Derivative Feedback Research Articles

Stability of Human Balance With Reflex Delays Using Galerkin Approximations

Falling is the leading cause of both fatal and nonfatal injury in the elderly, often requiring expensive hospitalization and rehabilitation. We study the stability of human balance during stance using inverted single- and double-pendulum models, accounting for physiological reflex delays in the controller. The governing second-order neutral delay differential equation (NDDE) is transformed into an equivalent partial differential equation (PDE) constrained by a boundary condition and then into a system of ordinary differential equations (ODEs) using the Galerkin method. The stability of the ODE system approximates that of the original NDDE system; convergence is achieved by increasing the number of terms used in the Galerkin approximation. We validate our formulation by deriving analytical expressions for the stability margins of the double-pendulum human stance model. Numerical examples demonstrate that proportional–derivative–acceleration (PDA) feedback generally, but not always, results in larger stability margins than proportional–derivative (PD) feedback in the presence of reflex delays.

Entry trajectory planning based on three-dimensional acceleration profile guidance

A new entry trajectory generation approach based on rapid planning three-dimensional acceleration profile (TDAP) is proposed in this paper. The TDAP planner concept means extending the traditional drag planning approach into three dimensional drag space to accommodate much larger downrange or cross-range, and improve the maneuvering capability by utilizing both angle of attack and bank as primary control commands. To figure out this problem, firstly, the planner transforms the generation of TDAP into scheming two sub-profiles, longitudinal drag acceleration profile and lateral lift to drag acceleration profile in parallel. Each profile is generated in the corridor converted by all path constraints correspondingly. Secondly, a reduced order dynamics system is employed to extract all standard state variables and adjust the three-dimensional acceleration profile, ensuring the terminal position precision requirement to be met. Finally, a combined proportional derivative (PD) feedback law is designed to track the reference profile. Simulations with the Common Aero Vehicle (CAV) model show that the 3-D trajectories of both planned and generated by the guidance law can successfully satisfy all path constraints and flight task requirements.

Delay-dependent decentralized control for nonlinear similar interconnected large-scale systems

In this paper, the problem of delay-dependent decentralized control for a class of nonlinear large-scale interconnected systems with similar structure is investigated, where the linear state vectors, the nonlinear state vectors and the nonlinear interconnections involve time delays. The new similar structure is presented via memory feedback. Based on which, by exploiting the structure of interconnected systems, the new integral inequalities, constrained Lyapunov equations and LMI method, a decentralized memory derivative feedback control strategy is proposed to stabilize the resulting interconnected systems uniformly asymptotically, in addition, the stability domain is estimated. Finally, simulation results show the effectiveness of the proposed approach.

Размещение полюсов при управлении MIMO-системой с обратной связью по производным состояния

Размещение полюсов при управлении MIMO-системой с обратной связью по производным состояния

Flatness-based active disturbance rejection control for linear systems with unknown time-varying coefficients

A flatness-based active disturbance rejection control approach is proposed to deal with the linear systems with unknown time-varying coefficients and external disturbances. By selecting appropriate nominal values for the parameters of the system, all the deviation between the nominal and actual dynamics of the controlled process, as well as all the external disturbances can be viewed as a total disturbance. Based on the accurately estimated total disturbance with the aid of the proposed extended state observer, a linear proportional derivative feedback control law taking into account the derivatives of the desired output is designed to eliminate the effect of the total disturbance on the system performance. Finally, the load frequency control problem of a single-area power system with non-reheated unit is employed as an illustrative example to demonstrate the effectiveness of the proposed approach.

Time-Delayed Control of SISO Systems for Improved Stability Margins

While time delays typically lead to poor control performance, and even instability, previous research shows that time delays can, in some cases, be beneficial. This paper presents a new benefit of time-delayed control (TDC) for single-input single-output (SISO) linear time invariant (LTI) systems: it can be used to improve robustness. Time delays can be used to approximate state derivative feedback (SSD), which together with state feedback (SF) can reduce sensitivity and improve stability margins. Additional sensors are not required since the state derivatives are approximated using available measurements and time delays. A systematic design approach, based on solution of delay differential equations (DDEs) using the Lambert W method, is presented using a scalar example. The method is then applied to both single- and two-degree of freedom (DOF) mechanical systems. The simulation results demonstrate excellent performance with improved stability margins.

