Derivative Feedback Research Articles

An Active Damping Method Using Inductor-Current Feedback Control for High-Power PWM Current-Source Rectifier

Due to the inductor-capacitor filter, a pulse width modulation current-source rectifier (CSR) may experience LC resonance. A smaller ratio between the switching frequency and the resonant frequency of the CSR presents a challenge in designing active resonance damping methods in high-power applications. In this paper, different feedback states of filter inductor current and capacitor voltage are investigated to damp out the LC resonances. Besides proportional capacitor-voltage feedback (CVF), the derivative inductor-current feedback (ICF) provides an alternative approach for active damping and is comprehensively analyzed. Compared with the virtual-resistance (VR)-based active damping strategy, controller design is simpler in this method. Furthermore, the active damping method is able to damp the resonance under short-circuited dc-link conditions. The ICF-based active damping strategy works well for CSRs with low switching frequencies. Simulation and experimental results verify the feasibility and validity of the method.

Ineluctability of oscillations in systems with digital implementation of derivative feedback

Differentiation in feedback is common practice in digital control. Yet, the fundamental behavior of the universally employed backward difference of quantized signals has not been studied thus far. We show that velocity always oscillates when this type of feedback is applied to a forced, linear second-order system for any system parameter. We then compute a bound for the oscillation amplitude, which can be easily computed given the parameters of the system. Experimental results are in close agreement with the theory. If the system has dry friction, our study yields a sufficient condition for the quenching of spontaneous oscillations.

SU-E-T-543: The Use of a Proportional-Integral-Derivative Design for Optimized Real-Time Head Motion Correction in Frameless SRS

Purpose: While less invasive, the immobilization devices used in frameless SRS techniques generally allow for more head movement than a frame, leading to a larger PTV. To maintain traditional SRS accuracies, we have developed a robotic 3D head motion stage to correct for these sub‐ millimeter head deviations occurring during treatment. To achieve optimal head motion management we report on our use of a proportional‐integral‐ derivative (PID) feedback loop to monitor and compensate for real‐time patient motion during frameless SRS. Methods: A PID controller consists of three corrective parameters: a proportional term to account for the error difference between the desired patient position and the actual position; an integral term that accelerates the position correction toward the desired setpoint value; and a derivative term that accounts for the instantaneous rate of change of the patient position error. These parameters were tuned according to manual and heuristic Zielger‐Nichols methods. The PID algorithm was integrated into existing Labview software designed to control patient motion via a computer‐controlled 3D stepper motor stage. For realtime head position feedback either a Polaris external marker tracker or VisionRT system was used. The PID correction was tested both on phantom and healthy volunteers. Results: With volunteers in a relaxed supine position, the PID method maintained head motion to under 0.25 mm as based on the optical monitoring system in all three directions for greater than 90% of the time. Artificial introduction of extreme 1–5 mm head shifts by manual couch moving were corrected 2–3 times faster by PID when compared to our prior constant motor velocity approach Conclusions: In the event of patient head deviations, a properly tuned PID controller can offer significant time sparing advantages. This would allow for quicker initial setup after coarse couch positioning and a higher duty cycle during treatment.

A Wearable Device for Real-Time Motion Error Detection and Vibrotactile Instructional Cuing

We have developed a mobile instrument for motion instruction and correction (MIMIC) that enables an expert (i.e., physical therapist) to map his/her movements to a trainee (i.e., patient) in a hands-free fashion. MIMIC comprises an expert module (EM) and a trainee module (TM). Both the EM and TM are composed of six-degree-of-freedom inertial measurement units, microcontrollers, and batteries. The TM also has an array of actuators that provide the user with vibrotactile instructional cues. The expert wears the EM, and his/her relevant body position is computed by an algorithm based on an extended Kalman filter that provides asymptotic state estimation. The captured expert body motion information is transmitted wirelessly to the trainee, and based on the computed difference between the expert and trainee motion, directional instructions are displayed via vibrotactile stimulation to the skin. The trainee is instructed to move in the direction of the vibration sensation until the vibration is eliminated. Two proof-of-concept studies involving young, healthy subjects were conducted using a simplified version of the MIMIC system (pre-specified target trajectories representing ideal expert movements and only two actuators) during anterior-posterior trunk movements. The first study was designed to investigate the effects of changing the expert-trainee error thresholds (0.5(°), 1.0(°), and 1.5(°)) and varying the nature of the control signal (proportional, proportional plus derivative). Expert-subject cross-correlation values were maximized (0.99) and average position errors (0.33(°)) and time delays (0.2 s) were minimized when the controller used a 0.5(°) error threshold and proportional plus derivative feedback control signal. The second study used the best performing activation threshold and control signal determined from the first study to investigate subject performance when the motion task complexity and speed were varied. Subject performance decreased as motion speed and complexity increased.

