Amalendu Mukherjee

Impedance Control of Space Robots Using Passive Degrees of Freedom in Controller Domain

Impedance control is an efficient and stable method of providing trajectory and force control in robotic systems. The procedure by which the impedance of the manipulator is changed is a very important aspect in the design of impedance based control schemes. In this work, a scheme is presented in which the control of impedance at the interface of the end effector and the space structure is achieved by introduction of a passive degree of freedom (DOF) in the controller of the robotic system. The impedance is shown to depend upon a compensation gain for the dynamics of the passive DOF. To illustrate the methodology, an example of a two DOF planer space robot is considered.

A scheme for robust trajectory control of space robots

Abstract This paper presents a scheme for robust trajectory control of free-floating space robots. The idea is based on the overwhelming robust trajectory control of a ground robot on a flexible foundation and robust foundation disturbance compensation presented elsewhere. No external jets/thrusters are required or used in the scheme. An example of a three-link robot mounted on a free-floating space platform is considered for demonstrating the efficacy of the control scheme. Bond graph technique has been used for the purpose of modeling and simulation. Robustness of the control scheme is guaranteed since the controller does not require the knowledge of the manipulator parameters.

Improvements to Single-Fault Isolation Using Estimated Parameters

A method for finer fault isolation or localization in the model-based fault detection and isolation (FDI) paradigm is developed using parallely computed bond graph models. Many of the existing modelbased FDI methods are based on the evaluation of model consistency expressed in terms of analytical redundancy relations (ARR). These evaluations lead to residuals, and a number of sensors are to be installed in the plant to generate independent signatures needed for fault isolation. However, all the possible faults may not be isolable with the available instrumentation, and it is sometimes expensive or technically impossible to install necessary sensors in the plant to physically measure each and every state. In such situations, all component faults may not be uniquely isolated. However, a unique fault parameter subspace can be identified. One of the possible solutions, as proposed in this article, is to estimate parameters of that subspace from the ARR by assuming a single-fault hypothesis and then to incorporate the estimated values in separate models to run parallel with the plant during the fault. Thereafter, comparison of model behaviors leads to localization of the faulty parameters. This method is applied to an example system.

Modelling of basic induction motors and source loading in rotor–motor systems with regenerative force field

Abstract In this article a short route to arrive at bondgraph model of induction motor is discussed. Creating a model of an induction motor with electrical, magnetic and mechanical ports is a considerably puzzling issue. The usual approach is to view induction motor as an extended transformer with a resistor varying as a function of slip. Such models are inadequate when motors are driving a general class of loads and when electrical input is not a pure harmonic. Though there are several models with intertance fields derived in classical manner they obscure the physics of the system and are often intractable. In this article a general principle of modelling induction motors is presented by viewing the fluctuation of magnetic field from two coordinates, one fixed to stator and other to the rotor. The mechanical port emerges out naturally and the model is computationally efficient and compact. An interesting phenomenon of such a motor driving a rotor with material damping beyond its threshold speed of instability is simulated and discussed. Rotors with internal damping tend to become unstable when driven beyond a speed which is entirely determined by a ratio of external and internal dampings and the critical speed. When such rotors are driven by an induction motor with supply frequency beyond the threshold speed of instability very interesting phenomena are observed in the coupled system like entrainment of rotor speed, existence of limiting oribit of the rotor, small fluctuation of angular speed caused by unbalance and seemingly chaotic behaviour. This example shows the power of bondgraph modelling of induction motor with a mechanical port which can be coupled to a general class of loads.

Impedance Control of Space Robot

Abstract The force control of a space robot is a difficult task, as the interaction of robot tip with the environment causes the base to change its position and orientation. Impedance control is an efficient method for trajectory and force control in a robotic system. The procedure by which the impedance of the manipulator is changed is a very important aspect in the design of impedance-based control schemes. This paper presents a scheme in which the control of impedance at the end-effector environment interface is achieved by introduction of a passive degree of freedom (DOF) in the robotic system in the controller. The impedance depends upon a gain compensation for the dynamics of the passive DOF.