MaCACH: An adaptive cache-aware hybrid FTL mapping scheme using feedback control for efficient page-mapped space management

Flash memories based storage systems have some specific constraints leading designers to encapsulate some management services into a hardware/software layer called the Flash Translation Layer (FTL). The performance of flash based storage systems such as Solid State Drives (SSDs) are strongly driven by the FTL intricacies and also by a cache system placed on top of the FTL. Those systems are generally developed independently. In order to accelerate I/O request processing, FTLs use some space of the flash memory called the over-provisioning space. The over-provisioning space is thus not dedicated to data storage and should be small and of fixed size. This paper presents MaCACH, a maximum page-mapped region usage, cache-aware, and configurable hybrid mapping scheme. MaCACH design is based on two motivations: (1) the FTL should make full profit of the fixed size over-provisioning space to accelerate I/O processing, (2) as in most cases cache systems are put on top of FTLs, the latter should use information about the former in order to optimize data management. MaCACH is mainly based on two solutions: (1) it uses a proportional–integral–derivative (PID) feedback control system to keep the over-provisioning space fully used whatever the I/O workload characteristics, making it more efficient, (2) it is cache-aware as it uses a common feature of flash specific caches in order to route evicted data toward a page-mapped or block-mapped area which helps in optimizing the write operation costs. The performance evaluation shows very good behavior of MaCACH as compared to state-of-the-art FTLs in addition to a high flexibility as MaCACH has a large configuration space.

Decentralised memory static output feedback control for the nonlinear time-delay similar interconnected systems

In this paper, the problem of decentralised memory static output feedback control for a class of nonlinear time-delayed interconnected systems with similar structure is investigated, where both the linear and nonlinear state vectors involve time delay. The contributions of the paper include the following: (1) a new similar structure is presented via memory static output feedback; (2) by exploiting the structure of interconnected systems, the new integral inequalities, constrained Lyapunov equations and LMI method, the decentralised memory static output derivative feedback controllers with similar structure are designed, which is dependent of time delays, to stabilise the interconnected systems uniformly asymptotically; and (3) the stability domain is estimated. The conservatism of the results obtained is reduced by full using the system output information. Finally, the numerical examples are given to demonstrate the effectiveness of the results obtained in this paper.

Impulsive Controllability/Observability for Interconnected Descriptor Systems with Two Subsystems

The problem of decentralized impulse controllability/observability for large-scale interconnected descriptor systems with two subsystems by derivative feedback is studied. Necessary conditions for the existence of a derivative feedback controller for the first subsystem of the large-scale interconnected descriptor systems ensuring the second subsystem to be impulse controllable and impulse observable are derived, respectively. Based on the results, a derivative feedback controller for the first subsystem of the large-scale interconnected descriptor systems is constructed easily such that the second subsystem is impulse controllable or impulse observable. Finally, examples are given to illustrate the effectiveness of the results obtained in this paper.

Experiments on resonant vibration suppression of a piezoelectric flexible clamped–clamped plate using filtered-U least mean square algorithm

This article investigates the adaptive filtered-U least mean square feed-forward algorithm for active resonant vibration control of a clamped–clamped flexible piezoelectric plate structure under persistent harmonic excitation. Different from the widely used filtered-X least mean square algorithm based on the finite impulse response filter, the filtered-U least mean square algorithm uses the infinite impulse response filter. An infinite impulse response filter can be constituted simply by using two adaptive transversal filters. The filtered-U least mean square algorithm can model the system accurately with much fewer coefficients. Moreover, the filtered-U least mean square algorithm has better control performance and stability in the presence of vibration control feedback, owing to the inherent zero-pole structure of the infinite impulse response filter. In this investigation, the filtered-U least mean square algorithm is implemented only in experiments. Two experimental cases are carried out, including the reference signal extracted from the function signal generator and the lead zirconate titanate sensor. A proportional–derivative feedback control algorithm is also applied as a comparison. The experimental results demonstrate the feasibility and performance of the designed proportional–derivative controller and filtered-U least mean square controller.