Impact of Combined Feedback–Feedforward Control‐Based Ordering Policies on Supply Chain Stability and Responsiveness

The design of ordering policies for inventory management in supply chains has traditionally relied on the proportional feedback control structure as a foundation for the design process. Consequently, the impact of ordering policies that use both proportional–integral–derivative feedback control and feedforward control has been relatively unexplored. We evaluate the impact of ordering policies based on the combined control structure on supply chain stability and responsiveness. Copyright © 2011 John Wiley & Sons, Ltd.

Parametric eigenstructure assignment for descriptor systems via proportional plus derivative state feedback

Eigenstructure assignment for descriptor systems with proportional plus derivative state feedback is studied. Based on a simple complete explicit parametric solution to a group of recursive equations, a parametric approach for eigenstrucure assignment in descriptor systems via proportional plus derivative state feedback is proposed. The proposed approach possesses the following features: 1) it does not impose any condition on the closed-loop eigenvalues, simultaneously assigns arbitrary n finite and infinite eigenvalues to the closed-loop system and guarantees the closed-loop regularity; 2) it is simple and needs less computational work; 3) it gives general complete parametric expressions for the closed-loop eigenvectors, the proportional state feedback gain matrix and the derivative state feedback gain matrix.

Vibration and damping characteristics of cylindrical shells with active constrained layerdamping treatments

In this paper, the application of active constrained layer damping (ACLD) treatments isextended to the vibration control of cylindrical shells. The governing equation of motion ofcylindrical shells partially treated with ACLD treatments is derived on the basis of theconstitutive equations of elastic, piezoelectric and visco-elastic materials and an energyapproach. The damping of a visco-elastic layer is modeled by the complex modulusformula. A finite element model is developed to describe and predict the vibrationcharacteristics of cylindrical shells partially treated with ACLD treatments. A closed-loopcontrol system based on proportional and derivative feedback of the sensor voltagegenerated by the piezo-sensor of the ACLD patches is established. The dynamic behaviorsof cylindrical shells with ACLD treatments such as natural frequencies, loss factors andresponses in the frequency domain are further investigated. The effects of several keyparameters such as control gains, location and coverage of ACLD treatmentson vibration suppression of cylindrical shells are also discussed. The numericalresults indicate the validity of the finite element model and the control strategyapproach. The potential of ACLD treatments in controlling vibration and soundradiation of cylindrical shells used as major critical structures such as cabins ofaircraft, hulls of submarines and bodies of rockets and missiles is thus demonstrated.

A fast and robust whole-body control algorithm for running

Dynamic simulation of human motion in real-time is a challenging problem due to the high mobility of human body and the redundancy of body control. This paper presents a robust whole-body control algorithm for simulating human running in real-time. The control algorithm tracks a reference motion through a proportional derivative (PD) feedback control rule for computing desired joint accelerations and an efficient and novel procedure for predicting ground reaction force (GRF) and joint actuation torques, which are subsequently applied to a forward dynamics simulation. The proposed control algorithm is firstly demonstrated to track a measured running motion and the predicted GRF is shown in good agreement with the experimental data. Further, the capability to handle extra loads is demonstrated with load carriage studies. In summary, the present approach offers a fast and robust way to synthesise physically valid dynamic motions from captured motion samples without the need of measured GRF.

Investigation of Active Damping Approaches for PI-Based Current Control of Grid-Connected Pulse Width Modulation Converters With LCL Filters

This paper deals with various active damping approaches for PI-based current control of grid-connected pulsewidth-modulation (PWM) converters with LCL filters, which are based on one additional feedback. Filter capacitor current, as well as voltage feedback for the purpose of resonance damping, are analyzed and compared. Basic studies in the continuous Laplace domain show that either proportional current feedback or derivative voltage feedback yields resonance damping. Detailed investigations of these two approaches in the discrete <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$z$</tex></formula> -domain, taking into account the discrete nature of control implementation, sampling, and PWM, are carried out. Several ratios of LCL resonance frequency and control frequency are considered. At high resonance frequencies, only current feedback stabilizes the system. At medium resonance frequencies, both approaches have good performance. At low resonance frequencies, stability gets worse, even though voltage feedback offers slightly better damping properties. Measurements validate the theoretical results.

