Improving the position control of a two degrees of freedom robotic sensing antenna using fractional-order controllers
TL;DR: In this paper, a closed-loop control strategy is proposed to drive a flexible link-based sensor, based on combining a feedforward term and a feedback phase-lag compensator of fractional order.
Abstract: Flexible links combined with force and torque sensors can be used to detect obstacles in mobile robotics, as well as for surface and object recognition. These devices, called sensing antennae, perform an active sensing strategy in which a servomotor system moves the link back and forth until it hits an object. At this instant, information of the motor angles combined with force and torque measurements allow calculating the positions of the hitting points, which are valuable information about the object surface. In order to move the antenna fast and accurately, this article proposes a new closed-loop control for driving this flexible link-based sensor. The control strategy is based on combining a feedforward term and a feedback phase-lag compensator of fractional order. We demonstrate that some drawbacks of the control of these sensing devices like the apparition of spillover effects when a very fast positioning of the antenna tip is desired, and actuator saturation caused by high-frequency sensor ...
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TL;DR: A new closed-loop control schema that cancels vibrations and improves the free movements of the antenna is proposed and algorithms to estimate the 3D beam position and the instant and point of contact with an object are proposed.
Abstract: Some insects or mammals use antennae or whiskers to detect by the sense of touch obstacles or recognize objects in environments in which other senses like vision cannot work. Artificial flexible antennae can be used in robotics to mimic this sense of touch in these recognition tasks. We have designed and built a two-degree of freedom (2DOF) flexible antenna sensor device to perform robot navigation tasks. This device is composed of a flexible beam, two servomotors that drive the beam and a load cell sensor that detects the contact of the beam with an object. It is found that the efficiency of such a device strongly depends on the speed and accuracy achieved by the antenna positioning system. These issues are severely impaired by the vibrations that appear in the antenna during its movement. However, these antennae are usually moved without taking care of these undesired vibrations. This article proposes a new closed-loop control schema that cancels vibrations and improves the free movements of the antenna. Moreover, algorithms to estimate the 3D beam position and the instant and point of contact with an object are proposed. Experiments are reported that illustrate the efficiency of these proposed algorithms and the improvements achieved in object detection tasks using a control system that cancels beam vibrations.
15 citations
TL;DR: A fractional-order sliding mode control scheme equipped with a disturbance observer for robust impedance control of a single-link flexible robot arm when it comes into contact with an unknown environment is presented.
Abstract: This paper presents a fractional-order sliding mode control scheme equipped with a disturbance observer for robust impedance control of a single-link flexible robot arm when it comes into contact with an unknown environment In this research, the impedance control problem is studied for both unconstrained and constrained maneuvers The proposed control strategy is robust with respect to the changes of the environment parameters (such as stiffness and damping coefficient), the unknown Coulomb friction disturbances, payload, and viscous friction variations The proposed control scheme is also valid for both unconstrained and constrained motions Our novel approach automatically switches from the free to the constrained motion mode using a simple algorithm of contact detection In this regard, an impedance control scheme is proposed with the inner loop position control This means that in the free motion, the applied force to the environment is zero and the reference trajectory for the inner loop position control is the desired trajectory However, in the constrained motion the reference trajectory for the inner loop is determined by the desired impedance dynamics Stability of the closed loop control system is proved by Lyapunov theory Several numerical simulations are carried out to indicate the capability and the effectiveness of the proposed control scheme
14 citations
TL;DR: An efficient scheme based on fractional order sliding mode control approach for precision tip position control of a single link flexible robot arm that is robust against the system parameters variations such as payload and viscous friction variations in the presence of the sinusoidal disturbance and the unknown Coulomb friction disturbances.
Abstract: This article presents an efficient scheme based on fractional order sliding mode control approach for precision tip position control of a single link flexible robot arm. The proposed control strate...
12 citations
Cites background from "Improving the position control of a..."
...In Feliu-Talegon and Feliu-Batlle (2017a, 2017b), a control strategy, consisting of two inner and outer loops, is proposed to realize the position control of a two degrees of freedom flexible link....
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TL;DR: An innovative control system is designed to remove vibrations using the singular perturbation theory combined with the input-state linearization technique, which includes fractional-order controllers that nearly remove unknown sensor offset and sensor ramp disturbances while reducing the high-frequency component of the control signal caused by sensor noise.
