Open-loop Dynamics Research Articles

Decoupled Quadrature and Force Feedback Control of Capacitive MEMS Gyroscopes

AbstractThis contribution presents the mathematical model of a capacitive MEMS gyroscope containing specific actuators which are capable of compensating mechanical unbalance (quadrature error) as well as the system response to an external angular rate (force feedback). Based on this model a quadrature controller is systematically designed. In order to eliminate the typically weakly damped open-loop dynamics of the gyroscope additionally a combined concept of closed-loop quadrature and force feedback control is introduced. The presented theory is validated by means of both numerical simulations and measurement results utilizing a prototype gyroscope.

Output Regulation with Actuator Saturation for the Benchmark Active Control Technology Model

Output Regulation with Actuator Saturation for the Benchmark Active Control Technology Model

Bouncing between Model and Data: Stability, Passivity, and Optimality in Hybrid Dynamics

ABSTRACT Rhythmically bouncing a ball with a racket is a seemingly simple task, but it poses all the challenges critical for coordinative behavior: perceiving the ball's trajectory to adapt position and velocity of the racket for the next ball contact. To gain insight into the underlying control strategies, the authors conducted a series of studies that tested models with experimental data, with an emphasis on deriving model-based hypotheses and trying to falsify them. Starting with a simple dynamical model of the racket and ball interactions, stability analyses showed that open-loop dynamics affords dynamical stability, such that small perturbations do not require corrections. To obtain this passive stability, the ball has to be impacted with negative acceleration—a strategy that subjects adopted in a variety of conditions at steady state. However, experimental tests that applied perturbations revealed that after perturbations, subjects applied active perceptually guided corrections to reestablish steady state faster than by relying on the passive model's relaxation alone. Hence, the authors derived a model with active control based on optimality principles that considered each impact as a separate reaching-like movement. This model captured some additional features of the racket trajectory but failed to predict more fine-grained aspects of performance. The authors proceed to present a new model that accounts not only for fine-grained behavior but also reconciles passive and active control approaches with new predictions that will be put to test in the next set of experiments.

Influence of Amplitude, Starting Point, and Age on First- and Second-Order Dynamics of Edinger-Westphal–Stimulated Accommodation in Rhesus Monkeys

In humans, accommodative and disaccommodative dynamics depend on response amplitude and starting point. The purpose of this study was to determine the influence of amplitude and starting point on open-loop accommodative dynamics in Edinger-Westphal (EW)-stimulated, anesthetized rhesus monkeys of different ages. One eye each of two younger and two older iridectomized rhesus monkeys, (aged 6.8, 8.9, 15.0, and 16.3 years) were studied. The experiment was repeated in one eye of one younger monkey. Lens thickness changes were recorded by dynamic ultrasound biometry at 100 Hz. Stimuli used produced accommodative responses: (1) starting from baseline with increasing amplitudes; (2) from increasing starting points to maximum accommodation; and (3) from increasing starting points with a constant amplitude of 1 D. The lens thickness measurements were converted into accommodation and velocities and accelerations of the responses were determined by using a two-point difference algorithm. Maximum accommodative amplitudes ranged from 4.68 to 6.37 D in the older monkeys and 9.33 to 11.59 D in the younger monkeys. The peak velocity of accommodation and disaccommodation increased linearly with response amplitude. Peak velocity and peak acceleration of accommodation and disaccommodation were independent of the response starting point. Subtle variations in disaccommodative response peak velocities were found to vary with age. The results suggest that, in anesthetized rhesus monkeys, disaccommodative rather than accommodative dynamics may be more sensitive to age-related changes and that, unlike in conscious human subjects, the starting configuration of the accommodative plant has little influence on accommodative dynamics.

