In order to increase the safety performance between human and the robot, the variable stiffness mechanism is commonly adopted due to its flexibility in various tasks. However, it makes the actuator more complex and increases the weight of the system. To deal with this problem, the active-passive variable stiffness elastic actuator (APVSEA) [1] and the variable stiffness control that uses a model matching control (MMC) with bond graph are proposed in this article. The APVSEA is modeled as a non-back drivable bond graph model. Combining the MMC with the non-back drivable bond graph model, the overall system can achieve active stiffness control. The simulations and the experiments show good control performance. They prove that the proposed method can achieve active stiffness control well. In the future, the proposed method can also be applied to the robot arm and exoskeletons for balancing safety and the control performance.
Fuzzy rules incorporated skyhook theory based vehicular suspension design for...IJERA Editor
The vehicle suspension system supports and isolate the vehicle body and payload from road vibrations due to surface roughness by maintaining a controllable damping traction force between tires and road surface. In modern luxury vehicles semi active suspension system are offering both the reliability and accuracy that has enhanced the passenger ride comfort with less power demand. In this paper we have proposed the design of a hybrid control system having a combination of skyhook theory with fuzzy logic control and applied on a semi-active vehicle suspension system for its ride comfort enhancement. A two degree of freedom dynamic model is simulated using Matlab/Simulink for a vehicle equipped with semi-active suspension system with focused on the passenger‟s ride comfort performance.
Stability Control System for a Two-WheelerIOSRJEEE
A two-wheeler is statically unstable but as the speed increases vehicle achieves stability. At low speed, the vehicle loses its stability. In order to achieve stability, the driver has to balance the vehicle. While negotiating a curve, a vehicle has to lean to a certain angle, if this angle exceeds the certain value, the vehicle tends to skid. In this paper the stability control system is incorporated, so that a vehicle will maintain stability even at low speeds. The stability of a two-wheeler depends on weight distribution, tyre dynamics, speed and steering angle. In this paper, only two parameters are considered, one is steering effect and another one is speed. For developing a simplified model, the speed of the vehicle is kept as constant, using which the effect of steering angle is analysed and accordingly a controller is incorporated for providing stability.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Fuzzy rules incorporated skyhook theory based vehicular suspension design for...IJERA Editor
The vehicle suspension system supports and isolate the vehicle body and payload from road vibrations due to surface roughness by maintaining a controllable damping traction force between tires and road surface. In modern luxury vehicles semi active suspension system are offering both the reliability and accuracy that has enhanced the passenger ride comfort with less power demand. In this paper we have proposed the design of a hybrid control system having a combination of skyhook theory with fuzzy logic control and applied on a semi-active vehicle suspension system for its ride comfort enhancement. A two degree of freedom dynamic model is simulated using Matlab/Simulink for a vehicle equipped with semi-active suspension system with focused on the passenger‟s ride comfort performance.
Stability Control System for a Two-WheelerIOSRJEEE
A two-wheeler is statically unstable but as the speed increases vehicle achieves stability. At low speed, the vehicle loses its stability. In order to achieve stability, the driver has to balance the vehicle. While negotiating a curve, a vehicle has to lean to a certain angle, if this angle exceeds the certain value, the vehicle tends to skid. In this paper the stability control system is incorporated, so that a vehicle will maintain stability even at low speeds. The stability of a two-wheeler depends on weight distribution, tyre dynamics, speed and steering angle. In this paper, only two parameters are considered, one is steering effect and another one is speed. For developing a simplified model, the speed of the vehicle is kept as constant, using which the effect of steering angle is analysed and accordingly a controller is incorporated for providing stability.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Fatigue or Durability Analysis of Steering Knuckleijsrd.com
the purpose of the study of this thesis is to discuss analysis the acting force upon the steering knuckle while in track or random load for a vehicle. Steering knuckle is main important part in the vehicle because that requires lots of attention in selection because once it is damaged then it have to replace with the new one. Structural Components such as a steering knuckle might be strong enough to withstand a single applied load. But what happens when the part operates over and over, day after today? To predict component failure in such cases requires what's called fatigue or durability analysis. For our purposes, a constant or static load does not cause failure. What counts is the impact of working or fluctuating loads. Failures, or fractures, take place when cracks get so large that remaining material can no longer endure stresses and strains. In classic structural analyses, failure predictions are based solely on material strength or yield strength. Durability analysis goes beyond this, evaluating failure based on repeated simple or complex loading.
The report was done to develop a MATLAB model of a suspension system of a 4 wheel vehicle going over an uneven road. A simulink model was developed to simulate the various forces acting on the suspension of the vehicle.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
The Effect of Arm Stiffness on the Elasto-Kinematic Properties of Single-Axle...theijes
The paper is focused on the stiffness analysis of the longitudinal arm of single-axle suspension on elastokinematic behaviour of the vehicle axle which is highly important when considering the handling characteristics related tovehicle safety.The elasto-kinematic behaviour of the axle determines the course of the geometrical parameters of wheel suspension, the toe angle and camber as the function of wheel movement during force loading. This paper presents the complex MBS (Multi-Body Simulation)model of the wheel suspension with nonlinear characteristics of rubber-metal bushings. The model also comprises force elements such as springs, shock absorbers, stops and the transverse stabilizer. The model of flexible arm is implemented in the MBS model using the Craig-Bampton method, which represents a flexible body based on the synthesis of its own modal shapes. Subsequently,elasto-kinematic simulations are performed with the help ofthe computational system Hyperwork. The computational part of the paper presents the results of the elasto-kinematic behaviour of wheel axle for the flexible arm with different sheet metal thicknesses (2, 3 and 4 mm) and different materials (steel and aluminium alloy AlSi7Mg). Individual calculation models are compared to each other and also to the model of suspension with therigidarm. Elasto-kinematic analyses are also validated by the measurement inthe testing stage.
