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Research Papers

J. Dyn. Sys., Meas., Control. 2009;131(4):041001-041001-10. doi:10.1115/1.3089561.

We present a boundary feedback law that stabilizes the velocity, pressure, and electromagnetic fields in a magnetohydrodynamic (MHD) channel flow. The MHD channel flow, also known as Hartmann flow, is a benchmark for applications such as cooling, hypersonic flight, and propulsion. It involves an electrically conducting fluid moving between parallel plates in the presence of an externally imposed transverse magnetic field. The system is described by the inductionless MHD equations, a combination of the Navier–Stokes equations and a Poisson equation for the electric potential under the MHD approximation in a low magnetic Reynolds number regime. This model is unstable for large Reynolds numbers and is stabilized by actuation of velocity and the electric potential at only one of the walls. The backstepping method for stabilization of parabolic partial differential equations (PDEs) is applied to the velocity field system written in appropriate coordinates. Control gains are computed by solving a set of linear hyperbolic PDEs. Stabilization of nondiscretized 3D MHD channel flow has so far been an open problem.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2009;131(4):041002-041002-8. doi:10.1115/1.3089565.

A novel active vibration control technique based on positive position feedback method is developed. This method, which is a modified version of positive position feedback, employs a first-order compensator that provides damping control and a second-order compensator for vibration suppression. In contrast, conventional positive position feedback uses a single second-order compensator. The technique is useful for strain-based sensors and can be applied to piezoelectrically controlled systems. After introducing the concept of modified positive position feedback, this paper investigates the stability of the new method for locating gain limits. Stability conditions are global and independent of the dynamical characteristics of the open-loop system. Using root locus plots, proper compensator frequency is identified and damping of the closed-loop system is studied. The performance of the modified positive position feedback for both steady-state and transient dynamic control is studied. The experimental and numerical results show that the proposed method is significantly more effective in controlling steady-state response and slightly advantageous for transient dynamics control, as compared with conventional positive position feedback.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2009;131(4):041003-041003-10. doi:10.1115/1.3117185.

Flexibility at the joint of a manipulator is an intrinsic property. Even “rigid-joint” robots, in fact, possess a certain amount of flexibility. Previous experiments confirmed that joint flexibility should be explicitly included in the model when designing a high-performance controller for a manipulator because the flexibility, if not dealt with, can excite system natural frequencies and cause severe damage. However, control design for a flexible-joint robot manipulator is still an open problem. Besides being described by a complicated system model for which the passivity property does not hold, the manipulator is also underactuated, that is, the control input does not drive the link directly, but through the flexible dynamics. Our work offers another possible solution to this open problem. We use three-layer neural networks to represent the system model. Their weights are adapted in real time and from scratch, which means we do not need the mathematical model of the robot in our control algorithm. All uncertainties are handled by variable-structure control. Backstepping structure allows input efforts to be applied to each subsystem where they are needed. Control laws to adjust all adjustable parameters are devised using Lyapunov’s second method to ensure that error trajectories are globally uniformly ultimately bounded. We present two state-feedback schemes: first, when neural networks are used to represent the unknown plant, and second, when neural networks are used to represent the unknown parts of the control laws. In the former case, we also design an observer to enable us to design a control law using only output signals—the link positions. We use simulations to compare our algorithms with some other well-known techniques. We use experiments to demonstrate the practicality of our algorithms.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2009;131(4):041004-041004-11. doi:10.1115/1.3089560.

A hybrid nonlinear optimal control design is experimentally implemented on a magnetostrictive Terfenol-D actuator to illustrate enhanced tracking control at relatively high speed. The control design employs a homogenized energy model to quantify rate-dependent nonlinear and hysteretic ferromagnetic switching behavior. The homogenized energy model is incorporated into a finite-dimensional nonlinear optimal control design to directly compensate for the nonlinear and hysteretic magnetostrictive constitutive behavior of the Terfenol-D actuator. Additionally, robustness to operating uncertainties is addressed by incorporating proportional-integral (PI) perturbation feedback around the optimal open loop response. Experimental results illustrate significant improvements in tracking control in comparison to PI control. Accurate displacement tracking is achieved for sinusoidal reference displacements at frequencies up to 1 kHz using the hybrid nonlinear control design, whereas tracking errors become significant for the PI controller for frequencies equal to or greater than 500 Hz.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2009;131(4):041005-041005-10. doi:10.1115/1.3089564.

