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IN THIS ISSUE

### Research Papers

J. Dyn. Sys., Meas., Control. 2009;131(3):031001-031001-11. doi:10.1115/1.3072093.

Many active materials exhibit nonlinearities and hysteresis when driven at field levels necessary to meet stringent performance criteria in high performance applications. This often requires nonlinear control designs to effectively compensate for the nonlinear, hysteretic, field-coupled material behavior. In this paper, an optimal control design is developed to accurately track a reference signal using magnetostrictive transducers. The methodology can be directly extended to transducers employing piezoelectric materials or shape memory alloys due to the unified nature of the constitutive model employed in the control design. The constitutive model is based on a framework that combines energy analysis at lattice length scales with stochastic homogenization techniques to predict macroscopic material behavior. The constitutive model is incorporated into a finite element representation of the magnetostrictive transducer, which provides the framework for developing the finite-dimensional nonlinear control design. The control design includes an open loop nonlinear component computed off-line with perturbation feedback around the optimal state trajectory. Estimation of immeasurable states is achieved using a Kalman filter. It is shown that when operating in a highly nonlinear regime and as the frequency increases, significant performance enhancements are achieved relative to conventional proportional-integral control.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2009;131(3):031002-031002-7. doi:10.1115/1.3089557.

Unlike input deadband, the sandwiched deadband between actuator and plant dynamics is very difficult to be explicitly compensated for due to the proceeding actuator dynamics whose effect may not be negligible. The paper presents a practical way to overcome the design conservativeness of existing methods in dealing with sandwiched deadband. Specifically, a describing function based nonlinear analysis method is proposed to characterize the effect of the sandwiched deadband on the stability and performance of the overall closed-loop system. The analysis results can be used to determine the highest closed-loop bandwidth that can be achieved without inducing residual limit cycles and instability. Optimal controller parameters can then be found to maximize the achievable closed-loop control performance. The technique is applied to an electrohydraulic system controlled by closed-center valves and a nonlinear feedback controller. Simulation results showed severe oscillations as the feedback control gains are increased to the predicted threshold values. Comparative experimental results also showed the effectiveness of the proposed method in reducing the conservativeness of traditional design and the improved closed-loop control performance in implementation.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2009;131(3):031003-031003-11. doi:10.1115/1.3072106.

This paper is concerned with the problem of identifying and controlling flexible structures. The structures used exhibit some of the characteristics found in large flexible space structures (LFSSs). Identifying LFSS are problematic in the sense that the modes are of low frequency, lightly damped, and often closely spaced. The proposed identification algorithm utilizes modal contribution coefficients to monitor the data collection. The algorithm is composed of a two-step process, where the input signal for the second step is recomputed based on knowledge gained about the system to be identified. In addition, two different intelligent robust controllers are proposed. In the first controller, optimization is concerned with performance criteria such as rise time, overshoot, control energy, and a robustness measure among others. Optimization is achieved by using an elitism based genetic algorithm (GA). The second controller uses a nested GA resulting in an intelligent linear quadratic regulator/linear quadratic Gaussian (LQR/LQG) controller design. The GAs in this controller are used to find the minimum distance to uncontrollability of a given system and to maximize that minimum distance by finding the optimal coefficients in the weighting matrices of the LQR/LQG controller. The proposed algorithms and controllers are tested numerically and experimentally on a model structure. The results show the effectiveness of the proposed two-step identification algorithm as well as the utilization of GAs applied to the problem of designing optimal robust controllers.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2009;131(3):031004-031004-8. doi:10.1115/1.3072128.

Previous work by the authors developed algorithms for simplifying the structure of a lumped dynamic system model and reducing its order. This paper extends this previous work to enable simultaneous model structure and order reduction. Specifically, it introduces a new energy-based metric to evaluate the relative importance of energetic connections in a model. This metric (1) accounts for correlations between energy flow patterns in a model using the Karhunen–Loève expansion; (2) examines all energetic connections in a model, thereby assessing the relative importance of both energetic components and their interactions, and enabling both order and structural reduction; and (3) is realization preserving, in the sense of not requiring a state transformation. A reduction scheme based on this metric is presented and illustrated using a simple example. The example shows that the proposed method can successfully concurrently reduce model order and structure without requiring a realization change, and that it can provide an improved assessment of the importance of various model components due to its correlation-based nature.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2009;131(3):031005-031005-12. doi:10.1115/1.3072148.