Design, fabrication and performance evaluation of melon shelling machineeSAT Journals
Abstract The design, fabrication and testing of melon shelling machine were carried out. Considering the numerous nutritional and economical importance of the melon seed (Egusi) it is only binding to fashion drudgery free and less expensive means of processing the seed. An insight was carefully taken from previous attempts on this work by various scholars. The machine has a power rating of 1.5hp, power transmitted was 1656.70 wattsand was constructed using basically mildsteel. Performance test was carried out and the machine has efficiency of 62.5% for shelled melon, 10% for unshelled melon, 10% for breakage and 17.5% for partially shelled melon.
Keywords: Design, fabrication, melon seed, shelled, unshelled.
Stress analysis on steering knuckle of the automobile steering systemeSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
ELECTRONIC SYNCHRONOUS SHAFT FOR SWIVEL AXES DRIVEN BY COUPLED SELFLOCKING WO...ijmech
Coupling worm gears in large machine tool manipulator units (axes) can lead to overload damages under some operating conditions, like asymmetrical driving and emergency stop. This behaviour is caused by the self locking characteristic of worm gears with small pitch. If operated in the direction opposite to the designated one, self-locking can occur in the gears, subjecting the gears to an arbitrary torque which can be destructive. This condition can occur without counter torque on the driving side. In most gears, tooth engagement is based on a rolling motion. The slip component increases with a growing axis angle between the paired gears. In case of worm gears, the axis angle is 90_, and therefore the coupling is purely frictious.This friction coupling is important in modelling. Especially the transition between the static and dynamic friction, where the system parameters change abruptly by a factor of two, should not be neglected.Based on the evaluated model a synchronous controller has been developed. This controller gives the oppertunity to drive swiveling axes with coupled selflocking gears by a standard gantry topology with an overlayed state changing master-slave topology
COMPARISON OF RESPONSE TO UNBALANCE OF OVERHUNG ROTOR SYSTEM FOR DIFFERENT SU...IAEME Publication
Rotor unbalance is most common fault found in the rotating machines. Methods
are adopted to analyze the position of unbalance and to bring its effect into acceptablelimit. Vibration analysis is the most common technique used to analyze the rotor
system. Research have been performed on rotor supported atboth ends, however lessstudy has been done for overhung rotor. In this paper the response of overhung rotoron isotropic support and anisotropic support subject tounbalance has been presented.and equations aresolved using MATLAB programming. The effect of unbalancehas been studied on thebode plot. Forward and Reverse whirl are observed through Campbell diagram andmode shapes are plotted.
Fatigue or Durability Analysis of Steering Knuckleijsrd.com
the purpose of the study of this thesis is to discuss analysis the acting force upon the steering knuckle while in track or random load for a vehicle. Steering knuckle is main important part in the vehicle because that requires lots of attention in selection because once it is damaged then it have to replace with the new one. Structural Components such as a steering knuckle might be strong enough to withstand a single applied load. But what happens when the part operates over and over, day after today? To predict component failure in such cases requires what's called fatigue or durability analysis. For our purposes, a constant or static load does not cause failure. What counts is the impact of working or fluctuating loads. Failures, or fractures, take place when cracks get so large that remaining material can no longer endure stresses and strains. In classic structural analyses, failure predictions are based solely on material strength or yield strength. Durability analysis goes beyond this, evaluating failure based on repeated simple or complex loading.
The report was done to develop a MATLAB model of a suspension system of a 4 wheel vehicle going over an uneven road. A simulink model was developed to simulate the various forces acting on the suspension of the vehicle.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
The Effect of Arm Stiffness on the Elasto-Kinematic Properties of Single-Axle...theijes
The paper is focused on the stiffness analysis of the longitudinal arm of single-axle suspension on elastokinematic behaviour of the vehicle axle which is highly important when considering the handling characteristics related tovehicle safety.The elasto-kinematic behaviour of the axle determines the course of the geometrical parameters of wheel suspension, the toe angle and camber as the function of wheel movement during force loading. This paper presents the complex MBS (Multi-Body Simulation)model of the wheel suspension with nonlinear characteristics of rubber-metal bushings. The model also comprises force elements such as springs, shock absorbers, stops and the transverse stabilizer. The model of flexible arm is implemented in the MBS model using the Craig-Bampton method, which represents a flexible body based on the synthesis of its own modal shapes. Subsequently,elasto-kinematic simulations are performed with the help ofthe computational system Hyperwork. The computational part of the paper presents the results of the elasto-kinematic behaviour of wheel axle for the flexible arm with different sheet metal thicknesses (2, 3 and 4 mm) and different materials (steel and aluminium alloy AlSi7Mg). Individual calculation models are compared to each other and also to the model of suspension with therigidarm. Elasto-kinematic analyses are also validated by the measurement inthe testing stage.