The prediction of a mechanical structure’s rigid dynamic behavior requires knowledge of ten inertia parameters. In cases where no accurate models of the structure’s geometry and mass distribution are available, the ten inertia parameters must be determined experimentally. Experimental methods based on measurements of frequency response functions (FRFs) are subject to bias errors due to suspension effects. This paper proposes a method for eliminating these errors by using a single-wire suspension condition and modeling the suspension’s effect on the FRFs. The suspension model depends only on the unknown rigid body properties and on three easy-to-measure parameters. The rigid body properties are determined by fitting FRFs derived from the suspension model and from the rigid body mass matrix directly to the experimental FRF data. Eliminating the suspension bias makes it possible to use low-frequency FRF data, which in turn justifies the assumption of rigid behavior. In this way, bias-free rigid body property identification can be achieved without modal curve fitting. Simulation and experimental results are presented showing the effectiveness of the approach.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2009;131(4):041006-041006-8. doi:10.1115/1.3117189.

An autonomous vibration controller that adapts to variations in a system’s mass, stiffness, and excitation, and that maximizes dissipation through synchronized switching is described. In the model and laboratory measurements, a cantilever beam is driven through base excitation and two piezoelectric elements are attached to the beam for vibration control purposes. The distributed-parameter model for the beam-element system is discretized by using Galerkin’s method, and time histories of the system’s response describe the controller’s attenuation characteristics. The system is piecewise linear, and a state-to-state modal analysis method is developed to simulate the coupled dynamics of the beam and piezoelectric circuit by mapping the generalized coordinates between the sets of modes for the open-switch and closed-switch configurations. In synchronized switching control, the elements are periodically switched to an external resonant shunt, and the instants of optimal switching are identified through a filtered velocity signal. The controller adaptively aligns the center frequency of a bandpass filter to the beam’s fundamental frequency through a fuzzy logic algorithm in order to maximize attenuation even with minimal a priori knowledge of the excitation or the system’s mass and stiffness parameters. In implementation, the controller is compact owing to its low inductance and computational requirement. The adaptive controller attenuates vibration over a range of excitation frequencies and is robust to variations in system parameters, thus outperforming traditional synchronized switching.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2009;131(4):041007-041007-7. doi:10.1115/1.3117192.

Thermoacoustic instabilities in combustors have been suppressed using phase-shift algorithms pulsing an on-off actuator at the limit cycle frequency (flc) or at the subharmonics of flc. It has been suggested that control at a subharmonic rate may extend the actuator lifetime and possibly require less actuator bandwidth. This paper examines the mechanism of subharmonic control in order to clarify the principles of operation and subsequently identify potential advantages for combustion control. Theoretical and experimental arguments show that there must be a Fourier component of the subharmonic control signal at flc in order to stabilize the limit cycling behavior. It is also demonstrated that the magnitude of that Fourier component must be equivalent to the signal magnitude for a linear phase-shift controller that operates directly at flc. The concept of variable-subharmonic control is introduced whereby the actuator is pulsed at the instability frequency to initially stabilize the system and then is pulsed at a subharmonic frequency to maintain stability. These results imply that an actuator used for subharmonic control cannot be effective unless its bandwidth spans the instability frequency. The advantage of reduced cycling may still be realized but will require higher control authority to produce the same effect as an actuator pulsed at the instability frequency.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2009;131(4):041008-041008-11. doi:10.1115/1.3117197.

It is shown that output sensitivities of dynamic models can be better delineated in the time-scale domain. This enhanced delineation provides the capacity to isolate regions of the time-scale plane, coined as parameter signatures, wherein individual output sensitivities dominate the others. Due to this dominance, the prediction error can be attributed to the error of a single parameter at each parameter signature so as to enable estimation of each model parameter error separately. As a test of fidelity, the estimated parameter errors are evaluated in iterative parameter estimation in this paper. The proposed parameter signature isolation method (PARSIM) that uses the parameter error estimates for parameter estimation is shown to have an estimation precision comparable to that of the Gauss–Newton method. The transparency afforded by the parameter signatures, however, extends PARSIM’s features beyond rudimentary parameter estimation. One such potential feature is noise suppression by discounting the parameter error estimates obtained in the finer-scale (higher-frequency) regions of the time-scale plane. Another is the capacity to assess the observability of each output through the quality of parameter signatures it provides.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2009;131(4):041009-041009-11. doi:10.1115/1.3023142.