Abstract: This article deals with the control of two degrees of freedom manipulators that have a flexible and very lightweight link. These robots have a single low-frequency and high-amplitude vibration mode. Their actuators have high friction, and their vibration sensors are often strain gauges that have offset and high-frequency noise. These problems reduce the robot precision and produce noisy control signals that saturate actuators. An efficient control system is proposed to overcome these drawbacks. Actuator friction effect is nearly removed by closing a high gain position control loop around the actuator. It causes the separation of the robot dynamics into the controlled actuator fast subsystem and the link dynamics slow subsystem. Based on that, an innovative control system is designed to remove vibrations using the singular perturbation theory combined with the input-state linearization technique. This control system includes fractional-order controllers that nearly remove unknown sensor offset and sensor ramp disturbances while reducing the high-frequency component of the control signal caused by sensor noise. Simulated and experimental results show the superior performance of these controllers over other standard integer-order controllers of similar complexity and nominal behavior.
10 citations
TL;DR: Experimental results show that coupling dynamic modelling of the flexible manipulator system with harmonic drive match well with the proposed structure, both in the time and frequency domain.
Abstract: This paper formulates a coupling dynamic model for a flexible manipulator system with harmonic drive using experimental identification method. Parameters of the driven model of the harmonic joint a...
10 citations
References
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Book•
01 Jan 1999
TL;DR: In this article, the authors present a method for computing fractional derivatives of the Fractional Calculus using the Laplace Transform Method and the Fourier Transformer Transform of fractional Derivatives.
Abstract: Preface. Acknowledgments. Special Functions Of Preface. Acknowledgements. Special Functions of the Fractional Calculus. Gamma Function. Mittag-Leffler Function. Wright Function. Fractional Derivatives and Integrals. The Name of the Game. Grunwald-Letnikov Fractional Derivatives. Riemann-Liouville Fractional Derivatives. Some Other Approaches. Sequential Fractional Derivatives. Left and Right Fractional Derivatives. Properties of Fractional Derivatives. Laplace Transforms of Fractional Derivatives. Fourier Transforms of Fractional Derivatives. Mellin Transforms of Fractional Derivatives. Existence and Uniqueness Theorems. Linear Fractional Differential Equations. Fractional Differential Equation of a General Form. Existence and Uniqueness Theorem as a Method of Solution. Dependence of a Solution on Initial Conditions. The Laplace Transform Method. Standard Fractional Differential Equations. Sequential Fractional Differential Equations. Fractional Green's Function. Definition and Some Properties. One-Term Equation. Two-Term Equation. Three-Term Equation. Four-Term Equation. Calculation of Heat Load Intensity Change in Blast Furnace Walls. Finite-Part Integrals and Fractional Derivatives. General Case: n-term Equation. Other Methods for the Solution of Fractional-order Equations. The Mellin Transform Method. Power Series Method. Babenko's Symbolic Calculus Method. Method of Orthogonal Polynomials. Numerical Evaluation of Fractional Derivatives. Approximation of Fractional Derivatives. The "Short-Memory" Principle. Order of Approximation. Computation of Coefficients. Higher-order Approximations. Numerical Solution of Fractional Differential Equations. Initial Conditions: Which Problem to Solve? Numerical Solution. Examples of Numerical Solutions. The "Short-Memory" Principle in Initial Value Problems for Fractional Differential Equations. Fractional-Order Systems and Controllers. Fractional-Order Systems and Fractional-Order Controllers. Example. On Viscoelasticity. Bode's Analysis of Feedback Amplifiers. Fractional Capacitor Theory. Electrical Circuits. Electroanalytical Chemistry. Electrode-Electrolyte Interface. Fractional Multipoles. Biology. Fractional Diffusion Equations. Control Theory. Fitting of Experimental Data. The "Fractional-Order" Physics? Bibliography. Tables of Fractional Derivatives. Index.
3,962 citations
"Improving the position control of a..." refers methods in this paper
...Expression (71) has been obtained from combining the Grünwald–Letnikov (GL) definition of the discretised fractional operator (Vinagre, Podlubny, Hernandez, & Feliu, 2000) and the well-known property of the Laplace transform: L−1(F(s + 1/a)) = f (t )e−t/a being f (t ) = L−1(F(s)). Moreover, we have applied the short memory approximation in Podlubny (1998) with N = 500....
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...Moreover, we have applied the short memory approximation in Podlubny (1998) with N = 500....
