Frank J. Kern

The stability of polynomials under correlated coefficient perturbations

In this paper the robust stability of polynomials with repect to real parameter variations is investigated. The coefficients of the polynomial are assumed to be linear functions of several real parameters. An algorithm to calculate the maximum allowable variations of the parameters so that the roots still remain in prescribed regions of the complex plane is presented. Examples are given to illustrate the method.

Robust control of flexible structures using multiple shape memory alloy actuators

The design and implementation of control strategies for large, flexible smart struc tures presents challenging problems. To demonstrate the capabilities of shape-memory-alloy (SMA) actuators, we have designed and fabricated a three-mass test article with multiple shape-memory- alloy, NiTiNOL, actuators. Both force and moment actuators were implemented on the structure to examine the effects of control structure interaction and to increase actuation force. These SMA actu ators exhibit nonlinear effects due to dead band and saturation. The first step in the modeling process was the experimental determination of the transfer function matrix derived from frequency response data. A minimal state space representation was determined based on this transfer function matrix. Finally, a reduced order state space model was derived from the minimal state space representation. The simplified analytical models were compared with models developed by structural identification techniques based on vibration test data. From the reduced order model, a controller was designed to dampen vibrations in the test bed. To minimize the effects of uncertainties on the closed-loop system performance of smart structures, a linear quadratic Gaussian loop transfer recovery, LQG / LTR, control methodology was utilized. A standard LQG/LTR controller was designed; however, this controller could not achieve the desired performance robustness due to saturation effects. Therefore, a modified LQG / LTR design methodology was implemented to accommodate for the limited control force provided by the actua tors. The closed-loop system response of the multiple input multiple output (MIMO) test article with robustness verification was experimentally obtained and is presented in this paper. The modified LQG / LTR controller demonstrated performance and stability robustness to both sensor noise and parameter variations.

Robust Control of a CSI-Fed Induction Motor Drive System

An application of modern control theory to the control of a current-source-inverter (CSI) fed induction motor drive system is presented. A linear quadratic Gaussian (LQG) control scheme is developed in which the Kalman filter is tuned for high robustness by a method of Doyle and Stein. The design is carried out for a sample system, and the robustness analysis and computer simulation results are included.

Multivariable Neural Network Based Controllers for Smart Structures

This paper details identification and robust control of smart structures using artificial neural networks. To demonstrate the use of artificial neural networks in the control of smart structural systems, two smart structure test articles were fabricated. Active materials like piezoelectric (PZT), polyvinylidene (PVDF) and shape memory alloys (SMA) were used as actuators and sensors. The Eigensystem Realization Algorithm (ERA), a structural identification method has been utilized to determine a minimal order discrete time state space model of the test articles. The ERA requires the Markov parameters of the physical system. A neural network based method has been developed to estimate the Markov parameters of a multi input multi output system from experimental test data. The accelerated adaptive learning rate algorithm and the adaptive activation function were utilized to improve the learning characteristics of the network and reduce the learning time. The identified models were used to design a robust controllers for vibration suppression of smart structures using a modified Linear Quadratic Gaussian with Loop Transfer Recovery (LQG/LTR) method. This control design methodology has better loop transfer recovery properties while accommodating the limited control force available from the SMA and the PZT actuators. This controller was copied into a feedforward neural network using the connectionist approach. This neural network controller was implemented using a PC based data acquisition system. The closed loop performance and robustness properties of the conventional and the neural network based controller are compared experimentally.

Modeling and robust control of smart structures

The design and implementation of control strategies for large, flexible smart structures presents challenging problems. One of the difficulties arises in the approximation of high- order finite element models with low order models. Another difficulty in controller design arises from the presence of unmodeled dynamics and incorrect knowledge of the structural parameters. In this paper, the balance-truncation reduced-order models are employed in deriving lower-order models for complex smart structures. These methods do not introduce any spill-over problems in the closed-loop response of the system. The simplified analytical models are compared with models developed by structural identification techniques based on vibration test data. To minimize the effects of uncertainties on the closed-loop system performance of smart structures, robust control methodologies have been employed in the design of controllers. The reduced order models are employed in the design of robust controllers. To demonstrate the capabilities of shape-memory-alloy actuators, we have designed and fabricated a three-mass test article with multiple shape-memory-alloy (NiTiNOL) actuators. Generally, the non-collocation of actuators and sensors presents difficulties in the design of controllers. Controllers for a test article with non-collocated sensors and actuators are designed, implemented and tests. The closed-loop system response of the test article with two actuators and sensors has been experimentally determined and presented in the paper.