Degradation in the cooling effectiveness of a charge-air cooler (CAC) in a medium-duty turbocharged diesel engine has significant impact on engine performance. This degradation lowers the boost pressure and raises the intake manifold temperature. As a result, the engine provides lower horsepower and higher hydrocarbon levels than the rated values. The objective of this research is to monitor the health of the charge-air cooler by analyzing the intake manifold temperature signal. Experiments were performed on a Cummins ISB series turbocharged diesel engine, a 6-cylinder inline configuration with a 5.9 l displacement volume. Air flowing over the cooler was blocked by varying amounts, while various engine temperatures and pressures were monitored at different torque-speed conditions. Similarly, data were acquired without the introduction of any fault in the engine. For the construction of the manifold temperature trajectory vector, average mutual information estimates and a global false nearest neighbor analysis were used to find the optimal time parameter and embedding dimensions, respectively. The prediction of the healthy temperature vector was done by local linear regression using torque, speed, and their interaction as exogenous variables. Analysis of residuals generated by comparing the predicted healthy temperature vector and the observed temperature vector was successful in detecting the degradation of the charge-air cooler. This degradation was quantified by using box plots and probability density functions of residuals generated by comparing intake manifold temperature of healthy and faulty charge-air coolers. The general applicability of the model was demonstrated by successfully diagnosing a fault in the exhaust gas recirculation cooler of a different engine.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2009;131(4):041010-041010-8. doi:10.1115/1.3117200.

Modeling dynamic systems incurring stochastic disturbances for deriving a control policy is a ubiquitous task in engineering. However, in some instances obtaining a model of a system may be impractical or impossible. Alternative approaches have been developed using a simulation-based stochastic framework, in which the system interacts with its environment in real time and obtains information that can be processed to produce an optimal control policy. In this context, the problem of developing a policy for controlling the system’s behavior is formulated as a sequential decision-making problem under uncertainty. This paper considers the problem of deriving a control policy for a dynamic system with unknown dynamics in real time, formulated as a sequential decision-making under uncertainty. The evolution of the system is modeled as a controlled Markov chain. A new state-space representation model and a learning mechanism are proposed that can be used to improve system performance over time. The major difference between the existing methods and the proposed learning model is that the latter utilizes an evaluation function, which considers the expected cost that can be achieved by state transitions forward in time. The model allows decision-making based on gradually enhanced knowledge of system response as it transitions from one state to another, in conjunction with actions taken at each state. The proposed model is demonstrated on the single cart-pole balancing problem and a vehicle cruise-control problem.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2009;131(4):041011-041011-7. doi:10.1115/1.3117202.

The increasing complexity of engineering systems has motivated continuing research on computational learning methods toward making autonomous intelligent systems that can learn how to improve their performance over time while interacting with their environment. These systems need not only to sense their environment, but also to integrate information from the environment into all decision-makings. The evolution of such systems is modeled as an unknown controlled Markov chain. In a previous research, the predictive optimal decision-making (POD) model was developed, aiming to learn in real time the unknown transition probabilities and associated costs over a varying finite time horizon. In this paper, the convergence of the POD to the stationary distribution of a Markov chain is proven, thus establishing the POD as a robust model for making autonomous intelligent systems. This paper provides the conditions that the POD can be valid, and be an interpretation of its underlying structure.

Topics: Chain , Probability
Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2009;131(4):041012-041012-9. doi:10.1115/1.3117205.

A substantial opportunity exists to reduce carbon dioxide (CO2) emissions, as well as dependence on foreign oil, by developing strategies to cleanly and efficiently use biodiesel, a renewable domestically available alternative diesel fuel. However, biodiesel utilization presents several challenges, including decreased fuel energy density and increased emissions of smog-generating nitrogen oxides (NOx). These negative aspects can likely be mitigated via closed-loop combustion control provided the properties of the fuel blend can be estimated accurately, on-vehicle, in real-time. To this end, this paper presents a method to practically estimate the biodiesel content of fuel being used in a diesel engine during steady-state operation. The simple generalizable physically motivated estimation strategy presented utilizes information from a wideband oxygen sensor in the engine’s exhaust stream, coupled with knowledge of the air-fuel ratio, to estimate the biodiesel content of the fuel. Experimental validation was performed on a 2007 Cummins 6.7 l ISB series engine. Four fuel blends (0%, 20%, 50%, and 100% biodiesel) were tested at a wide variety of torque-speed conditions. The estimation strategy correctly estimated the biodiesel content of the four fuel blends to within 4.2% of the true biodiesel content. Blends of 0%, 20%, 50%, and 100% were estimated to be 2.5%, 17.1%, 54.2%, and 96.8%, respectively. The results indicate that the estimation strategy presented is capable of accurately estimating the biodiesel content in a diesel engine during steady-state engine operation. This method offers a practical alternative to in-the-fuel type sensors because wideband oxygen sensors are already in widespread production and are in place on some modern diesel vehicles today.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2009;131(4):041013-041013-10. doi:10.1115/1.3117209.

Among other applications, accelerometer arrays have been used extensively in crashworthiness to measure the acceleration field of the head of a dummy subjected to impact. As it turns out, most accelerometer arrays proposed in the literature were analyzed on a case-by-case basis, often not knowing what components of the rigid-body acceleration field the sensor allows to estimate. We introduce a general model of accelerometer behavior, which encompasses the features of all acclerometer arrays proposed in the literature, with the purpose of determining their scope and limitations. The model proposed leads to a classification of accelerometer arrays into three types: point-determined; tangentially determined; and radially determined. The conditions that define each type are established, then applied to the three types drawn from the literature. The model proposed lends itself to a symbolic manipulation, which can be readily automated, with the purpose of providing an evaluation tool for any acceleration array, which should be invaluable at the development stage, especially when a rich set of variants is proposed.

