Robert K. Butler

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.

A state space modeling and control method for multivariable smart structural systems

A system identification technique for the derivation of minimal, continuous time state variable models for multivariable smart structural systems is presented. The structural identification technique is based on the measurement of eigenvalues and eigenvectors of the structure. Two sensors are required for each mode included in the structural system model. Unlike computational system identification techniques, the relatively large number of sensors simplifies the identification process making it ideal for systems with several inputs and outputs. Additionally, the identification technique allows the implementation of multi-input multi-output full state feedback controllers with simple analog hardware. The amount of hardware required for the implementation of an analog linear quadratic regulator is significantly reduced from standard discrete control implementation methods and stability margins are retained. The eigenvectors of distributed parameter structural systems are examined. For a general unknown system, the eigenvalues and eigenvectors cannot be directly measured. For the lightly damped structural systems considered in this paper however, it is shown that these measurements are possible. Eigenvalues are conspicuous in the frequency domain and the eigenvectors exist at near steady state conditions. By utilizing a priori knowledge of the structural system, the eigenvectors can be estimated from steady state sinusoidal amplitude measurements. The identification procedure utilizes n measurement variables of the structural system with n/2 modes to produce a nth order model. This allows for the measurements to be defined as the model states. It is shown that an array consisting of n/2 sensors on the structure and some simple analog hardware suffice for the identification. For symmetrical systems, it is shown that the number of sensors required for the model identification is reduced further. A variety of measurement devices and techniques are discussed in relation to the proposed system identification technique. A sensor array consisting of shaped and segmented polyvinylidene fluoride film is presented as an inexpensive and practical measurement device. A procedure for the generation of distributed sensors for state variable measurement is presented. Identification and control are successfully implemented on a multivariable cantilever plate system and experimental results are presented.

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.

Identification and control of two-dimensional smart structures using distributed sensors

In recent years, polyvinylidene fluoride (PVDF) film has been extensively used in the development of distributed sensors. However, very few results are available for shaping distributed sensors for control of two dimensional structures. In this study, we have utilized simple geometric shapes for the implementation of feedback controllers on a cantilevered plate system. Multiple distributed sensors along with their time derivatives are used for system identification and the implementation of complex controllers. The resulting direct implementation minimizes the electronic hardware requirements of the controller. A system identification technique for deriving a state variable representation of the structural system using distributed sensors is studied. The state variables of the model are defined as the quantities being measured by the distributed sensors. This technique was originally developed for one-dimensional structures and is extended to the two-dimensional plate system in this paper. The availability of the states of the system simplifies the state space control system design and the implementation of full-state feedback controllers. Linear quadratic regulator (LQR) and H(infinity ) controllers can be implemented with simple analog hardware. A full state feedback LQR controller is implemented on the experimental system which incorporates all of the necessary signal conditioning electronics. The results of simulation and experimental results are presented.

Design of Robust Controllers for Smart Structural Systems with Actuator Saturation

The design and implementation of robust controllers on smart structural systems is often constrained by available control force of the actuators. The Lead Zirconite Titanate (PZT) actuators which are used for the control of flexible structures have limited control authority. The performance of the smart structural systems is often limited by the control effort constraint instead of the closed loop stability and performance. Due to the limited availability of control effort, it is desirable to utilize all of the control force in order to obtain the best performance. The research results described in this paper integrate robust control design methodologies with constrained actuator techniques for designing controllers for smart structural systems. In order to implement the proposed controllers, a two-dimensional lattice structure is designed and fabricated. The robust controllers in this paper have been designed for this test article. We have also developed the uncertainty modeling for this test article. An H2/H. controller has been designed and implemented on the lattice structure. The experimental results of the closed-loop system and the verification of the robustness properties are also presented.