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Book•
13 May 1980
TL;DR: This chapter discusses single-Input/Single-Output Relationships, nonstationary data analysis techniques, and procedures to Solve Multiple- Input/Multiple-Output Problems.
Abstract: Discusses engineering applications and recent developments based upon correlation and spectral analysis. Illustrations deal with applications to acoustics, mechanical vibrations, system identification, and fluid dynamics problems in aerospace, automotive, industrial noise control, civil engineering and oceanographic fields, as well as similar problems in other fields. Tackles problems and solutions, assuming reader has required hardware and software to compute estimates of correlation, spectra, coherence, and phase functions.
2,447 citations
"Improving the position control of a..." refers methods in this paper
...There are different ways to do it, however in this section, the method described in Piersol and Bendat (1993) has been employed, which is easy to use and is well suited for systems with little damped and very decoupled vibration modes....
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TL;DR: In this article, a method for tuning the PI λ D μ controller is proposed to fulfill five different design specifications, including gain crossover frequency, phase margin, and iso-damping property of the system.
881 citations
TL;DR: In this paper, the authors consider the class of flexible systems that can be described by a generalized wave equation, which relates the displacementu(x,t) of a body Θ in 3D space to the applied force distribution.
Abstract: Since mechanically flexible systems are distributed-parameter systems, they are infinite-dimensional in theory and, in practice, must be modelled by large-dimensional systems. The fundamental problem of actively controlling very flexible systems is to control a large-dimensional system with a much smaller dimensional controller. For example, a large number of elastic modes may be needed to describe the behavior of a flexible satellite; however, active control of all these modes would be out of the question due to onboard computer limitations and modelling error. Consequently, active control must be restricted to a few critical modes. The effect of the residual (uncontrolled) modes on the closed-loop system is often ignored. In this paper, we consider the class of flexible systems that can be described by a generalized wave equation,u
tt+Au=F, which relates the displacementu(x,t) of a body Θ inn-dimensional space to the applied force distributionF(x,t). The operatorA is a time-invariant symmetric differential operator with a discrete, semibounded spectrum. This class of distributed parameter systems includes vibrating strings, membranes, thin beams, and thin plates. The control force distribution
$$F(x,t) = \sum\limits_{i = 1}^M { \delta (x - x_i )f_i (t)} $$
is provided byM point force actuators located at pointsx
i on the body. The displacements (or their velocities) are measured byP point sensorsy
i(t)=u(z
j,t), oru
t(z
j,t),j=1, 2, ...,P, located at various pointsz
j along the body. We obtain feedback control ofN modes of the flexible system and display the controllability and observability conditions required for successful operation. We examine the control and observation spillover due to the residual modes and show that the combined effect of spillover can lead to instabilities in the closed-loop system. We suggest some remedies for spillover, including a straightforward phase-locked loop prefilter, to remove the instability mechanism. To illustrate the concepts of this paper, we present the results of some numerical studies on the active control of a simply supported beam. The beam dynamics are modelled by the Euler-Bernoulli partial differential equation, and the feedback controller is obtained by the above procedures. One actuator and one sensor (at different locations) are used to control three modes of the beam quite effectively. A fourth residual mode is simulated, and the destabilizing effect of control and observation spillover together on this mode is clearly illustrated. Once observation spillover is eliminated (e.g., by prefiltering the sensor outputs), the effect of control spillover alone on this system is negligible.
753 citations
"Improving the position control of a..." refers background in this paper
...The neglected vibration modes may produce observation and control spillover effects (Balas, 1978)....
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Book•
20 Mar 2006
TL;DR: In this article, Piezoelectric Shunt Damping is used to control the feedback control of structural vibration in a multi-port P2P system, and the feedback structure of P2D shunt damping is described.
Abstract: Fundamentals of Piezoelectricity- Feedback Control of Structural Vibration- Piezoelectric Shunt Damping- Feedback Structure of Piezoelectric Shunt Damping Systems- Instrumentation- Multi-port Shunts- Adaptive Shunt Damping- Negative Capacitor Shunt Impedances- Optimal Shunt Synthesis- Dealing with Hysteresis- Nanopositioning
548 citations
"Improving the position control of a..." refers methods in this paper
...In order to remove high-frequency vibrations of small amplitudes, piezoelectrics have been often used in flexible structures (e.g. Moheimani & Fleming, 2006)....
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