The small-scale bioethanol steam reforming system (FBSR), using sunlight applied to a heat source, is a very clean method, which can supply fuel to a fuel cell. However, it is difficult to analyze the operation planning of this system with high precision. If such an analytical algorithm is developed, the optimum operation of this system will be realized by the command of the control device. However, the difficulty of weather forecasts, such as solar radiation and outside-air-temperature, to date has made it difficult to achieve rapid and highly precise results and to analyze the system operation. In this paper, an algorithm, which analyzes the operation planning of the FBSR on arbitrary days, is developed using the neural network. The weather pattern for the past 1 year is input into this algorithm, and the operation planning of the FBSR, based on the same weather pattern, is given as a training signal. In this paper, the operation results of the system obtained via genetic algorithm (GA) were used as the training signal for the neural network. Operation planning (the amount of hydrogen production and the amount of exhaust heat storage) of the system on arbitrary days could be obtained rapidly by ensuring that input data (the weather and energy-demand patterns) are channeled into the learned neural network following this study. Moreover, in order to investigate the accuracy of the operational analysis via the proposed algorithm, it is compared with the analysis result of operation planning using the GA.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2009;131(3):031006-031006-10. doi:10.1115/1.3072149.

This paper considers the design of linear iterative learning control algorithms using the discrete Fourier transform of the measured impulse response of the system or plant under consideration. It is shown that this approach leads to a transparent design method whose performance is then experimentally benchmarked on an electromechanical system. The extension of this approach to the case when there is uncertainty associated with the systems under consideration is also addressed in both algorithm development and experimental benchmarking terms. The robustness results here have the applications oriented benefit of allowing the designer to manipulate the convergence and robustness properties of the algorithm in a straightforward manner.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2009;131(3):031007-031007-9. doi:10.1115/1.3072150.

Eddy current sensors provide an inexpensive means of detecting surface and embedded flaws in metallic structures due to fatigue, corrosion, and manufacturing defects. However, use of eddy current sensors for imaging flaws to determine their geometry is limited by sensitivity and mathematical uniqueness issues, as the magnetic flux distribution sensed at the boundary of a structure can be similar for dissimilar flaw geometries or flaw depths. This paper investigates the use of feedback control based on measured magnetic flux at a point on the boundary of the structure in order to address sensitivity and uniqueness issues for eddy current sensors and thus to enhance the ability to use these simple inexpensive sensors to determine flaw geometry. Using a parametrized two-dimensional flaw in which width and depth of the flaw are to be determined, scalar metrics are developed to relate the forward solution of the electromagnetic dynamics to the inverse problem of damage geometry reconstruction. Geometry is determined by interpolating metrics on a mesh and employing a systematic ranking process that is robust to weakly unique inverse problems. Finally, the concept of sensitivity enhancing feedback control (SEC) is applied to enrich the data set in order to improve damage geometry reconstruction. SEC feeds back measured magnetic flux at a single point along a scan line to affect the current density. Closed-loop compensation of eddy current dynamics is shown to improve uniqueness of scalar damage metrics to damage geometry parameters. Performance is demonstrated by simulation of geometry construction using finite-element models of two-dimensional flaws embedded in a material, both with and without feedback control and for noisy and noiseless simulated magnetic flux density measurement. For noiseless data, flaw depth and width are reconstructed within the resolution of the mesh (0.01 mm) using feedback control, while the relative accuracy of damage geometry identification for open-loop data is on the order of 0.1 mm in each dimension. Simulation of damage geometry identification with noisy data demonstrates lower relative error using closed-loop data, as measured by the mean and standard deviation in identified depth and width.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2009;131(3):031008-031008-11. doi:10.1115/1.3072151.