Effect of displacement, velocity, and combined vibrotactile tilt feedback on postural control of vestibulopathic subjects

Vibrotactile tilt feedback was used to help vestibulopathic subjects control their anterioposterior (AP) sway during sensory organization tests 5 and 6 of Equitest computerized dynamic posturography. We used four kinds of signals to activate the feedback. The first signal was proportional (P) to the measured tilt of the subject, while the second used the first derivative (D) of the tilt. The third signal was the sum of the proportional and one half of the first derivative signals (PD). The final signal used a prediction of the subject's sway projected 100 msec in advance. The signals were used to activate vibrators mounted on the front of the torso to signal forward motion, and on the back of the torso for backward motion. Subject responses varied significantly with the kind of feedback signal. Proportional and derivative feedback resulted in similar root mean squared tilt, but the PD signal significantly reduced the tilt compared to either P or D feedback. The predicted motion signal also reduced the response compared to the PD signal. These preliminary results are somewhat consistent with an inverted pendulum model of postural control, but need to be confirmed with a larger study that also considers mediolateral tilt and feedback. The improvement by using a predictor is consistent with compensating for a neural processing delay.

Role of current profiles and atomic force microscope tips on local electric crystallization of amorphous silicon

Various types of conductive tips in atomic force microscope (AFM) are used to localize field-enhanced metal-induced solid phase crystallization (FE-MISPC) of amorphous silicon at room temperature down to nanoscale dimensions. The process is driven by electrical currents ranging from 0.1 nA to 3 nA between the tip and the bottom nickel electrode. The amplitude of the current is controlled by a metal-oxide-semiconductor field-effect transistor-based regulation circuit using proportional and derivative feedback loops. We analyze the results of the FE-MISPC process as a function of exposition current profiles, topographic changes, local conductivity changes (using current-sensing AFM) and regulation parameters. We found out that the FE-MISPC crystallization requires fluctuations of the exposition current rather than its stability. This is independent of the actual current set-point level. We also show the influence of the process on the AFM probes employed and vice versa. Bulk diamond probes exhibit superior endurance compared to bare or coated silicon probes, nevertheless all tips produce similar FE-MISPC results.

Design and Application of Improved PDF Controller in Higher-Order System

This article focuses on improving PDF (Pseudo Derivative Feedback) controller and employing it in electro-hydraulic position servo system of pump-controlled cylinder. Based on PDF theory, the derivative controller has been improved according to zero-placement theory. System’s stability has been analyzed. Moreover, the improved PDF is compared to 1DF PID and traditional PDF through simulation using an approximated dynamic system model of a higher-order hydraulic system, which consists of PLC, digital valve, hydraulic cylinder and optical sensor. The results show that the improved PDF controller provides satisfactory control performance on contrast with 1DF PID control strategy and traditional PDF controller in hydraulic system.

Active control of secondary resonances piezoelectric sandwich beams

Secondary resonances of piezoelectric/elastic/piezoelectric sandwich beams submitted to active control are studied in this paper. The proportional and derivative nonlinear potential feedback controls via piezoelectric sensor and actuator layers are used. The dynamics of the beam is modelled by a highly nonlinear ordinary-differential equation. The method of multiple scales is applied and approximate solutions are obtained for hard excitations. Analytical frequency and phase-amplitude relationships as well as the time response are explicitly given for various super- and subharmonic resonances. Static and dynamic stability criteria are elaborated and critical displacement and excitation amplitudes associated to the resulting unstable zones are analytically given. The feedback parameters effects on the subharmonic and superharmonic resonances and on their stability are investigated.

Feedback control of the position of the levitated superconducting magnet in the RT-1 device

The Ring Trap-1 (RT-1) device confines a high- β plasma in a magnetospheric configuration which is generated by a high-temperature-superconducting coil levitated in a vacuum chamber. The levitated coil is unstable with respect to the vertical motion when it is attracted from above. The vertical motion has been analyzed from the equation of motion and the flux conservation law and the response of the P D (proportional–derivative) feedback system of RT-1 has been formulated by using a transfer function. The result of the model analysis has shown sufficient agreement with experiments. To meet the various requirements in order to conduct the plasma experiments and measurement, the feedback gains are optimized to suppress a feedback noise in parallel with ensuring the stability of the system.

Response of a MEMS (microelectromechanical systems) directional microphone diaphragm with active Q control.

Measured results are presented that demonstrate the use of proportional and derivative electronic feedback to improve the performance of a directional microphone. The microphone diaphragm consists of a 1 × 2 mm stiffened plate fabricated out of polycrystalline silicon that is supported on a central hinge. The sound pressure gradient incident on the diaphragm produces a rocking motion about the central hinge. Interdigitated comb fingers at each end of the diaphragm enable both capacitive sensing and electrostatic actuation. The sound pressure gradient near the diaphragm has been measured by numerically differentiating the pressure measured by a probe microphone at locations around the diaphragm. The sound‐induced motion of the diaphragm was measured using a laser vibrometer. From these measurements, estimates of the mechanical parameters of the diaphragm were obtained. By applying a known quasi‐static voltage across the interdigitated fingers and measuring the resulting diaphragm deflection, an estimate fo...