Design, fabrication and performance evaluation of melon shelling machineeSAT Journals
Abstract The design, fabrication and testing of melon shelling machine were carried out. Considering the numerous nutritional and economical importance of the melon seed (Egusi) it is only binding to fashion drudgery free and less expensive means of processing the seed. An insight was carefully taken from previous attempts on this work by various scholars. The machine has a power rating of 1.5hp, power transmitted was 1656.70 wattsand was constructed using basically mildsteel. Performance test was carried out and the machine has efficiency of 62.5% for shelled melon, 10% for unshelled melon, 10% for breakage and 17.5% for partially shelled melon.
Keywords: Design, fabrication, melon seed, shelled, unshelled.
Stress analysis on steering knuckle of the automobile steering systemeSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
ELECTRONIC SYNCHRONOUS SHAFT FOR SWIVEL AXES DRIVEN BY COUPLED SELFLOCKING WO...ijmech
Coupling worm gears in large machine tool manipulator units (axes) can lead to overload damages under some operating conditions, like asymmetrical driving and emergency stop. This behaviour is caused by the self locking characteristic of worm gears with small pitch. If operated in the direction opposite to the designated one, self-locking can occur in the gears, subjecting the gears to an arbitrary torque which can be destructive. This condition can occur without counter torque on the driving side. In most gears, tooth engagement is based on a rolling motion. The slip component increases with a growing axis angle between the paired gears. In case of worm gears, the axis angle is 90_, and therefore the coupling is purely frictious.This friction coupling is important in modelling. Especially the transition between the static and dynamic friction, where the system parameters change abruptly by a factor of two, should not be neglected.Based on the evaluated model a synchronous controller has been developed. This controller gives the oppertunity to drive swiveling axes with coupled selflocking gears by a standard gantry topology with an overlayed state changing master-slave topology
COMPARISON OF RESPONSE TO UNBALANCE OF OVERHUNG ROTOR SYSTEM FOR DIFFERENT SU...IAEME Publication
Rotor unbalance is most common fault found in the rotating machines. Methods
are adopted to analyze the position of unbalance and to bring its effect into acceptablelimit. Vibration analysis is the most common technique used to analyze the rotor
system. Research have been performed on rotor supported atboth ends, however lessstudy has been done for overhung rotor. In this paper the response of overhung rotoron isotropic support and anisotropic support subject tounbalance has been presented.and equations aresolved using MATLAB programming. The effect of unbalancehas been studied on thebode plot. Forward and Reverse whirl are observed through Campbell diagram andmode shapes are plotted.
The scheme of an identifier determines almost nothing about its behavior compared to a resolver that's ready to map it to various services. When resolver infrastructure is shared across schemes instead of siloed, all schemes benefit. With suitable prefixing dozens of well-known, so-called non-actionable schemes can become available from a single unified base URL. The idealized resolver would adopt a fully open infrastructure, and support all schemes and the best features from modern resolvers -- deduplication, content negotiation, link checking, inflections, suffix passthrough, etc.
Robust Fault Detection and Isolation using Bond Graph for an Active-Passive V...CSCJournals
A robot is a complex machine, comprising mechanism, actuators, sensors, and electrical system. It is, therefore, hard to guarantee that all the components can always function normally. If one component fails, the robot might harm humans. In order to develop the active-passive variable serial elastic actuator (APVSEA) [1] that can detect the occurrence of any component fault, this paper uses bond graph to design a robust fault detection and isolation (RFDI) system. When the robot components malfunction, the RFDI system will execute suitable isolation strategies to guarantee human safety and use zero-gravity control (ZGC) to simultaneously compensate for the torque caused by gravity. Thus, the user can consistently interact with the robot easily and safely. From the experimental results, the RFDI system can filter out uncertain parameters and identify the failed component. In addition, the zero-gravity control can lessen potentially physical damage to humans.
Design and Analysis of Mechanism for Dynamic Characterization of Power Transm...iosrjce
Power transmission systems are being widely used for transmission of power between two members.
Once a particular transmission system is realized it needs to be qualified before its course of application. As
part of this intended torque of the transmission systems needs to be measured and tested. Conventional means of
dynamic characterization of power transmission system has got the demerit of energy consumption to a greater
extent. Because of this more effort is to be put in terms of power for the sake of testing the intended system.
Great need exists for a system which consumes less or ideally no energy while performing test. This project
aims at evolution of a novel technique for evaluating the torque transmitting capability of power transmission
systems without consuming more energy. To start with all the subsystems of the proposed design will be
identified and each of them will be designed for getting their dimensions. Then these dimensional models will be
transformed to solid model of the assembled configuration using 3D CAD software. Functional load which will
be experienced by this design will be assessed and structural analysis will be carried out against these loads
using Finite Element Method (FEM) in commercial FEA software i.e. ANSYS
Optimization of Modified Sliding Mode Controller for an Electro-hydraulic Act...IJECEIAES
This paper presents the design of the modified sliding mode controller (MSMC) for the purpose of tracking the nonlinear system with mismatched disturbance. Provided that the performance of the designed controller depends on the value of control parameters, gravitational search algorithm (GSA), and particle swarm optimization (PSO) techniques are used to optimize these parameters in order to achieve a predefined system’s performance. In respect of system’s performance, it is evaluated based on the tracking error present between reference inputs transferred to the system and the system output. This is followed by verification of the efficiency of the designed controller in simulation environment under various values, with and without the inclusion of external disturbance. It can be seen from the simulation results that the MSMC with PSO exhibits a better performance in comparison to the performance of the similar controller with GSA in terms of output response and tracking error.
