Direct Strain Feedback Research Articles

Adaptive Notch Filter in a Two-Link Flexible Manipulator for the Compensation of Vibration and Gravity-Induced Distortion

This paper presents a 2-link, 2-DOF flexible manipulator control using an inverse feedforward controller and an adaptive notch filter with a direct strain feedback controller. In the flexible manipulator, transient and residue vibrations inhibit the full potential of the manipulator. Vibrations caused by abrupt changes in the direction of the links are referred to as transient vibrations, whereas residual vibrations occur when the arm takes too long to settle after engaging in the intended task. The feedforward adaptive notch filter will reduce transient vibration caused by the manipulator arm beginning and halting suddenly, while the strain feedback will assure the quick decay of leftover vibrations. Maple, Maplesim, and MATLAB tools were used to model the manipulator and create the inverse controller and adaptive notch filter. The experiments took place in the dSPACE control desk environment. The experimental results of the spectral power of strain resulting from the two strategies are compared. From the results, the adaptive notch filter control had over an 80% improvement in the reduction in resonant frequencies that contribute to vibration. The results confirmed the feasibility of the approach, characterized by very minimal transient vibrations and a quick settling of the end effector.

Hybrid vibration control of an industrial CFRP composite robot-manipulator system based on reduced order model

This paper introduces a novel hybrid vibration control of an industrial flexible link manipulator (FLM) with carbon-fiber reinforced polymer (CFRP) composite material. The hybrid controller consists of a closed-loop direct strain feedback controller (DSFC) and a new open-loop input shaper (OLIS), and its performance is examined and compared by numerical simulation and experiment. Vibration attenuation is also verified by a spare sensor, an accelerometer. Thanks to the design of an analog isolator circuit, data acquisition of the real-time experiments are carried out noise-free from the servo driver. Reduced-order-model (ROM) is generated for the composite link with three different loading conditions and model for servo system is derived via system identification. Impulse force test hammer (IFTH) equipment is used to excite the system with force input and the results of the experiments/simulations confirm that the controller is robust against the impulse disturbances. As a result, a decrease of 88 ± 6.9 percent in vibration amplitudes and a decrease of 90 ± 7 percent in vibration duration confirms that the proposed controller is effective for vibration control of the flexible arm even under disturbance. Controller performance also enabled the FLM to work with payloads 16 times of its own weight.

On the Equivalence of Direct Strain Feedback and Lumped Parameter Wave Echo Control for Oscillation Damping of Elastic-Link Arms

The work discusses two control concepts. Both approach oscillation damping for elastic link robotic arms from fundamentally different theoretical directions. Despite their principal difference, the work consolidates both control schemes by mathematically deriving the equivalence of the resulting control laws. This letter demonstrates the practical application of the oscillation damping on a multi-elastic-link experimental setup. With a special emphasis on the influence of static deflections due to gravity, the letter finally compares the damping action as a modulation to the joint position, joint velocity, and joint motor current reference. The comparison leads to recommendations for strain-based oscillation damping of elastic-link arms under gravitational influence.

On the Stabilization of the Disk-Beam System via Torque and Direct Strain Feedback Controls

This note deals with the stabilization problem of a rotating disk-beam system. The proposed feedback law consists of a nonlinear torque control exerted on the disk, whereas a direct strain control is applied at the beam with a rigid offset. As a consequence, we end up with a nondissipative nonlinear hybrid PDE-ODE system and hence the existence and stability of solutions of the system cannot be addressed by using standard methods such as energy-multiplier or frequency-domain. To overcome this situation, we adopt the Riesz basis methodology and show that the closed-loop system is well-posed and stable as long as the angular velocity of the disk is less than a well-defined value related to the beam. The results are illustrated through a wide set of numerical examples.

Feedback stabilization of rotating Timoshenko beam with adaptive gain

The problem of boundary feedback stabilization of rotating Timoshenko beam, arising from control of flexible robot arms, is studied in this paper. First, under gain adaptive direct strain feedback controls, a counterexample is given to show that the corresponding closed loop system is not asymptotically stable, which is contrary to traditional conjecture. The counterexample given in this paper also exemplifies an interesting result: certain two two-order linear partial differential equations with five homogeneous boundary conditions have non-trivial solutions. Then, with an additional boundary feedback control, the related energy of the closed loop system is proved to be strongly stable, or more precisely, the configuration of the beam can be exponentially stabilized with some suitable non-linear boundary feedback controls with adaptive gain.