Position feedback control for electrostatically controlled linear actuator

In this paper, we introduce a position feedback control for an electrostatically controlled linear actuator. The electrostatically controlled linear actuator, which is fabricated using microelectromechanical systems technology, drives sliders in parallel, precise motion, and a large stroke. In literature, novel technologies have been studied for an improvement of this actuator. Among these, a micro-potentiometer that utilized probe dipping into a μ-pool technology has been employed to detect position of the slider for electrostatically controlled linear actuator control. In this research, we are interested in proportional---integral---derivative feedback control using a micro-potentiometer and microcontroller as our current development stage of the electrostatically controlled linear actuator. Experimental results show that the feedback control with tuning gains performed a significant improvement compared to that without tuning gains. The slider was moved to the desired position with reduced control time, no overshoot, oscillation, and acceptable steady-state error.

Simultaneous robust normalization and delay‐dependent robust H∞ stabilization for singular time‐delay systems with uncertainties in the derivative matrices

SummaryThis paper investigates the problem of simultaneous robust normalization and delay‐dependent H∞ control for a class of singular time‐delay systems with uncertainties. Not only the state and input matrices but also the derivative matrices of the considered systems are assumed to have uncertainties. New sufficient conditions for the existence of a proportional plus derivative state feedback H∞ controller are derived as LMIs such that the closed‐loop singular system is normal, stable, and guarantee a specific level of performance. Specially, a static state feedback H∞ controller alone or a state‐derivative feedback H∞ controller alone can unite to be dealt with by applying our proposed method. Two simulation examples are provided to demonstrate the effectiveness of the proposed approach in this paper. Copyright © 2014 John Wiley & Sons, Ltd.

State derivative feedback for adaptive cancellation of unmatched disturbances in unknown strict-feedback LTI systems

Solutions exist for the problem of canceling sinusoidal disturbances by the measurement of the state or by the measurement of an output for linear and nonlinear systems. In this paper, an adaptive backstepping controller is designed to cancel sinusoidal disturbances forcing an unknown linear time-invariant system in controllable canonical form which is augmented by a linear input subsystem with unknown system parameters. The state-derivatives of the original subsystem and the state of the input subsystem are the only measurements that are used in the design of the controller. The design is based on four steps, (1) parametrization of the sinusoidal disturbance as the output of a known feedback system with an unknown output vector that depends on unknown disturbance parameters, (2) design of an adaptive disturbance observer for both disturbance and its derivative, (3) design of an adaptive controller for the virtual control input, and (4) design of the final adaptive controller by using the backstepping procedure. It is proven that the equilibrium of the closed-loop adaptive system is stable and the state of the considered original subsystem converges to zero as t→∞ with perfect disturbance estimation. The effectiveness of the controller is illustrated with a simulation example of a third order system.

Design an intelligent proportional-derivative PD feedback linearization control for nonholonomic-wheeled mobile robot

This paper proposes a novel optimal Proportional--derivative PD Feedback linearization controller to achieve the best trajectory tracking for nonholonomic Wheeled Mobile Robots WMRs. In the core of...

A negative derivative feedback design algorithm

Vibration control logics based on the modal approach allow damping to be increased on a certain number of modes. The main limit associated with these strategies is represented by spillover on non-modelled modes. Negative derivative feedback (NDF) proves particularly robust against spillover since modal velocity is fed back through a band-pass filter so that undesired effects can be limited both at high and low frequencies. Unfortunately, the definition of the control gains for this logic is generally more difficult than other resonant controls owing to the lack of physical meaning. In this paper a design strategy for an NDF controller based on an optimal approach is proposed for single and multi-degrees of freedom systems and is tested on a cantilever beam finite element model.