Comparison Of Multibody Dynamic Analysis Of Double Wishbone Suspension Using ...IJRES Journal
This paper presents the multibody dynamic analysis of wishbone suspension for automotive cars. Modeling and analysis of suspension is carried out using MATLAB SimMechanics toolbox. Rigid dynamic analysis of suspension is also carried out using ANSYS software. Results of both the analysis are compared and it is observed that results of both the analysis are similar.
Kineto-Elasto Dynamic Analysis of Robot Manipulator Puma-560IOSR Journals
Current industrial robots are made very heavy to achieve high Stiffness
which increases the accuracy of their motion. However this heaviness limits the robot speed and in masses the
required energy to move the system. The requirement for higher speed and better system performance makes it
necessary to consider a new generation of light weight manipulators as an alternative to today's massive
inefficient ones. Light weight manipulators require Less energy to move and they have larger payload abilities
and more maneuverability. However due to the dynamic effects of structural flexibility, their control is much
more difficult. Therefore, there is a need to develop accurate dynamic models for design and control of such
systems.This project presents the flexibility and Kineto - Elasto dynamic analysis of robot manipulator
considering deflection. Based on the distributed parameter method, the generalized motion equations of robot
manipulator with flexible links are derived. The final formulation of the motion equations is used to model
general complex elastic manipulators with nonlinear rigid-body and elastic motion in dynamics and it can be
used in the flexibility analysis of robot manipulators and spatial mechanisms. Manipulator end-effector path
trajectory, velocity and accelerations are plotted. Joint torques is to be determined for each joint trajectory
(Dynamics) .Using joint torques, static loading due to link’s masses, masses at joints, and payload, the robot
arms elastic deformations are to be found by using ANSYS-12.0 software package. Elastic compensation is
inserted in coordinates of robotic programming to get exact end-effectors path. A comparison of paths
trajectory of the end-effector is to be plotted. Also variation of torques is plotted after considering elastic
compensation. These torque variations are included in the robotic programming for getting the accurate endeffect
or’s path trajectory
We focus a modern methodology in this paper for adding the fuzzy logic control as well as sliding model control. This combination can enhance the MLS position control robustness and enhanced performance of it.In the start, for an application in an area to control the loops placement and position for the synchronous motor what has permanent magnetic linearity we tend to control the fuzzy sliding mode control. To resolve the chattering issues a designed controller is investigated and, in this way, steady state motion in sliding with higher accuracy is obtained. In this case, method of online tuning with the help of fuzzy logic is used in order to adjust the thickness of boundary layer and switching gains.For the suggested scheme technique, the outcomes of simulation suggest that with the classical SMC the accurate state and good dynamic performance is compared due to force chattering resistance, response by quick dynamic force and external disturbance elements and robustness against them.
This paper proposes a long-stroke linear switched reluctance machine (LSRM) with a primary and a secondary translator for industrial conveyance applications. The secondary one can translate according to the primary one so that linear compound motions can be achieved. Considering the fact that either one translator imposes a time-variant, nonlinear disturbance onto the other, the self-tuning position controllers are implemented for the compound machine and experimental results demonstrate that the absolute steady-state error values can fall into 0.03 mm and 0.05 mm for the secondary and primary translator, respectively. A composite absolute precision of less than 0.6 mm can be achieved under the proposed control strategy.
Comparative analysis of passenger ride comfort using various semi active susp...ijmech
In this paper, different semi-active control strategies for non-linear quarter car model equipped with controllable magneto-rheological (MR) shock absorbers and fuzzy logic controller are compared.Polynomial model is selected to characterize the experimental results of MR shock absorber. A combination of Forward Fuzzy Logic Controller (FFLC) and Inverse Fuzzy Logic Controller (IFLC) is
designed for proper working of MR shock absorber i.e. generation and supply of control current to MR shock absorber, which provides damping force to suspension system for vibration control purpose.Simulink responses of four different cases are evaluated for passenger ride comfort analysis taking uncontrolled, primary suspension controlled, secondary suspension controlled and fully controlled quarter car models. The obtained results in graphical and mathematical form demonstrate that the fully controlled quarter car system provides excellentperformance in suppression of passenger seat vibrations compared to other control strategies while the vehicle travels over the sinusoidal type of input road profile
Evolutionary Design of Mathematical tunable FPGA Based MIMO Fuzzy Estimator S...Waqas Tariq
In this research, a Multi Input Multi Output (MIMO) position Field Programmable Gate Array (FPGA)-based fuzzy estimator sliding mode control (SMC) design with the estimation laws derived in Lyapunov sense and application to robotic manipulator has proposed in order to design high performance nonlinear controller in the presence of uncertainties. Regarding to the positive points in sliding mode controller, fuzzy inference methodology and Lyapunov based method, the controllers output has improved. The main target in this research is analyses and design of the position MIMO artificial Lyapunov FPGA-based controller for robot manipulator in order to solve uncertainty, external disturbance, nonlinear equivalent part, chattering phenomenon, time to market and controller size using FPGA. Robot manipulators are nonlinear, time variant and a number of parameters are uncertain therefore design robust and stable controller based on Lyapunov based is discussed in this research. Studies about classical sliding mode controller (SMC) show that: although this controller has acceptable performance with known dynamic parameters such as stability and robustness but there are two important disadvantages as below: chattering phenomenon and mathematical nonlinear dynamic equivalent controller part. The first challenge; nonlinear dynamic part; is applied by inference estimator method in sliding mode controller in order to solve the nonlinear problems in classical sliding mode controller. And the second challenge; chattering phenomenon; is removed by linear method. Asymptotic stability of the closed loop system is also proved in the sense of Lyapunov. In the last part it can find the implementation of MIMO fuzzy estimator sliding mode controller on FPGA; FPGA-based fuzzy estimator sliding mode controller has many advantages such as high speed, low cost, short time to market and small device size. One of the most important drawbacks is limited capacity of available cells which this research focuses to solve this challenge. FPGA can be used to design a controller in a single chip Integrated Circuit (IC). In this research the SMC is designed using Very High Description Language (VHDL) for implementation on FPGA device (XA3S1600E-Spartan-3E), with minimum chattering.