An Investigation into the Physics Behind the Stabilizing Effects of Two-Phase Lubricants in Journal Bearings

Solid phase particles in two-phase lubricants used in journal bearings undergo deformation in the bearing clearance space during large amplitude journal whirl. The orbital energy causing instability of the rotor shaft is drawn from the drive and it is proportional to the orbital area whereas energy dissipation offered by the fluid film is a path function. The balance of these two energies decides the stability of rotor-bearing system. In the first part of this paper, equivalent snubber springs have been used to represent contact with solid phase particles and purely elastic collision is modeled. It is analytically shown that any perturbation of a circular orbit increases dissipative work, which may entrain the response of an otherwise unstable system (i.e., without perturbation) to a stable orbit. In the second part of this paper, a rigid rotor supported on journal bearings using two-phase lubricants is studied and it is shown that discontinuity in the support forces arising out of contact with solid-phase particles, irrespective of the nature of deformation of particles, is responsible for controlling the whirl orbit size.

Bond graph model of a solid oxide fuel cell with a C-field for mixture of two gas species

A true bond graph model of a solid oxide fuel cell (SOFC) is presented in this paper. The constitutive relations of a C-field for two species of gases are formulated in order to model the cathode and the anode channels of the fuel cell. Moreover, an existing R-field model has been extended for modelling of forced convection of a mixture of two gas species. For given values of system operating pressure, the air source and hydrogen source pressures, the outlet pressures and the inlet gas compositions, the fuel utilization (FU), and air utilization (AU) are interpreted in terms of the partial pressures of the gases in the anode channel and cathode channel. The model is simulated and various static and dynamic characteristic curves for the SOFC are obtained. It is found that the model is capable of capturing all the essential dynamics of the SOFC. Availability of this bond graph model will aid in designing robust model-based control strategies for the fuel cell system and also for performing exergy analysis of the system.

Attitude Control of a Free-Flying Space Robot using a Novel Torque Generation Device

In this paper we present a new torque generation device that can be used to control the attitude of space robots. The device is based on the principle of continuously variable transmission. A detailed analytical study of the device has been performed, and the behavior and stability of the overall system have been studied. Bond graph modeling has been used to conceive the device. The advantage of using this device is that many control strategies are possible for the control of a space vehicle.

A Methodology for Finding Invariants of Motion for Asymmetric Systems with Gauge-Transformed Umbra Lagrangian Generated by Bond Graphs

The purpose of this article is to obtain conservation laws (invariants of motion) for different energy domains through the extended Noether theorem and bond graphs. Bond graphs are profitably used in representing the physics of a system as well as obtaining its umbra-Lagrangian. The article extends Lagrangian-Hamiltonian mechanics to deal with asymmetries in the system, which incorporates dissipative and nonpotential fields in a compact Lagrangian form, such that one may obtain invariants of motion through extension of Noether’s theorem. A detailed methodology is outlined in this article for obtaining the invariants of motion for a general class of asymmetric systems with a gauge-transformed umbra-Lagrangian. Symmetrization of an asymmetric system is introduced through the concept of gauge functions, for which the classical Noether theorem is extended over vector fields in the extended manifold comprising real and umbra displacements and velocities, as well as real time. A generalization of the variational principle or least action principle is also presented, which leads to the proposed form of the umbra-Lagrange equation through recursive minimization of functionals. Several illustrative examples are given to elucidate this concept in different physical contexts.

A Study of a Bi-symmetric Electro-mechanical System through Umbra-Lagrangian Generated by Bondgraphs, and Noether's Theorem

This paper presents a dynamic analysis of an electro-mechanical system through the umbra-Lagranges equation proposed in a previous paper, which includes dissipative and non-potential fields in a compact Lagrangian form. An eXtended Noethers theorem along with an umbra-Hamiltonian is employed to get invariants of motion, or possible invariant trajectories. The umbra-Lagrangian of this electro-mechanical system is obtained through an eXtended Karnopps algorithm. The major contribution of this paper is the dynamic analysis eXploiting the symmetries of an electromechanical system comprising an eXternally and internally damped, symmetric, elastic rotor driven by a two-phase induction motor. For such a system the umbra-Lagrangian remains unchanged under two families of continuous transformations. The behavior of the limiting dynamics is obtained and validated through simulations. The stability issue of this system is also eXamined. Similar analysis is also eXtended to an identical rotor driven by a three-phase induction motor. As SO (2) symmetries are not obvious in this case due to the presence of three stator inertances, the three-phase induction motor is reduced to an equivalent SO (2) symmetric two-phase induction motor, to which the analysis is applied.