presence of parametric uncertainties and external disturbances. An attractive feature of this SMOFC algorithm is that the parametric uncertainties or external disturbances of the system do not need to satisfy the so-called matching conditions or invariance conditions provided that certain bounds are known. In addition, a smoothed hyperbolic tangent function is introduced to eliminate the chattering phenomenon. Compared with the conventional methods, the proposed scheme guarantees not only the stability of the closed-loop system, but also the good performance as well as the robustness. Simulation results for the spacecraft model show that the precise attitudes control and vibration suppression are successfully achieved

Analytical Optimal Currents for Multiphase PMSMs Under Fault Conditions and Saturation

An original analytical expression is presented in this paper to obtain optimal currents minimizing the copper losses of a multi-phase Permanent Magnet Synchronous Motor (PMSM) under fault conditions. Based on the existing solutions [i]opt1 (without zero sequence of current constraint) and [i]opt2 (with zero sequence constraint), this new expression of currents [i]opt3 is obtained by means of a geometrical representation and can be applied to open-circuit, defect of current regulation, current saturation and machine phase short-circuit fault. Simulation results are presented to validate the proposed approach

Optimization of adaptive test design methods for the determination of steady-state data-driven models in terms of combustion engine calibration

This thesis deals with the development of a model-based adaptive test design strategy with a focus on steady-state combustion engine calibration. The first research topic investigates the question how to handle limits in the input domain during an adaptive test design procedure. The second area of scope aims at identifying the test design method providing the best model quality improvement in terms of overall model prediction error. To consider restricted areas in the input domain, a convex hull-based solution involving a convex cone algorithm is developed, the outcome of which serves as a boundary model for a test point search. A solution is derived to enable the application of the boundary model to high-dimensional problems without calculating the exact convex hull and cones. Furthermore, different data-driven engine modeling methods are compared, resulting in the Gaussian process model as the most suitable one for a model-based calibration. To determine an appropriate test design method for a Gaussian process model application, two new strategies are developed and compared to state-of-the-art methods. A simulation-based study shows the most benefit applying a modified mutual information test design, followed by a newly developed relevance-based test design with less computational effort. The boundary model and the relevance-based test design are integrated into a multicriterial test design strategy that is tailored to match the requirements of combustion engine test bench measurements. A simulation-based study with seven and nine input parameters and four outputs each offered an average model quality improvement of 36 % and an average measured input area volume increase of 65 % compared to a non-adaptive space-filling test design. The multicriterial test design was applied to a test bench measurement with seven inputs for verification. Compared to a space-filling test design measurement, the improvement could be confirmed with an average model quality increase of 17 % over eight outputs and a 34 % larger measured input area

A Hierarchical Procedure for the Synthesis of ANFIS Networks

Adaptive neurofuzzy inference systems (ANFIS) represent an efficient technique for the solution of function approximation problems. When numerical samples are available in this regard, the synthesis of ANFIS networks can be carried out exploiting clustering algorithms. Starting from a hyperplane clustering synthesis in the joint input-output space, a computationally efficient optimization of ANFIS networks is proposed in this paper. It is based on a hierarchical constructive procedure, by which the number of rules is progressively increased and the optimal one is automatically determined on the basis of learning theory in order to maximize the generalization capability of the resulting ANFIS network. Extensive computer simulations prove the validity of the proposed algorithm and show a favorable comparison with other well-established techniques

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

Optimization of adaptive test design methods for the determination of steady-state data-driven models in terms of combustion engine calibration

This thesis deals with the development of a model-based adaptive test design strategy with a focus on steady-state combustion engine calibration. The first research topic investigates the question how to handle limits in the input domain during an adaptive test design procedure. The second area of scope aims at identifying the test design method providing the best model quality improvement in terms of overall model prediction error. To consider restricted areas in the input domain, a convex hull-based solution involving a convex cone algorithm is developed, the outcome of which serves as a boundary model for a test point search. A solution is derived to enable the application of the boundary model to high-dimensional problems without calculating the exact convex hull and cones. Furthermore, different data-driven engine modeling methods are compared, resulting in the Gaussian process model as the most suitable one for a model-based calibration. To determine an appropriate test design method for a Gaussian process model application, two new strategies are developed and compared to state-of-the-art methods. A simulation-based study shows the most benefit applying a modified mutual information test design, followed by a newly developed relevance-based test design with less computational effort. The boundary model and the relevance-based test design are integrated into a multicriterial test design strategy that is tailored to match the requirements of combustion engine test bench measurements. A simulation-based study with seven and nine input parameters and four outputs each offered an average model quality improvement of 36 % and an average measured input area volume increase of 65 % compared to a non-adaptive space-filling test design. The multicriterial test design was applied to a test bench measurement with seven inputs for verification. Compared to a space-filling test design measurement, the improvement could be confirmed with an average model quality increase of 17 % over eight outputs and a 34 % larger measured input area