Novel Artificial Control of Nonlinear Uncertain System: Design a Novel Modifi...Waqas Tariq
This research is focused on novel particle swarm optimization (PSO) SISO Lyapunov based fuzzy estimator sliding mode algorithms derived in the Lyapunov sense. The stability of the closed-loop system is proved mathematically based on the Lyapunov method. PSO SISO fuzzy compensate sliding mode method design a SISO fuzzy system to compensate for the dynamic model uncertainties of the nonlinear dynamic system and chattering also solved by nonlinear fuzzy saturation like method. Adjust the sliding function is played important role to reduce the chattering phenomenon and also design acceptable estimator applied to nonlinear classical controller so PSO method is used to off-line tuning. Classical sliding mode control is robust to control model uncertainties and external disturbances. A sliding mode method with a switching control low guarantees the stability of the certain and/or uncertain system, but the addition of the switching control low introduces chattering into the system. One way to reduce or eliminate chattering is to insert a nonlinear (fuzzy) boundary like layer method inside of a boundary layer around the sliding surface. Classical sliding mode control method has difficulty in handling unstructured model uncertainties. One can overcome this problem by applied fuzzy inference system into sliding mode algorithm to design and estimate model-free nonlinear dynamic equivalent part. To approximate a time-varying nonlinear dynamic system, a fuzzy system requires a large amount of fuzzy rule base. This large number of fuzzy rules will cause a high computation load. The addition of PSO method to a fuzzy sliding mode controller to tune the parameters of the fuzzy rules in use will ensure a moderate computational load. The PSO method in this algorithm is designed based on the PSO stability theorem. Asymptotic stability of the closed loop system is also proved in the sense of Lyapunov.
ANALYSIS OF FRICTION INDUCED VIBRATION DURING ENGAGEMENT OF CLUTCHESIAEME Publication
Safety aspect in automotive engineering is of prime importance and given priority in design and development of vehicle. This vehicle development needs to meet safety requirement. Braking system along with good suspension systems, good handling and safe cornering, is one of the most critical system in the vehicle. The objective of this work is to design, analyze and investigate the temperature distribution of rotor disc during braking operation using suitable numerical tools. The numerical study uses the finite element analysis techniques to predict the temperature distribution on the full and ventilated brake disc. This analysis is further used to identify the critical temperature of the rotor by varying geometric design of the disc. The analysis also gives us, the heat flux distribution for the disc rotors with various groove patterns.
LMI based antiswing adaptive controller for uncertain overhead cranes IJECEIAES
This paper proposes an adaptive anti-sway controller for uncertain overhead cranes. The state-space model of the 2D overhead crane with the system parameter uncertainties is shown firstly. Next, the adaptive controller which can adapt with the system uncertainties and input disturbances is established. The proposed controller has ability to move the trolley to the destination in short time and with small oscillation of the load despite the effect of the uncertainties and disturbances. Moreover, the controller has simple structure so it is easy to execute. Also, the stability of the closed-loop system is analytically proven. The proposed algorithm is verified by using Matlab/ Simulink simulation tool. The simulation results show that the presented controller gives better performances (i.e., fast transient response, no ripple, and low swing angle) than the state feedback controller when there exist system parameter variations as well as input disturbances.
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Load speed regulation in compliant mechanical transmission systems using feed...ISA Interchange
The problem of controlling the load speed of a mechanical transmission system consisting of a belt- pulley and gear-pair is considered. The system is modeled as two inertia (motor and load) connected by a compliant transmission. If the transmission is assumed to be rigid, then using either the motor or load speed feedback provides the same result. However, with transmission compliance, due to belts or long shafts, the stability characteristics and performance of the closed-loop system are quite different when either motor or load speed feedback is employed. We investigate motor and load speed feedback schemes by utilizing the singular perturbation method. We propose and discuss a control scheme that utilizes both motor and load speed feedback, and design an adaptive feedforward action to reject load torque disturbances. The control algorithms are implemented on an experimental platform that is typically used in roll-to-roll manufacturing and results are shown and discussed.
MODELLING AND OPTIMIZATION OF ELECTROMAGNETIC TYPE ACTIVE CONTROL ENGINE-MOUN...IAEME Publication
This paper presents a low-cost prototype active control engine mount (ACM) designed for commercial passenger vehicles, requiring a good engine vibration isolation performance. To
construct such an ACM system, all feedback sensors normally required for full ACM systems are replaced by the model based feed forward algorithm, consisting of a vibration estimation algorithm, a current shaping controller and an enhanced ACM model. The current shaping control compensates for degradation of control performance due to elimination of feedback control sensors. The proposed
current shaping control improves the actuator control performance, and the vibration estimation algorithm provides the anti-vibration signals for vibration isolation
Similar to Model Matching Control for an Active-Passive Variable Stiffness Actuator (20)
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
The Indian economy is classified into different sectors to simplify the analysis and understanding of economic activities. For Class 10, it's essential to grasp the sectors of the Indian economy, understand their characteristics, and recognize their importance. This guide will provide detailed notes on the Sectors of the Indian Economy Class 10, using specific long-tail keywords to enhance comprehension.