Theoretical analysis of the stability problem for the control systems with distributed parameters shall be given. The approach to the analysis of such systems can be composed of two parts. First, the distributed parameter element is modeled by a frequency response function. Second, approximate conditions of parametric resonance are derived by a method of stationarization (describing functions of time-variant elements). The approach is illustrated by two examples. One is a robot-manipulator arm (distributed mechanical parameter system) controlled by a controller with a modulator/demodulator cascade (time-varying element). Another is an electromechanical transformer that consists of a constant current motor and a synchronous generator. Inductance between stator windings and the rotor of the synchronous generator serves as a periodical time-varying parameter, and a long electrical line plays the role of an element with distributed parameters. In both examples, dangerous (in terms of the first parametric resonance) regions for time-varying parameter are obtained theoretically and compared with simulation experiment.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2009;131(3):031009-031009-10. doi:10.1115/1.3072152.

Explicit motion-planning reference solutions are presented for flexible beams with Kelvin–Voigt (KV) damping. The goal is to generate periodic reference signals for the displacement and deflection angle at the free-end of the beam using only actuation at the base. The explicit deflection angle reference solution is found as a result of writing the shear beam model in a strict-feedback form. Special “partial differential equation (PDE) backstepping” transformations relate the strict-feedback model to a “target system,” governed by an exponentially stable wave equation with KV damping, whose displacement reference solution is relatively easy to find. The explicit beam displacement reference solution is found using the target system solution and an inverse backstepping transformation. The explicit reference solutions for the wave equation and shear beam with KV damping are novel results. State-feedback tracking boundary controllers are found by extending previous PDE backstepping stabilization results. Application of the shear beam results to the more complicated Timoshenko beam is discussed.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2009;131(3):031010-031010-7. doi:10.1115/1.3072157.

This paper presents a robust design scheme for an inertial measurement unit (IMU) composed only of accelerometers. From acceleration data measured by a redundant set of accelerometers, the IMU proposed in this paper can estimate the linear acceleration, angular velocity, and angular acceleration of the rigid-body to which it is attached. The robustness of our method to the uncertainty of the locations of the sensors and the measurement noise is obtained through redundancy and optimal configuration of the onboard sensors. In addition, the fail-diagnostics and fail-safe issues are also addressed for reliable operation.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2009;131(3):031011-031011-11. doi:10.1115/1.3089562.

The aim of this article is to present the theoretical and experimental work related to the vacuum system used for controlling the actuation of pneumatic valves in internal combustion engines in order to obtain a physical model of this system. In this context, these valves control the turbocharger operation in a two-stage sequential turbocharged diesel engine. With the purpose of providing the model with information, several characterization tests of the elements that integrate the vacuum system were performed. Related to the theoretical contents, two models of the vacuum system were developed and compared, either by using a 1D or a 0D approach. Within the experimental section the obtained instantaneous pressure in the actuator chamber of four air valves and two storage reservoirs of the circuit are measured and compared with the modeling results. Since the simulations show good agreement when comparing the instantaneous pressure evolutions and valve movement with the experimental data, the model can be used to predict the behavior of the vacuum system. Finally, the model is used to optimize the transient turbocharger sequential operation under real engine running conditions. The simulation results predict with accuracy the measurements acquired in an engine test bench. Therefore a consistent methodology has been established in order to reproduce the vacuum system behavior and can be used as a designing tool for complex applications devoted to engine controlling tasks.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2009;131(3):031012-031012-15. doi:10.1115/1.3089558.