Commentary by Dr. Valentin Fuster

Technical Briefs

J. Dyn. Sys., Meas., Control. 2009;131(4):044501-044501-7. doi:10.1115/1.3117183.

The automotive cooling system has unrealized potential to improve internal combustion engine performance through enhanced coolant temperature control and reduced parasitic losses. Advanced automotive thermal management systems use controllable actuators (e.g., smart thermostat valve, variable speed water pump, and electric radiator fan) that must work in harmony to control engine temperature. One important area of cooling system operation is warm-up, during which fluid flow is regulated between the bypass and radiator loops. A fundamental question arises regarding the usefulness of the common thermostat valve. In this paper, four different thermostat configurations were analyzed, with accompanying linear and nonlinear control algorithms, to investigate warm-up behaviors and thermostat valve operations. The configurations considered include factory, two-way valve, three-way valve, and no valve. Representative experimental testing was conducted on a steam-based thermal bench to examine the effectiveness of each valve configuration in the engine cooling system. The results clearly demonstrate that the three-way valve has the best performance as noted by the excellent warm-up time, temperature tracking, and cooling system power consumption.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2009;131(4):044502-044502-6. doi:10.1115/1.3117199.

Asynchronous measurement of process output characterizes a series of discrete process cycles in batch production. A multirate Kalman filtering scheme was proposed by Lee (2008, “Estimation Strategy for a Series of Grinding Cycles in Batch Production,” IEEE Trans. Contr. Syst. Technol., 16(3, pp. 556–561)) for estimating immeasurable variables through integration of other sensor signals with postprocess inspection data. In this paper, a new state-space model structure for a series of discrete process cycles is proposed based on a semicontinuous system under the process noise of multiple frequencies due to the within-cycle drift and the cycle-to-cycle variation. An improvement is made to the previous estimation scheme by deriving the propagation of estimation errors between consecutive cycles under the multirate noise. Following a simulation demonstrating the advantage of the proposed change, experiments are conducted on an actual grinding process to validate the estimation scheme.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2009;131(4):044503-044503-5. doi:10.1115/1.3023112.

A novel information-theoretic stepwise feature selector (ITSFS) is designed to reduce the dimension of diesel engine data. This data consist of 43 sensor measurements acquired from diesel engines that are either in a healthy state or in one of seven different fault states. Using ITSFS, the minimum number of sensors from a pool of 43 sensors is selected so that eight states of the engine can be classified with reasonable accuracy. Various classifiers are trained and tested for fault classification accuracy using the field data before and after dimension reduction by ITSFS. The process of dimension reduction and classification is repeated using other existing dimension reduction techniques such as simulated annealing and regression subset selection. The classification accuracies from these techniques are compared with those obtained by data reduced by the proposed feature selector.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2009;131(4):044504-044504-4. doi:10.1115/1.3117187.

In linear systems, designers use zeros for loop-shaping and the attenuation of disturbances. For example, imaginary-axis zeros can be used to reject sinusoids at a specific frequency such as a 50 Hz or 60 Hz power line interference. If the disturbance is nonsinusoidal, repetitive control methods may be used but additional controller states for each harmonic are required. Thus, rejecting periodic disturbance that are nonsinusoidal with low controller order remains an open problem. In this paper, we constructively design low-order nonlinear dynamics that reject a nonsinusoidal disturbance. We identify a particular case of the nonlinear regulator theory wherein the Byrnes–Isidori PDE has a simple solution. This case leads to a constructive procedure for designing nonlinear zero dynamics in systems with input disturbances. The constructive procedure is accessible to designers who do not have experience with the nonlinear geometric control theory.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2009;131(4):044505-044505-8. doi:10.1115/1.3117207.

This work provides an analysis of the steady state response of a prototype repetitive controller applied to a class of nonlinear systems, i.e., systems with actuator saturation. First, it is shown that the steady state solution of the closed loop nonlinear system can be obtained by an iterative Picard process, which establishes the periodic nature of the steady state solution. Second, the conditions for obtaining bounded steady state responses are analyzed for a saturating nonlinearity commonly found in mechatronic applications. Valuable insight is provided into the effects of input signals and saturating actuators on the closed loop performance of a prototype repetitive controller. In order to improve the transient closed loop response, a simple antiwindup strategy tailored to repetitive controllers is proposed.

Commentary by Dr. Valentin Fuster

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