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The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
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Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
Model Matching Control for an Active-Passive Variable Stiffness Actuator
1. Po-Jen Cheng & Han-Pang Huang
International Journal of Robotics and Automation (IJRA), Volume (6) : Issue (3) : 2015 48
Model Matching Control for an Active-Passive Variable Stiffness
Actuator
Po-Jen Cheng u9014028@gmail.com
Department of Mechanical Engineering
National Taiwan University
Taipei, 10617, Taiwan
H.P. Huang hanpang@ntu.edu.tw
Department of Mechanical Engineering
National Taiwan University
Taipei, 10617, Taiwan
Abstract
In order to increase the safety performance between human and the robot, the variable stiffness
mechanism is commonly adopted due to its flexibility in various tasks. However, it makes the
actuator more complex and increases the weight of the system. To deal with this problem, the
active-passive variable stiffness elastic actuator (APVSEA) [1] and the variable stiffness control
that uses a model matching control (MMC) with bond graph are proposed in this article. The
APVSEA is modeled as a non-back drivable bond graph model. Combining the MMC with the
non-back drivable bond graph model, the overall system can achieve active stiffness control. The
simulations and the experiments show good control performance. They prove that the proposed
method can achieve active stiffness control well. In the future, the proposed method can also be
applied to the robot arm and exoskeletons for balancing safety and the control performance.
Keywords: Serial Elastic Actuator, Bond Graph, Model Matching Control.
1. INTRODUCTION
Robots will not only exist in factories but will also service in our life in the near future. They will
help humans and interact with people directly, for example, security in companies, home care,
restaurant service, and rehabilitation in patients’ homes. Traditionally, the properties of industrial
robots have been heavy, fast, and powerful. Those industrial robots have no capacity for safe
interaction with humans. Therefore, a robot that achieves precision and high-speed performance
is becoming an important issue. In order to interact with humans, researchers in the robotics field
have been focused on human-robot interaction (HRI) in the past decade. To guarantee safety
during the human-robot interaction, several approaches dealing with this problem have been
developed.
Recently, researchers tried to develop intrinsically safe robot actuation. One approach is to use a
serial elastic actuator (SEA) between human and the robot. The effect of SEA is to absorb impact
force during HRI [2-4]. SEA uses elastic elements between transmission mechanisms and loads
serially, and [5-7] have presented both linear and rotary SEA designs.
The main problem in SEA is that the stiffness is constant. The constant stiffness limits the
dynamic range of force control and makes the SEA unusable in many daily activities in human
life. Therefore, the variable stiffness system is important for dealing with variable tasks. To
achieve the variable stiffness property, some researchers purposed the concept of a variable
stiffness elastic actuator (VSEA) for robot manipulation and interaction between human and the
robot [8-9]. In [10-13], the safe link mechanism (SLM) and safe joint mechanism (SJM) combined
with the slider structure, transmission shafts, and non-linear springs were proposed to achieve
2. Po-Jen Cheng & Han-Pang Huang
International Journal of Robotics and Automation (IJRA), Volume (6) : Issue (3) : 2015 49
collision safety. The actuator performs nonlinear characteristics by using the four-bar linkage and
slider mechanism in combination with springs. The variable stiffness actuator adopts a variable
stiffness transmission to change mechanism stiffness. Migliore purposed an approach that allows
to change the mechanism’s stiffness using two non-linear springs working in an antagonistic
configuration [14]. In order to control the position and stiffness of the system, some researchers
used two actuators to change the effective length of the spring or link position [15-16].
The common problem in realizing the mechanism with VSEA is that the system will become
heavy with huge volume. In [17], the actuator of the robot is a pneumatic artificial muscle which is
flexible and has a light weight. However, the variable stiffness property is limited.
To develop an effective active variable stiffness system, we adopt bond graph and model
matching controller (MMC) to model the SEA system and to achieve the variable stiffness control
[19-22]. Bond graph is an excellent model language that can describe multi-domain physical
dynamic systems. It also has extension ability and can accomplish mechatronics design or
integrate multi-domain models easily. In reference [18], Hernani modeled Hill’s muscle model
using bond graph and extended the unit muscle model to the human gait musculoskeletal system.
There have been many SEA studies in the past. However, few papers discuss SEA modeling
using bond graph. In this paper, the active-passive variable stiffness elastic actuator (APVSEA)
[1], developed by our laboratory, will be introduced first. We model the non-back drivable
APVSEA based on bond graph. It can be served as a module for future development.
The aims of MMC are to generate a reference model and make the plant’s output approximate
the reference model’s response. Nevertheless, there are few literatures to describe the design
flow and step of MMC using bond graph and apply to the SEA system. In this paper, the APVSEA
system is the first modeled using bond graph and the design of the MMC controller is followed.
The paper is organized as follows. In Section II, the principle and properties of the active-passive
variable stiffness actuator (APVSEA) are introduced [1] and modeled using bond graph. The
MMC controller design is applied to the APVSEA through the model of the APVSEA in Section III.
In addition, the system’s solvability, the inverse system, and the disturbance decouple problem
(DDP) will also be addressed. In Section IV, the analysis and simulation of the MMC will be
conducted. The MMC controller will be realized in the APVSEA, and experiment results will be
shown in Section V. The last section draws our conclusions.
