Accepted Manuscripts

Nicholas Vlajic, Melissa Davis and Corey Stambaugh
J. Dyn. Sys., Meas., Control   doi: 10.1115/1.4040504
This paper explains the control scheme that is to be used in the Magnetic Suspension Mass Comparator (MSMC), an instrument designed to directly compare mass artifacts in air to those in vacuum, at the United States National Institute of Standards and Technology. More specifically, the control system is used to apply a magnetic force between two chambers to magnetically suspend mass artifacts, which allows for a direct comparison (i.e., a calibration) between the mass held in air and a mass held in vacuum. Previous control efforts that have been demonstrated on a proof-of-concept of this system utilized PID-based control with measurements of the magnetic field as the control signal. Here, we implement state-feedback control using a laser interferometric displacement measurement with a noise floor of approximately 5 nm (root-mean-square). One of the unique features and main challenges in this system is that, in order to achieve the necessary accuracy (relative uncertainty of 20 x 10-9 in the MSMC), the magnetic suspension must not impose appreciable lateral forces or moments. Therefore, in this design, a single magnetic actuator is used to generate a suspension force in the vertical direction, while gravity and the symmetry of the magnetic field provide the lateral restoring forces. The combined optical measurement and state-feedback control strategy presented here demonstrate an improvement over the previously reported results with magnetic field measurements and a PID-based control scheme.
TOPICS: Magnetic levitation, Vacuum, Metrology, Magnetic fields, State feedback, National Institute of Standards and Technology, Uncertainty, Gravity (Force), Calibration, Displacement measurement, Signals, Noise (Sound), Actuators, Design, Instrumentation, Lasers, Optical measurement, Control systems
Vahid Azimi, Seyed Abolfazl Fakoorian, Thang Tien Nguyen and Dan Simon
J. Dyn. Sys., Meas., Control   doi: 10.1115/1.4040463
This paper presents, compares and tests two robust model reference adaptive impedance controllers for a three degree-of-freedom (3-DOF) powered prosthesis / test robot. We first present a model for a combined system that includes a test robot and a transfemoral prosthetic leg. We design these two controllers so the error trajectories of the system converge to a boundary layer and the controllers show robustness to ground reaction forces (GRFs) as non-parametric uncertainties and also handle model parameter uncertainties. We prove the stability of the closed-loop systems for both controllers for the prosthesis / test robot in the case of non-scalar boundary layer trajectories using Lyapunov stability theory and Barbalat's lemma. We design the controllers to imitate the biomechanical properties of able-bodied walking and to provide smooth gait. We finally present simulation results to confirm the efficacy of the controllers for both nominal and off-nominal system model parameters. We achieve good tracking of joint displacements and velocities, and reasonable control and GRF magnitudes for both controllers. We also compare performance of the controllers in terms of tracking, control effort, and parameter estimation for both nominal and off-nominal model parameters.
TOPICS: Prostheses, Robots, Control equipment, Uncertainty, Boundary layers, Design, Stability, Scalars, Biomechanics, Degrees of freedom, Artificial limbs, Closed loop systems, Errors, Parameter estimation, Robustness, Simulation results, Tracking control
Technical Brief  
Mumtazcan Karagoz and Melih Cakmakci
J. Dyn. Sys., Meas., Control   doi: 10.1115/1.4040443
In the current era of miniaturization for complex, ubiquitous and energy efficient systems, micro-manufacturing had become one of the most popular fields for engineering development. This paper introduces a modular robust cross-coupled controller design structure for a three axis micro-machining system that can be extended to more axis systems and configurations. In order to develop a robust controller that can withstand the disturbances due to tool-workpiece interactions a dynamic model of the whole system is needed. Developing control oriented models for micro-machining systems can be challenging. Using the Sum of Sines identification input essential non-linearities including the effects of assembly and slider orientation is included. Verification data shows these transfer function models represent the physical system satisfactorily while avoiding an over-fit. Using the transfer functions from the identified model, a controller structure with robust axis controllers with cross-coupled control are developed and fine-tuned with simulations. Machining experiments are also done in order to compare the performance of the PID control design, an adaptive robust controller (both from earlier work in literature) and the new H_{\infty} robust controller. According to results of experiments, the new robust controller showed the best tracking and contouring performance with improved surface quality due to reduced oscillations.
TOPICS: Control equipment, Micromachining, Transfer functions, Design, Engineering simulation, Dynamic models, Surface quality, Micromanufacturing, Manufacturing, Simulation, Oscillations, Machining
Ting Yang, Junfeng Hu, Wei Geng, Dan Wang, Yi Li Fu and Mahdi Tavakoli
J. Dyn. Sys., Meas., Control   doi: 10.1115/1.4040440
Hybrid analog/digital control of bilateral teleoperation systems can lead to superior performance (transparency) while maintaining stability compared to pure analog or digital control methods. Such hybrid control is preferable over pure analog control, which is inflexible and not ideal for realizing complex teleoperation control algorithms, and pure digital control, which restricts teleoperation performance due to a well-known stability-imposed upper bound on the product of the digital controller's proportional gain and the sampling period. In this paper, a hybrid controller combining a Field Programmable Analog Array (FPAA) based analog controller and a personal computer based digital controller is compared in terms of performance and stability to its analog and digital counterparts. A stability analysis indicates that the addition of analog derivative term widens the range of teleoperation controls gains that satisfy the stability conditions, paving the way for improving the teleoperation performance. We also show how the hybrid controller leads to better teleoperation performance. To this end, we study the human's performance of a switch flipping task and a stiffness discrimination task in the teleoperation mode. In both tasks, the hybrid analog/digital controller allows the human operators to achieve the highest task success rates.