H∞ optimal control of smart structures

The design and implementation of control strategies for large, flexible smart structures presents challenging problems. Uncertainties stem from control structure interaction, modeling errors, and parameter variations (such as fuel consumption). We developed a new algorithm called H(infinity ) robust control for natural frequency variations (H(infinity )/NF) that includes the knowledge of the natural frequency uncertainty bounds. In addition, we were successful in implementing this algorithm on a flexible smart structure in our laboratory. This smart structure was a cantilever beam that used NiTiNOL shape memory alloy (SMA) actuators. The performance of H(infinity )/NF algorithm was compared with the modified LQG/LTR algorithm using a settling time specification. The H(infinity )/NF controller exhibited dramatically reduced sensitivity to natural frequency uncertainty as compared to the modified LQG/LTR controller. The standard LQG/LTR control algorithm produced controllers that saturated the NiTiNOL actuators used on the test article. To overcome this saturation problem, we used a modified LQG/LTR design algorithm. We successfully implemented the proposed algorithm on a simple cantilever beam test article.

Robust control of smart structures using neural network hardware

In this paper, the use of Intels Electronically Trainable Analog Neural Network (ETANN) chipi80170NX for implementing single-chip robust controllers for smart structures is successfully demonstrated. Robust controllers like the linear quadratic regulator (LQR) and linear quadratic Gaussian with loop transfer recovery (LQG/LTR) are implemented in various configurations using the ETANN chip on the smart structure test article. The test article is a cantilevered plate with PZTs as actuators and shaded PVDF film as sensors. The spatially distributed sensors allow direct measurement of the states of the system enabling the implementation of the LQR controller. A two step connectionist approach is used to design and implement the neural network based controllers. First a robust controller is designed using conventional design techniques to meet the required closed loop performance. The controller dynamics are copied into the ETANN chip and the trained chip is used to control the test structure. A custom interface board and external signal conditioning circuits are developed to interface the neural network chip with the sensors and actuators on the smart structure test article. The steps involved in training and implementing the robust controllers on a smart structure are detailed. Some of the practical considerations of implementing the controller using the ETANN chip are pointed out and some suggestions made to deal with the limitations. Simulation and experimental results of the closed loop system with all the controller implementation models are presented.

Identification and robust control of flexible structures using shape memory actuators

The application of shape memory alloy materials as actuators and sensors in the active control of flexible structures has been extensively reported in the literature. The design of active controllers plays an important role in the overall development of smart structures for a given application. To design active controllers for flexible structures, a mathematical representation of the system is needed. The process of constructing a model to describe the vibration properties of a structure based on experimental test data is known as structural identification method. To account for any uncertainties in the structural models and to accomplish good closed loop system performance and noise suppression properties, we have developed robust control design methodologies for flexible structures. We have utilized the eigensystem realization algorithm (ERA) for system identification and linear quadratic Gaussian with loop transfer recovery (LQG/LTR) method for designing robust controllers for a simple cantilever beam test article. The shape memory alloy, NiTiNOL, is used as an actuator. The LQG/LTR method has been modified to accommodate the limited control force provided by the actuators. The closed loop performance of the cantilever beam is experimentally determined for various types of uncertainties. The properties of robust controllers are demonstrated.

Control of smart structures using analog neural network hardware

In this paper a robust controller has been implemented on a smart structure test article using the Intels Electronically Trainable Analog Neural Network (ETANN) chip i80170NX. The smart structure test article used in this study was a cantilever plate with a pair of PZTs as actuators and PVDF film sensors. A two step connectionist approach was used to design and implement the neural network based controller. To meet the desired closed loop performance requirements, a simple linear quadratic regulator (LQR) controller is designed. The spatially distributed sensors allow the direct measurement and feedback of the states of the system. A copy of this controller is transferred into the ETANN chip and the trained chip is used to control the test system. A custom board and electronic circuits were developed for interfacing the neural network chip and the smart structure test article. The steps involved in training and implementing robust controllers on a smart structure have been outlined. Some of the practical considerations of implementing a robust controller using the ETANN chip have been pointed out and dealt with. Experimental verification of the closed loop performance of the conventional LQR controller as well as the neural network controller are also shown.

Mixed H 2 and H ∞ optimal control of smart structures

The research described in this paper integrates robust control design methodologies with flexible smart structures for achieving desired performance in the presence of uncertainties. The primary parameter uncertainty associated with smart structures is natural frequency variations. A control algorithm that incorporates the natural frequency variations and accommodates the available control effort is presented. The robustness properties are varified by implementing the proposed controller on smart structure test articles.<<ETX>>