Robust multiobjective controllers for smart structures

Flexible smart structures are large mechanical structures with applications in which specific performance characteristics are desired in the presence of parameter variations and disturbances. These structures tend to have severe controller effort restrictions and tightly spaced lightly damped modes. When designing controllers for smart structures, H2 controllers are well suited for control effort restrictions and closed loop performance specifications while H. controllers are better suited for modeling uncertainties. This paper examines the application of H2 /H,,. controller design methodologies to smart structures. A unique feature of mechanical distributed systems is that state space systems can be determined from finite element models (FEM) in which the states have physical significance. For certain systems, these states can be directly measured by using a distributed PVDF film appropriately shaped and applied to the structure. This full state feedback system allows for the implementation of H2 /Ho:: full state feedback algorithms. The development of a control system implementing this type of algorithm is described for a simple cantilever beam. In addition, a H2 /HOD algorithm developed by Bernstein and Haddad is investigated for the cantilever beam. This method does not require state measurement, but the controller design algorithm is slightly more complicated. This algorithm requires the solution of one algebraic Riccati equation and two coupled algebraic Riccati equations which are solved iteratively.

Robust Control of Flexible Structures Using Multiple Shape Memory Alloy Actuators

The design and implementation of control strategies for large, flexible smart structures presents challenging problems. 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. The force and moment actuators were implemented on the structure to examine the effects of control structure interaction and to increase actuation force. These SMA actuators exhibit nonlinear effects due to deadband 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 in order to reduce the order of the controller, a reduced order state space model was derived from the minimal state space representation. The simplified analytical models are 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 LQG/LTR control methodology has been utilized. An initial 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 actuators. The closed-loop system response of the multiple input-multiple output (MIMO) test article with robustness verification has been experimentally obtained and presented in the paper. The modified LQG/LTR controller demonstrated performance and stability robustness to both sensor noise and parameter variations.

Controller implementation on infinite-order structural systems using distributed sensors

The design of spatially shaped distributed sensors for the control of infinite order structural systems has become a topic of interest in recent years. Sensor shape optimization techniques were developed for the design of optimal controllers on infinite order structural systems. In this paper, we investigate methods for the implementation of distributed sensors using polyvinylidene flouide (PVDF) film. The complexity of the sensor shapes depends on the mode shapes of the flexible structure and the performance measure of the controllers. The sensitivity of the sensor shape on the performance of the controller is being investigated. The problems associated with the practical implementation of distributed sensors with PVDF film are also identified. The shapes of the distributed sensors for the implementation of a linear quadratic regulator (LQR) and a pole- placement controller have been determined. These sensors are implemented on simple cantilever beam test articles using PVDF film. The details of hardware implementation of the controllers are presented. The closed loop performance of the controllers are compared with simulation studies. The sensitivity of the shapes of the distributed sensors for the LQR and pole-placement controllers is discussed.

Optimal control of infinite-order smart composite structural systems using distributed sensors☆

Abstract In recent years there has been considerable interest in the design of spatially shaped distributed sensors for the control of infinite-order structural systems. The smart materials polyvinylidene fluoride (PVDF) and shape-memory alloys can be utilized in the development of customized distributed sensors. Sensor shape-optimization techniques are needed for the implementation of optimal control strategies. In this paper, a method for generating the shapes of distributed sensors using finite-dimensional approximations to desired curvature and curvature rate kernels is examined. The output of these spatially distributed sensors is utilized directly as the control signal for suppressing vibrations in infinite-order structural systems. This paper shows that the desired kernels can be generated directly from finite element models of distributed structures without generating displacement and displacement-rate kernels. The curvature and curvature-rate kernels are the desired kernels in the development of shape functions for PVDF sensors for the implementation of controllers. This procedure requires covering the entire structure with a customized sensor for each kernel. To alleviate this problem, a sensor is proposed which covers a portion of the structure with spatially distributed material and uses an observer for the estimation of the states. The original control algorithm is implemented by using the proposed sensor and observer. The usefulness of a single, relatively small customized PVDF film sensor along with an observer to provide full state-feedback information for the entire structure is examined. The complexity and performance of the proposed control scheme are compared with the original distributed sensor implementation.

State measurement and system identification of a cantilever beam using distributed polyvinylidene fluoride (PVDF) film sensors

This paper contains theoretical and experimental results of controlling cantilever beams using distributed sensors. Shape functions for custom-made sensors are derived which allow for the identification and measurement of the states of a distributed system. This proposed technique allows for the direct identification of single-input single-output and multi-input multi-output system models as well as the implementation of full state feedback controllers without state estimation. Simple analog hardware circuits suffice to implement full state feedback controllers. System models can be identified quickly from time domain data for on-line controller adaptation. The suggested system identification method has the capacity to model only the modes of interest without relying on model reduction techniques.