Optimal control using derivative feedback for linear systems

This paper presents the solution of the linear optimal control problem using derivative feedback for continuous, time-invariant, linear systems. The state-derivative and output-derivative feedback controllers are investigated. In this work, the optimal feedback gain matrices are derived which minimize the non-standard quadratic performance index. An explicit expression of the optimal state-derivative feedback gain is derived. Additionally, a convergent algorithm to solve the output-derivative feedback gains is demonstrated. The problems are studied for non-singular and singular open-loop state matrices. The necessary conditions for the existence of optimal gains are established. Finally, simulation results are included to show the effectiveness of the proposed approach.

Optimization and evaluation of a proportional derivative controller for planar arm movement

In most clinical applications of functional electrical stimulation (FES), the timing and amplitude of electrical stimuli have been controlled by open-loop pattern generators. The control of upper extremity reaching movements, however, will require feedback control to achieve the required precision. Here we present three controllers using proportional derivative (PD) feedback to stimulate six arm muscles, using two joint angle sensors. Controllers were first optimized and then evaluated on a computational arm model that includes musculoskeletal dynamics. Feedback gains were optimized by minimizing a weighted sum of position errors and muscle forces. Generalizability of the controllers was evaluated by performing movements for which the controller was not optimized, and robustness was tested via model simulations with randomly weakened muscles. Robustness was further evaluated by adding joint friction and doubling the arm mass. After optimization with a properly weighted cost function, all PD controllers performed fast, accurate, and robust reaching movements in simulation. Oscillatory behavior was seen after improper tuning. Performance improved slightly as the complexity of the feedback gain matrix increased.

Stabilization of Descriptor Systems by Derivative Feedback

Stabilization of Descriptor Systems by Derivative Feedback

Neural-Mechanical Feedback Control Scheme Generates Physiological Ankle Torque Fluctuation During Quiet Stance

We have recently demonstrated in simulations and experiments that a proportional and derivative (PD) feedback controller can regulate the active ankle torque during quiet stance and stabilize the body despite a long sensory-motor time delay. The purpose of the present study was to: 1) model the active and passive ankle torque mechanisms and identify their contributions to the total ankle torque during standing and 2) investigate whether a neural-mechanical control scheme that implements the PD controller as the neural controller can successfully generate the total ankle torque as observed in healthy individuals during quiet stance. Fourteen young subjects were asked to stand still on a force platform to acquire data for model optimization and validation. During two trials of 30 s each, the fluctuation of the body angle, the electromyogram of the right soleus muscle, and the ankle torque were recorded. Using these data, the parameters of: 1) the active and passive torque mechanisms (Model I) and 2) the PD controller within the neural-mechanical control scheme (Model II) were optimized to achieve potential matching between the measured and predicted ankle torque. The performance of the two models was finally validated with a new set of data. Our results indicate that not only the passive, but also the active ankle torque mechanism contributes significantly to the total ankle torque and, hence, to body stabilization during quiet stance. In addition, we conclude that the proposed neural-mechanical control scheme successfully mimics the physiological control strategy during quiet stance and that a PD controller is a legitimate model for the strategy that the central nervous system applies to regulate the active ankle torque in spite of a long sensory-motor time delay.

Enhancing Stability of an Autonomous Microgrid using a Gain Scheduled Angle Droop Controller with Derivative Feedback

This paper discusses the stability of an autonomous microgrid in which, load sharing by a gain scheduled angle droop controller with derivative feedback is proposed. It is assumed that all the DGs are connected through Voltage Source Converter (VSC). The VSCs are controlled by state feedback controller to achieve desired voltage and current outputs that are decided by a droop controller. First a load sharing strategy is derived in terms of droop controller gain and converter output inductance, combining angle droop controller and DC load flow analysis. Then state space models of converters with its associated feedback controller are derived to investigate system stability as a function of the droop controller gain and converter output inductance through eigen value analysis. It is shown that with proposed angle droop controllers, where the droop gains are scheduled based on the output power along with derivative feedback it is possible to achieve a higher stability margin with better load sharing. These observations are then verified through simulation studies using PSCAD/EMTDC. It will be shown that the simulation results closely agree with stability behavior predicted by the eigenvalue analysis.