TOPICS: Stability, Control equipment, Computers, Stiffness, Switches, Transparency, Hybrid control, Control algorithms
A. Sener Kaya and Mehmet Zeki Bilgin
J. Dyn. Sys., Meas., Control   doi: 10.1115/1.4040436
In this article, an output feedback sliding mode position controller/estimator scheme is proposed to control a SISO system subject to bounded nonlinearities and parametric uncertainties. Various works have been published addressing the theoretical effectiveness of the Third Order Sliding Mode Control (3-SMC) in terms of chattering alleviation and controller robustness. However, the application of 3-SMC with a feedback estimator to a flight actuators has not been treated explicitly. This is due to the fact that the accurate full state estimation is required since SMCs performance can be severely degraded by measurement or estimation noise. Aerodynamic control surface actuators in air vehicles mostly employ linear position controllers to achieve guidance and stability. The main focus of the paper is to experimentally demonstrate the stability and positioning performance of a third order SMC applied to a class of system with high relative degree and bounded parametric uncertainties. The performance of the closed loop system is also compared with a lower level SMC and classical controller to show the effectiveness of the algorithm. Realization of the proposed algorithm from an application perspective is the main target of this paper and it demonstrates that a shorter settling time and higher control action attenuation can be achieved with the proposed strategy.
TOPICS: Control equipment, Feedback, Flight, Surface mount components, Sliding mode control, Actuators, Algorithms, Uncertainty, Stability, Vehicles, Closed loop systems, Robustness, State estimation, Noise (Sound)
Tao Li, Zhipeng Li, Haitao Zhang and S.M. Fei
J. Dyn. Sys., Meas., Control   doi: 10.1115/1.4040327
This paper considers the problem on formation tracking control of second-order multi-agent systems with communication time-varying delay. Sufficient conditions on the directed interaction topology and existence of the feedback gains to ensure the desired control are presented. Through choosing two augmented Lyapunov-Krasovskii functionals and using some novel Wirtinger-based integral inequalities, the previously ignored information can be reconsidered and the application area of derived results can be greatly extended. Moreover, a novel constructive technique is given to compute out the controller gains by resorting to solving the achieved linear matrix inequalities. Finally, a numerical example with comparisons and simulations is provided to illustrate the obtained results.
TOPICS: Delays, Multi-agent systems, Tracking control, Topology, Feedback, Linear matrix inequalities, Control equipment, Simulation, Engineering simulation
Mohammad Reza Amini, Mahdi Shahbakhti and Selina Pan
J. Dyn. Sys., Meas., Control   doi: 10.1115/1.4040208
Sliding mode control (SMC) is a robust and computationally efficient model-based controller design technique for highly nonlinear systems, in the presence of model and external uncertainties. However, the implementation of the conventional continuous-time SMC on digital computers is limited, due to the imprecisions caused by data sampling and quantization, and the chattering phenomena, which results in high frequency oscillations. One effective solution to minimize the effects of data sampling and quantization imprecisions is the use of higher order sliding modes. To this end, in this paper, a new formulation of an adaptive second order discrete sliding mode control (DSMC) is presented for a general class of multi-input multi-output (MIMO) uncertain nonlinear systems. Based on a Lyapunov stability argument and by invoking the new Invariance Principle, not only the asymptotic stability of the controller is guaranteed, but also the adaptation law is derived to remove the uncertainties within the nonlinear plant dynamics. The proposed adaptive tracking controller is designed and tested in real-time for a highly nonlinear control problem in spark ignition combustion engine during transient operating conditions. The simulation and real-time processor-in-the-loop (PIL) test results show that the second order single-input single-output (SISO) DSMC can improve the tracking performances up to 90%, compared to a first order SISO DSMC under sampling and quantization imprecisions, in the presence of modeling uncertainties. Moreover, it is observed that by converting the engine SISO controllers to a MIMO structure, the overall controller performance can be enhanced by 25%, compared to the SISO second order DSMC, because of the dynamics coupling consideration within the MIMO DSMC formulation.
TOPICS: Sliding mode control, Control equipment, Uncertainty, Nonlinear systems, Engines, Dynamics (Mechanics), Stability, Combustion, Engineering design processes, Modeling, Simulation, Transients (Dynamics), Computers, Ignition, Oscillations
Technical Brief  
Pritthi Chattopadhyay, Sudeepta Mondal, Asok Ray and Achintya Mukhopadhyay
J. Dyn. Sys., Meas., Control   doi: 10.1115/1.4040210
A critical issue in design and operation of combustors in gas turbine engines is mitigation of thermoacoustic instabilities, because such instabilities may cause severe damage to the mechanical structure of the combustor. Hence, it is important to quantitatively assimilate the knowledge of the system conditions that would potentially lead to these instabilities. This technical brief proposes a dynamic data-driven technique for design of combustion systems by taking stability of pressure oscillations into consideration. Given appropriate experimental data at selected operating conditions, the proposed design methodology determines a mapping from a set of operating conditions to a set of quantified stability conditions for pressure oscillations. This mapping is then used as an extrapolation tool for predicting the system stability for other conditions for which experiments have not been conducted. Salient properties of the proposed design methodology are: 1. It is dynamic in the sense that no fixed model structure needs to be assumed; and a suboptimal model (under specified user-selected constraints) is identified for each operating condition. An information-theoretic measure is then used for performance comparison among different models of varying structures and/or parameters. 2. It quantifies a (statistical) confidence level in the estimate of system stability for an unobserved operating condition by using a Bayesian nonparametric technique. The proposed design methodology has been validated with experimental data of pressure time-series, acquired from a laboratory-scale lean-premixed swirl-stabilized combustor.
TOPICS: Combustion chambers, Design, Stability, Design methodology, Pressure, Oscillations, Combustion systems, Gas turbines, Time series, Mechanical structures, Damage

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