On the exponential stability of an initial-boundary equation arising from strain feedback control of flexible robot arms with rigid offset

This paper is concerned with an initial-boundary value equation arising from direct strain feedback control of flexible robot arms with a revolute joint and rigid offset. By analyzing the spectrum and by estimating the norm of the resolvent of the system operator associated with the equation, it is verified that the equation admits a unique solution and, furthermore, the solution is exponentially stable, no matter how long is the rigid offset.

Shear force feedback control of a single-link flexible robot with a revolute joint

In this paper we present a shear force feedback control method for a single-link flexible robot arm with a revolute joint for which it has been shown that direct bending strain feedback can suppress its vibration. Our primary concern is the stability analysis of the closed-loop equation which has not appeared in the literature. We show the existence of a unique solution and the exponential stability of this solution by doing spectral analysis and estimating the norm of the resolvent operator associated with this equation. Some experiments are also conducted to verify these theoretical developments.

Initial-boundary value problem and exponential decay for a flexible-beam vibration with gain adaptive direct strain feedback control

Initial-boundary value problem and exponential decay for a flexible-beam vibration with gain adaptive direct strain feedback control

A Generalization of Direct Strain Feedback Control for a Flexible Structure with Spatially Varying Parameters and a Tip Body

A Generalization of Direct Strain Feedback Control for a Flexible Structure with Spatially Varying Parameters and a Tip Body

Asymptotic behaviour of the spectrum of a direct feedback control system

AbstractThis paper establishes an estimate for the asymptotic behaviour of the spectrum of a direct strain feedback (DSF) control system. The results show that the system operator corresponding to the closed loop system cannot have an analytic extension and that the decay rate for the system energy is not proportional to the feedback constant.

Further theoretical results on direct strain feedback control of flexible robot arms

This paper is concerned with stability analyses for some nonstandard second-order partial differential equations arising from direct strain feedback control of flexible robot arms. Exponential stability issues are addressed for three types of differential equations, one of which is in general abstract evolution equation form and the other two are in partial differential equation form. The obtained results are of especially theoretical interest because they reveal the essence of direct strain feedback control and demonstrate its power in control of flexible arms.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Shear force feedback control of flexible robot arms

For flexible robots with rotational joints it has been shown previously by Luo (1993), that direct strain feedback can damp out vibrations very satisfactorily. In this paper, a simple sensor-based output feedback control law, called shear force feedback, is newly proposed to control vibrations arising from structural flexibility of robots of Cartesian or SCARA types. Closed-loop exponential stability of such shear force feedback system is proved. Experimental results on set point control and trajectory tracking control are reported. It is found that the simple PI+shear force feedback can yield good performance for both robot motion and vibration suppression.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Semigroup approach to the stability of a direct strain feedback control system of elastic vibration with structure damping

In this paper, we relate a kind of second order hyperbolic system to an analytic semigroup, which is most often applied to the direct strain feedback (DSFB) control of flexible robot arms. The spectrum analysis is presented to confirm the positive function of DSFB.

Direct strain feedback control of flexible robot arms: new theoretical and experimental results

This paper addresses control problems for flexible robot arms by using direct strain feedback. The purpose is to make clear why direct strain feedback can damp out vibration of flexible arms satisfactorily. We concentrate on one-link flexible robot arms whose dynamic models can be represented by linear partial differential equations with appropriate boundary conditions which have been well examined in a number of papers. A key contribution of this paper is the introduction of the concept of (strict) A-dependent operators, which allows us to prove rigorously the closed loop stability of direct strain feedback and the existence and uniqueness of nonstandard second order abstract differential equations in Hilbert spaces. Several control experiments are performed, verifying the main theoretical points of this paper, demonstrating satisfactory control results of direct strain feedback, and leading to potential application of this simple control method for flexible robot control. >

Strain rate control during deformation of ice: An assessment of the performance of a new servo-controlled triaxial testing system

A new ice triaxial testing system has been developed that necessitates the use of jacketed specimens which have prevented the use of a direct strain feedback signal from the specimen during servo-controlled experiments. An alternative arrangement has therefore been devised for which a thorough analysis is provided here, complementing the full apparatus description given in a companion paper. During testing, displacement is recorded using a remote transducer which measures deformation of both loading ram and ice specimen. The ram deformation component, which is elastic and proportional to the applied load, is continuously subtracted from the displacement signal within the servo-loop and thereby eliminated from the control signal. Because of the high strain rate sensitivity of ice deformation it is essential that proper control is maintained and consequently a series of calibration tests has been conducted to check the system performance. Results show close agreement between nominal test strain rates and those measured directly on polyethylene and polycrystalline ice specimens for strain rates in the range 10 −2–10 −5/s. Control was lost immediately after failure during brittle fracture, however, implying a limit to the response of the system when dealing with very severe changes in loading.