Refinement or improvement of a dynamic system to meet a frequency response specification can benefit from the option to use passive or active compensation, or a combination of both. The process becomes more effective when supplemented with methods derived from classical network theory to synthesize candidate designs for actuators and their control systems. The synthesis procedure presented here provides an explicit way to formulate system topologies that employ passive and active elements to achieve a desired targeted performance specification, i.e., frequency response. Active elements are used to represent elements that are not physically realizable, such as negative impedances and elements that have ill-defined connectivity. A working premise is that these elements indicate the need for actuation technology. Coupled with a topological description of the system, the synthesis procedure provides a systematic approach that offers design solutions not previously conceived of through insight or experience. These “first draft” designs can be improved upon by later utilizing complementary approaches, such as optimization methods, as dictated by detailed system requirements and operating regimes. The flexibility of this synthesis approach allows the consideration of design restrictions unrelated to frequency response, but critical nonetheless in assessing the viability of candidate designs. Further, the procedure does not require assumption of a particular control/compensation architecture at the outset; this renders novel architectures that depart from traditional architectures such as proportional integral, propotional-integral-derivative, etc. The procedure is couched within a simulation basis, so that extension to state-space simulation and thus growth of the system and inclusion of more complex and nonlinear representations become possible. The concept of a virtual state space is introduced, which is integral to the development of controller architectures and associated parameters. It is found that customized passive/active compensation systems can be derived using a bond graph approach, making this approach more easily applicable to multi-energetic systems. Examples are used to demonstrate the approach, including a case study of an electromechanical vehicle suspension, from which an experimental model is derived to illustrate the synthesis procedure. Comparison of results between these examples illustrate the practical utility of the synthesis procedure. In particular, simulations reveal that increasing the number of realized passive elements for a particular system does not necessarily minimize actuator energy consumption. Detailed analysis of synthesis results show that certain design candidates feature active devices that work against either passive elements or other active devices within the system.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2009;131(3):031013-031013-9. doi:10.1115/1.3089563.

This paper deals with the development and validation of an analytical dynamic model of an air-over-hydraulic (AOH) brake system that is widely used on loaders. The AOH system is broken into five simple and cascaded subsystems, pneumatic circuit, air-hydraulic actuator, brake line, wheel cylinder, and disk brake. Pneumatic, hydraulic, and mechanical dynamics are taken care of in each subsystem. The determination of model coefficients is introduced in detail. Many experiments are performed on an experimental setup of the real AOH system on a loader and the experimental data are compared with the simulation results. Preliminary analysis shows that the simulation results are in good agreement with the experimental data. Other researchers in the areas of brake systems in construction machinery would find the model useful for similar system modeling and analysis

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2009;131(3):031014-031014-9. doi:10.1115/1.3072155.

Input shaping is a control method that limits motion-induced oscillation in vibratory systems by intelligently shaping the reference command. As with any control method, the robustness of input shaping to parameter variations and modeling errors is an important consideration. For input shaping, there exists a fundamental compromise between robustness to such errors and system rise time. For all types of shapers, greater robustness requires a longer duration shaper, which degrades rise time. However, if a shaper is allowed to contain negative impulses, then the shaper duration may be shortened with only a small cost of robustness and possible high-mode excitation. This paper presents a thorough analysis of the compromise between shaper duration, robustness, and possible high-mode excitation for several negative input-shaping methods. In addition, a formulation for specified negative amplitude, specified insensitivity shapers is presented. These shapers provide a continuous spectrum of solutions for the duration/robustness/high-mode excitation trade-off. Experimental results from a portable bridge crane verify the theoretical predictions.

Commentary by Dr. Valentin Fuster

### Technical Briefs

J. Dyn. Sys., Meas., Control. 2009;131(3):034501-034501-7. doi:10.1115/1.3072158.

In this paper, we address the problem of robust stabilization and disturbance rejection for a class of hybrid linear systems subject to exponential uncertainties. By using Taylor series approximation and convex polytope technique, the exponentially uncertain hybrid linear system is transformed into an equivalent hybrid polytopic model subject to norm bounded uncertainty. For such equivalent hybrid linear model, we design its switching strategy and associated state feedback controllers so that such model is asymptotically stable with $H∞$ disturbance attenuation based on multiple Lyapunov function technology and linear matrix inequality (LMI) approach.

Commentary by Dr. Valentin Fuster