2. APVSEA OPERATION PRINCIPLE AND MODEL
It is necessary to deeply understand APVSEA system before designing bond graph. In this
section, the operational principle of the APVSEA will be described and the bond graph
representation of the APVSEA will be conducted.
2.1 APVSEA Operation Principle [1]
The APVSEA is a human-robot interaction mechanism with intrinsic safety properties. It was
developed by our laboratory. The APVSEA system, shown in figure 1, has two different parts: one
is SEA; the other can change the system’s stiffness. APVSEA can actively or passively change
the mechanism’s stiffness to satisfy the human-robot interaction requirement. APVSEA consists
of two DC motors, one ball screw, one driving screw, and four springs. The potentiometer above
the spring is used to measure spring displacement and three encoders can measure motor 01,
motor 02, and the output link angle. The main goal of motor 02 is to change the stiffness of the
APVSEA. However, this paper is focused on the SEA system and varies system stiffness using
the MMC controller. Therefore, this paper will not discuss the functional part of motor 02 that
changes the APVSEA stiffness.
3. Po-Jen Cheng & Han-Pang Huang
International Journal of Robotics and Automation (IJRA), Volume (6) : Issue (3) : 2015 50
Figure 1 shows how APVSEA drivers’ output is linked to motor 01. First, motor 01 rotates the ball
screw through time belt 01. Second, the ball screw moves the moving plant forward or backward.
Finally, the moving plant pulls timing belt 02 to rotate output link, as shown in figure 2.
FIGURE 1: APVSEA 3D diagram
FIGURE 2: Moving Plant is Moved by Motor 01.
If there are some external forces on the output link, the external forces will drive the moving plant
using timing belt 02. However, because the moving plant cannot drive the ball screw back, the
external forces generate axial force and make the ball screw and the moving plant slip on the
input shaft. As the translation of the moving plant occurs, the springs in the APVSEA absorb
those external forces through the connector, as shown in Figs. 3 and 4. This is the SEA property
which means the APVSEA can absorb an external force so that the human interacts with the
robot safely. The detailed specification of the APVSEA is listed in Table I.
FIGURE 3: External Force Generates Axial Slipping Motion.
FIGURE 4: The Spring Absorb Forces from External
Environment.
4. Po-Jen Cheng & Han-Pang Huang
International Journal of Robotics and Automation (IJRA), Volume (6) : Issue (3) : 2015 51
PARAMETERS VALUES
Mass (includes two motors) 2.2kg
Length*Width*Height 200*100*116 mm
Number of DC-motors 2
Max. Output Torque 29Nm
Max. Output Speed 24rpm
Spring Stiffness 152N/mm
Max. Output Link Deflection ±90°
TABLE 1: The Specification of APVSEA.
2.2 Model APVSEA by Bond Graph
From the discussion above, the user applies external force to the output link, and motor 01
simultaneously drives the output link. Because the APVSEA is a non-back drivable system, the
external force applied by the user cannot affect motor 01.
In order to simplify the APVSEA system, we can treat the system l as the user pushes a mass-
damper-spring system in a car. Because the user’s force is internal, it cannot move the car
forward, as shown in figure 5. In other words, the car can change the human’s absolute position,
but human force cannot move the car. The simplified APVSEA model is shown in figure 6. u is the
car velocity (i.e., u is the angular velocity from motor 01 .)
FIGURE 5: The APVSEA system can be described as human is pushing mass-damper-spring system in a car.
FIGURE 6: The Simplified APVSEA Model.
Based on the simplified APVSEA model, the system’s model is constructed using bond graph, as
shown in figure 7. xሶଵ and xሶଶ represent the force applied to output link and spring velocity,
respectively. SS is a source-sensor element. Se and Sf define the effort source and flow source,
respectively. The parameters m, k1 and r are defined as mass, spring stiffness and damping ratio,
respectively.
.
5. Po-Jen Cheng & Han-Pang Huang
International Journal of Robotics and Automation (IJRA), Volume (6) : Issue (3) : 2015 52
FIGURE 7: The APVSEA Bond Graph Diagram.
According to the Port-Hamiltonian dynamic equation [19], the following dynamic equation (1) is
derived from the bond graph:
[ ] [ ]
1
2
1 1
( )
1 0 0 1
1 ( ) 0
x r r
H x u
x
y r H x r u
− − − −
= ∇ −
= ∇ +
&
& (1)
whereu = (uୌ, u)
and the Hamiltonian H(x): x → ℜ is defined as H(x) = (xଵ
ଶ
/m + kଵxଶ
ଶ)/2, which
is the energy function. The ∇H(x) is a column gradient vector.
Figure 7 is the bond graph model of the non-back drivable APVSEA system, where the terminal
of u is the motor input, and uୌ is the operator input external force, respectively. In the case of the
APVSEA, u converts its power through the timing belt and ball-screw into a velocity that operates
on a system spring. The developer can add the motor, electric drive, electric power, etc., behind
u. We can also regard uୌ as a human input force that can be extended to Hill’s muscle model.
Therefore, the researcher can design a robot arm or exoskeleton system basing on the modular
APVSEA model, as shown in figure 7. The I, C, R mean inertia, spring and damper in mechanical
domain in bond graph, respectively. The junction elements are denoted as 1 and 0 (black
number). The bond numbers are defined as red words in Figure 7. The total forces apply to
output link is denoted as ݔሶଵ and velocity of spring is denoted as ݔሶଶ. Each arrow is used to
indicate positive effort or flow direction.