Simulation and Control of a Commercial Double Effect Evaporator: Tomato Juice

This work aims to present a detailed study on a commercial double-effect tomato paste evaporation system. The modeling equations formulated for process simulation belong to backward feeding arrangement. Open-loop process dynamics has been studied by rigorous simulation of the model structure. In the next, three multi-loop control schemes, namely conventional proportional integral (PI), gain-scheduled PI (GSPI) and nonlinear PI (NLPI), have been synthesized for the sample process. Finally, several simulation experiments have been conducted to investigate the comparative closed-loop performance based on set point tracking and disturbance rejection.

Multivariable Control with Generalized Decoupling for Disturbance Rejection

In this paper, a systematic procedure to design multivariable controllers that have options for selective decoupling of different structures (e.g., full or partial decoupler) is proposed. The controller structure is determined based on an analysis of relative load gain (RLG). For controller design, the adjoint of a template matrix is provided to design the MIMO decoupler that is needed for a given process. In the case where decoupling is desirable, according to the number of zero deficiency that the adjoint of the template matrix has, a pole-zero compensator is incorporated to preserve the properness of the decoupling controller and to define the decoupled open-loop dynamics. By incorporating the decoupler, the controller in the main loop is synthesized for disturbance rejection. Stability robustness of the system is tuned using measures of modeling errors in the decoupled open-loop process. Simulation examples are used to illustrate the proposed method and show its effectiveness in disturbance rejection in MIMO systems.

Vibration and damping characteristics of beams with active constrained layer treatments under parametric variations

Hybrid damping designs with active piezoelectric materials and passive viscoelastic materials (VEMs) combine the advantages of both active and passive constrained layer damping (ACLD/PCLD) treatments. Researchers have established the standards for the extent and placement of the PCLD treatment for common structures. However for ACLD treatment, such detailed studies are not available. This study is aimed to examine, the effect of parametric variation of active constrained layer on the vibration control of the beams treated with optimally placed active or passive constrained layer damping patches. Finite element model is developed to model the open-loop and close-loop dynamics of active/passive constrained layer damping treated beam. The placement strategies of ACLD patches are devised using the modal strain energy (MSE) approach. Extensive experimentation studies are conducted by making twenty one separate samples of ACLD/PCLD treated beams with variations in viscoelastic material layer thickness, ACLD/PCLD patch coverage and location of the patch. Effects of key parameters, such as control gain, viscoelastic material thickness, coverage and location variation of ACLD patch on the system loss factor have been investigated. The careful analysis of results from partially covered ACLD treated beam suggests that the maximum damping of the first mode can be achieved by attaching the ACLD patch only up to 50% coverage. It also reveals that with proper choice of the control voltage and thickness, the effective loss factor can be almost doubled. The present study suggests the potential use of parametric studies that establish some guide lines for the extent and placement of the ACLD patches on the cantilevered beam.

Active control of geometrically nonlinear vibrations of functionally graded laminated composite plates using piezoelectric fiber reinforced composites

This paper deals with the geometrically nonlinear dynamic analysis of functionally graded (FG) laminated composite plates integrated with a patch of active constrained layer damping (ACLD) treatment. The constraining layer of the ACLD treatment is considered to be made of the piezoelectric fiber reinforced composite (PFRC) material. Each layer of the substrate FG laminated composite plate is made of fiber-reinforced composite material in which the fibers are longitudinally aligned in the plane parallel to the top or bottom surface of the layer and the layer is assumed to be graded in the thickness direction by way of varying the fiber orientation angle across its thickness according to a power-law. The novelty of the present work is that, unlike the traditional laminated composite plates, the FG laminated composite plates are constructed in such a way that the continuous variation of material properties and stresses across the thickness of the plates is achieved. The constrained viscoelastic layer of the ACLD treatment is modeled using the Golla–Hughes–McTavish (GHM) method. Based on the first-order shear deformation (FSDT) theory, a finite element model has been developed to model the open-loop and closed-loop nonlinear dynamics of the overall FG laminated composite plates. Both symmetric and asymmetric FG laminated composite plates are considered as the substrate plates for presenting the numerical results. The analysis suggests the potential use of the ACLD treatment with its constraining layer made of the PFRC material for active control of geometrically nonlinear forced vibrations of FG laminated composite plates. The effect of piezoelectric fiber orientation in the active constraining PFRC layer on the damping characteristics of the overall FG plates is also investigated.