Dynamic model and input shaping control of a flexible link parallel manipulator considering the exact boundary conditions

SUMMARYIn this paper, a rigid–flexible planar parallel manipulator (PPM) actuated by three linear ultrasonic motors for high-accuracy positioning is proposed. Based on the extended Hamilton's principle, a rigid–flexible dynamic model of the proposed PPM is developed utilizing exact boundary conditions. To derive an appropriate low-order dynamic model for the design of the controller, the assumed modes method is employed to discretize elastic motion. Then to investigate the interaction between the rigid and elastic motions, a proportional derivative feedback controller combined with a feed-forward-computed torque controller is developed to achieve motion tracking while attenuating the residual vibration. Then the controller is extended to incorporate an input shaper for the further suppression of residual vibration of flexible linkages. Computer simulations are presented as well as experimental results to verify the proposed dynamic model and controller. The input shaping method is verified to be effective in attenuating residual vibration in a highly coupled rigid–flexible PPM. The procedure employed for dynamic modeling and control analysis provides a valuable contribution into the vibration suppression of such a PPM.

Development of a neural controller applied in a 5 DOF robot redundant

In this paper the development of a neural controller implemented in a five Degrees Of Freedom (DOF) redundant robot is presented. The design of the control law considers the robotic system inverse model, including the performance of the actuators for the five joints, obtained through a feedforward neural network with backpropagation learning algorithm. This inverse structure is weighted by desired acceleration and derivative proportional feedback loops to provide the appropriate supply voltage to the servo motors of the robotic manipulator. Tracking tests are performed to a path in Cartesian space using a simulator developed using MatLab/Simulink software tools. It assesses the neural controller performance versus classical computed torque controller, comparing the results of curves in the joint space and Cartesian through RMS errors indices of Cartesian and joint positions.

Bifurcation of a Duffing Oscillator Having Nonlinear Fractional Derivative Feedback

Active feedback control is commonly used to attenuate undesired vibrations in vibrating machineries and structures, such as bridges, highways and aircrafts. In this paper, we investigate the primary resonance and 1/3 subharmonic resonance of a harmonically forced Duffing oscillator under fractional nonlinear feedback control. By means of the first order averaging method, slow flow equations governing the modulations of amplitude and phase of the oscillator are obtained. An approximate solution for the steady state periodic response is derived and its stability is determined by the Routh–Hurwitz criterion. We demonstrate that appropriate choices on the control strategies and feedback gains can delay or eliminate the undesired bifurcations and reduce the amplitude peak both of the primary and subharmonic resonances. Analytical results are verified by comparisons with the numerical integration results.

Eliminating Impulse for Descriptor System by Derivative Output Feedback

The problem of impulse elimination for descriptor system by derivative output feedback is investigated in this paper. Based on a novelly restricted system equivalence between matrix pencils, the range of dynamical order of the resultant closed loop descriptor system is given. Then, for the different dynamical order, sufficient conditions for the existence of derivative output feedback to ensure the resultant closed loop system to be impulse free are derived, and the corresponding derivative output feedback controllers are provided. Finally, simulation examples are given to show the consistence with the theoretical results obtained in this paper.

Time Response Options for Structural Damage Mitigation Using an Actuator Load

It is well known that time responses in a single input system cannot be altered under a state variable based feedback control system design. The closed loop eigenvector options assignable using the linear state feedback controller is fixed in single input systems. As a result, time responses are also fixed. However, when state derivative feedback is augmented, similar to a multiple input system, several closed loop eigenvector options are possible. Hence, it allows time response shaping available in the single input systems. In this paper, a novel procedure to design simultaneous state and state derivative feedback controller for single input systems is presented. Then to illustrate its utility, structural damage growth mitigation (active structural prognosis) using time response shaping under a structural load is illustrated. It is shown that the life of the damaged structure in a dynamic environment is possible to extend using time response options resulting from a typical state/state derivative feedback controller. A discrete dynamic structure is considered to illustrate the underlying principles of active structural prognosis.