Process Simulation and Design of Reactive Distillation Column

This paper presents a systematic study on the homogeneously catalyzed reactive distillation (RD) process operated in both batch and continuous mode for the synthesis of ethyl acetate. In the first part, the fundamental model has been developed incorporating the reaction term within the model structure of the nonreactive distillation process. In case of batch rectifier, the process operation is simulated at the startup phase under total reflux condition for reaching the steady state. The open-loop process dynamics are also examined running the batch process at production phase under partial reflux condition.The concerned batch rectifier has the ability to provide high purity product. On the other hand, the continuous RD column exampled at the beginning of the second part produces relatively low quality product. In the present study, an attempt has been made to configure a feasible continuous column with improved product quality. In order to propose a RD setup, several simulation experiments have been performed for sensitivity analysis. An interesting phenomenon, the input multiplicity, is observed for both the batch as well as continuous column.

The influence of vergence adaptation on open-loop vergence dynamics

The objectives of this experiment were to measure the effect of sustained convergence on the open-loop vergence peak velocity and open-loop vergence amplitude, and to assess the correlation between changes in the phoria and changes in open-loop vergence peak velocity induced by sustained convergence. Subjects sustained convergence on a target that required 12° of convergence for 5 minutes. Convergence and divergence movements of 4° from the 12° convergent position were measured before and after sustained convergence. Following sustained convergence, the open-loop vergence peak velocity and vergence amplitude both increased for convergence (regression slope = 3.68, r = 0.47). Vergence velocity and vergence amplitude both decreased for divergence (regression slope = 1.76, r = 0.36). After sustained convergence, a convergent shift in the phoria was noted in most cases. This shift correlated with changes in open-loop peak vergence velocity more for convergence (regression slope = 1.1, r = 0.33) than for divergence (regression slope = 0.71, r = 0.22). The results might be due to shifts in disparity detection brought about by the period of sustained convergence.

A substructure shaking table test for reproduction of earthquake responses of high‐rise buildings

AbstractWhen subjected to long‐period ground motions, high‐rise buildings' upper floors undergo large responses. Furniture and nonstructural components are susceptible to significant damage in such events. This paper proposes a full‐scale substructure shaking table test to reproduce large floor responses of high‐rise buildings. The response at the top floor of a virtual 30‐story building model subjected to a synthesized long‐period ground motion is taken as a target wave for reproduction. Since a shaking table has difficulties in directly reproducing such large responses due to various capacity limitations, a rubber‐and‐mass system is proposed to amplify the table motion. To achieve an accurate reproduction of the floor responses, a control algorithm called the open‐loop inverse dynamics compensation via simulation (IDCS) algorithm is used to generate a special input wave for the shaking table. To implement the IDCS algorithm, the model matching method and the H∞ method are adopted to construct the controller. A numerical example is presented to illustrate the open‐loop IDCS algorithm and compare the performance of different methods of controller design. A series of full‐scale substructure shaking table tests are conducted in E‐Defense to verify the effectiveness of the proposed method and examine the seismic behavior of furniture. The test results demonstrate that the rubber‐and‐mass system is capable of amplifying the table motion by a factor of about 3.5 for the maximum velocity and displacement, and the substructure shaking table test can reproduce the large floor responses for a few minutes. Copyright © 2009 John Wiley & Sons, Ltd.

Model predictive control of low Earth-orbiting satellites using magnetic actuation

This paper presents a model predictive control approach for regulating the attitude of magnetically actuated satellites. Unlike other contributions in this area, a predictive control approach is developed which guarantees closed-loop stability of satellite configurations with unstable open-loop pitch dynamics. With the pitch axis being unstable, two magnetic dipoles are used exclusively for regulation of this axis. This allows the dynamics to be treated as a linear time-invariant system, and a simple proportional—derivative (PD) scheme is implemented. A model predictive controller is designed to regulate the lateral dynamics, with a Lyapunov function derived to guarantee asymptotic stability of the closed-loop system. The regulation of the lateral dynamics is achieved with a singe dipole moment, with a novel reformulation of the lateral dynamics also providing an explicit link between the two controllers. Simulations demonstrate the effectiveness and stability of the proposed algorithm when applied to the European Space Agency's GOCE satellite.

Bounded positive control for double-pipe heat exchangers

In this work, an outlet temperature control scheme for double-pipe heat exchangers is proposed. Compared to previously proposed approaches, the algorithm developed here takes into account and actually exploits the analytical and stability properties inherent to the open-loop dynamics. As a result, outlet temperature regulation is achieved through a simple controller which does not need to feed back the whole state vector and does not depend on the exact value of the process parameters. Moreover, the proposed approach guarantees positivity and boundedness of the input flow rate without entailing a complex control algorithm. The analytical developments are corroborated through simulation and experimental results.

Circadian Phase Resetting via Single and Multiple Control Targets

Circadian entrainment is necessary for rhythmic physiological functions to be appropriately timed over the 24-hour day. Disruption of circadian rhythms has been associated with sleep and neuro-behavioral impairments as well as cancer. To date, light is widely accepted to be the most powerful circadian synchronizer, motivating its use as a key control input for phase resetting. Through sensitivity analysis, we identify additional control targets whose individual and simultaneous manipulation (via a model predictive control algorithm) out-perform the open-loop light-based phase recovery dynamics by nearly 3-fold. We further demonstrate the robustness of phase resetting by synchronizing short- and long-period mutant phenotypes to the 24-hour environment; the control algorithm is robust in the presence of model mismatch. These studies prove the efficacy and immediate application of model predictive control in experimental studies and medicine. In particular, maintaining proper circadian regulation may significantly decrease the chance of acquiring chronic illness.

Comparative Control Study of a High-Purity Ternary Batch Distillation

This paper presents a comparative closed-loop performance study on a multicomponent batch distillation column that produces high-purity distillate product. Initially, the distillation model representing a ternary system of cyclohexane-toluene-chlorobenzene has been simulated to observe the open-loop dynamics at the start-up as well as production phase. The next three control schemes, namely classical proportional integral (PI) controller, nonlinear proportional integral (NLPI) control strategy and gain-scheduled proportional integral (GSPI) law, have been designed and applied on the simulated distillation column. Numerical experiments based on servo and regulatory tests show that the GSPI algorithm provides relatively better results than the other two PIs.

Dynamic considerations in the synthesis of self‐optimizing control structures

AbstractThis work builds on our prior results to develop novel control structure design principles for integrated plants featuring multiple time scale dynamics. Specifically, the concept of self‐optimizing control can be used to identify the variables that must be controlled to achieve acceptable economic performance during plant operation. This approach does not, however, provide guidelines on control structure design and control loop tuning; a detailed controllability and dynamic analysis is generally needed to this end. In this work, we employ a singular perturbation‐based framework, which accounts for the time scale separation present in the open loop dynamics of integrated plants, to identify the available controlled and manipulated variables in each time scale. The resulting controller design procedure thus accounts for both economic optimality and dynamic performance. The developed concepts are subsequently successfully applied on a reactor‐separator process with recycle and purge. © 2008 American Institute of Chemical Engineers AIChE J, 2008

Global stabilization of a class of partially known nonnegative systems

In this paper we deal with the problem of global output feedback stabilization of a class of n -dimensional nonlinear nonnegative systems possessing a one-dimensional analytically unknown part that is also a measured output. We first propose our main result, an output feedback control procedure, taking advantage of measurements of the uncertain part, able to globally stabilize the system toward an adjustable equilibrium point in the positive orthant. Though quite general, this result is based on hypotheses that might be difficult to check in practice. Then in a second step, through a theorem on a class of nonnegative systems linking the existence of a positive equilibrium to its global asymptotic stability, we propose other hypotheses for our main result to hold. These new hypotheses are more restrictive but much simpler to check. An illustrative example highlights both the potentially complex open loop dynamics of the considered systems and the interesting characteristics of the control procedure.

Passive Decomposition of Multiple Nonholonomic Mechanical Systems under Motion Coordination Requirements

We propose a novel framework, which, under a certain geometric condition, enables us to decompose the second-order Lagrangian dynamics of the multiple nonholonomic mechanical systems into two decoupled systems according to the two most fundamental aspects of the group behaviour: shape system describing the formation aspect (i.e. group's internal shape); and locked system abstracting the maneuver aspect (i.e. group's overall motion). By controlling these decoupled locked and shape systems individually, we can then control the formation and maneuver aspects separately without any crosstalk between them. Moreover, the framework enables us to do this while respecting/utilizing the Lagrangian structure/passivity of the system's open-loop dynamics. Due to this property, we call this framework nonholonomic passive decomposition. A control design example with numerical simulation is also given to highlight some properties of the proposed framework.

Dynamic Analysis of a Macro–Micro Redundantly Actuated Parallel Manipulator

In this paper the dynamic analysis of a macro–micro parallel manipulator is studied in detail. The manipulator architecture is a simplified planar version adopted from the structure of the Large Adaptive Reflector (LAR), the Canadian design of next-generation giant radio telescopes. In this structure it is proposed to use two parallel redundant manipulators at the macro and micro level, both actuated by cables. In this paper, the governing dynamic equation of motion of such a structure is derived using the Newton–Euler formulation. Next, the dynamic equations of the system are used in the open-loop inverse dynamics simulations, as well as closed-loop forward dynamics simulations. In the open-loop dynamic simulations it is observed that the inertial forces of the limbs contribute only 10% of the dynamic forces required to generate a typical trajectory and, moreover, the total dynamic forces contribute only 10% of the experimentally measured disturbance forces. Furthermore, in the closed-loop simulations using decentralized PD controllers at the macro and micro levels, it is shown that the macro–micro structure results in a 10 times more accurate positioning than that in the first stage of the macro–micro structure. This convincing result promotes the use of the macro–micro structure for LAR application.

Identification and High Bandwidth Control of Hard Disk Drive Servo Systems Based on Sampled Data Measurements

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> One of the key factors that determines the track density of a hard disk drive (HDD) is the performance characteristics of the HDD servo system, the control system that positions the <emphasis emphasistype="smcaps">read/write</emphasis> magnetic head close to the center of the desired track of the HDD. For most HDD servo systems, the deviation of the position of the magnetic head from the center of the desired track is measured whenever the head passes over sectors, referred to as servo burst sectors that carry prewritten position data. The position error signal (PES) is, therefore, generated at discrete points in time, the rate of which is limited by the number of the prewritten servo burst sectors and the spinning speed of the disk. This limited natural sampling rate puts limitations on how high the bandwidth of the controller can be as well as making it difficult to identify the continuous time modes which occur at frequencies close to or higher than the sampling frequency. In this paper, we first introduce a method for identifying the open-loop continuous-time dynamics of such HDD servo systems by processing the available sampled PES data. The method is based on exciting the system with two orthogonal sinusoids and constructing a linear complex equation that relates the sampled PES points with the unknown values of the transfer function. Then, we design a high bandwidth HDD servo controller with improved performance characteristics. In our control design we employ the “ACORN estimator” that generates estimates of the head position by processing the servo burst and data sector measurements, to provide PES estimates at higher sampling rates during <emphasis emphasistype="smcaps">read</emphasis>. Our control design is tested on an actual disk drive. The effect of the higher sampling rate, generated by the ACORN estimator, on the seek time and steady-state performance is evaluated. While our results show that the use of a higher sampling rate provides some improvement, the presence of varying high frequency resonance modes limits further increase in bandwidth that is now possible due to the higher sampling rate. Consequently, the proposed control scheme is expected to have additional benefits in future generations of disk drives employing dual stage actuators. </para>