3. MODEL MATCHING CONTROL (MMC)
The advantage of MMC is that the designer can specify the reference model’s response clearly.
Bond graph offers an excellent model language. It can be used to design a reference model
visually.
The MMC can be viewed as that there is a disturbance in the extended model system input uത.
Therefore, the MMC seems to be a disturbance decouple problem (DDP). This means that the
plant input u(t) can decouple the model input uത(t) and extend the system E to the output yୣ.
Figure 8 shows the flow chart of the MMC controller design.
6. Po-Jen Cheng & Han-Pang Huang
International Journal of Robotics and Automation (IJRA), Volume (6) : Issue (3) : 2015 53
FIGURE 8: MMC Controller Design Flow Chart.
In this paper, the MMC controller is designed using bond graph. The first step is to construct a
plant model using bond graph. The second step is to check the solvability of this plant. If the plant
is solvable, the inverse system using a bi-causal bond graph can be obtained. If the system does
not have an inverse system, we cannot find the MMC controller. Using the inverse system, we
can solve DDP and derive an error dynamic equation. A new control input μ୧
will force the error
dynamic equation to equal zero.
According to the first-order differential function of the energy, we can confirm if this error system
is an essential asymptotically stable system. Finally, we can determine if the asymptotic
conditions satisfy the asymptotic stability by defining a new energy function Hୱ(e) and control
input in the shaped Hamiltonian.
3.1 Solvability Checking
In order to determine the system’s solvability, Wlasowski, and Lorenz proposed an approach that
can check solvability using bond graph [23]. In this paper, we adopt this approach and derive the
following matrix from figure 7 as
1
5
2
7
3
1 1
1 1
0 1
EJ
f
f
f Ff
f
f
−
= − ≡
−
)
(2)
1
4
2
7
3
1 1 0
1 1 1
EJ
e
e
e Ee
e
e
− − = ≡ − −
)
(3)
where f୧ (e୧) means flow (effort) of the i-th bond from figure 7. The notation E means all bond
graph environment elements (I, C, R) except for 0, 1, TF, and GY elements. J is the system’s 0-
junction or 1-junction. Because there is no modulated bond graph element, we can convert t
equations (2) and (3) into the structure equation [23] as:
7. Po-Jen Cheng & Han-Pang Huang
International Journal of Robotics and Automation (IJRA), Volume (6) : Issue (3) : 2015 54
JE EJ
JE EJ
f Ff
e Ee
=
=
)
) (4)
where ݁ா( ݂ா ) means the effort (flow) transmit direction from the environment to junction node.
Similarly, the effort (flow) transmit direction from junction to environment node is represented as
݁ா( ݂ா ). Because the structure equation (4) has no singular matrix, i.e., Fˆ and Eˆ have an inverse
matrix, we can conclude the APVSEA is a solvable system and there exists an inverse system.
FIGURE 9: APVSEA’s Power Line.
3.2 Inverse System
Since the APVSEA is solvable, there exists an inverse system. We can generate input-output
power lines, as shown in figure 9, where the light blue dotted line is the flow direction and the deep
blue one is the effort direction. Based on the power line, the inverse system of the APVSEA can be
obtained using bi-causal bond graph, as shown in figure 10.
FIGURE 10: The Inverse System of APVSEA.
3.3 Reference Model
The reference model for the MMC is shown in figure 11. The bond graph of the reference model
is given in figure 12. The MMC design will make the APVSEA match to the reference model. Here,
the reference model not only preserves the APVSEA system, but also adds an extra spring ݇ௗ ,
which can vary the original system’s stiffness. Form figure 12, we can derive the system dynamic
equations as follows
8. Po-Jen Cheng & Han-Pang Huang
International Journal of Robotics and Automation (IJRA), Volume (6) : Issue (3) : 2015 55
FIGURE 11: Reference Model Definition.
FIGURE 12 Reference Model Bond Graph.
[ ]
1
2
3
1 1 1
1 0 0 ( ) 0
1 0 0 0
1 1 ( )
H
x r
x H x u
x
y r H x
− − −
= ∇ +
= ∇
&
&
& (5)
where uതୌ is an external force applied to the reference model. ̅ݔሶଵ and ̅ݔሶଶ represent the force which
apply to output link and spring velocity, respectively. The Hamiltonian Hഥ(xത): xത → ℜ is defined as
Hഥ(xത) = (xതଵ
ଶ
/m + kଵxതଶ
ଶ
+ kୢxതଷ
ଶ)/2, which is the reference model’s energy function. The ∇Hഥ(xത) is a
column gradient vector.
3.4 Disturbance Decouple Problem (DDP)
We can derive an inverse system relation equation from figure 10 directly as
( )( ) ( )
6 3 1 2
1 2
1
1 1
H
u f f dt
m
u y dt y k
m r
η η
η
= − = −
= − − −
∫
∫
& &%
(6)
where ηଵሶ and ηଶሶ are storage elements dynamics in the inverse system. In order to solve DDP, the
main concept of MMC is to match the dynamic parameters of the inverse system and the model,
i.e., set y = yത,uୌ = uതୌ, where yത can be derived by substituting equation (5) to equation (6). uതୌ is
seen as a disturbance as
9. Po-Jen Cheng & Han-Pang Huang
International Journal of Robotics and Automation (IJRA), Volume (6) : Issue (3) : 2015 56
( )( ) ( )1 2
1 1
Hu u y dt y k
m r
η µ= − − − +∫% (7)
where μ is a new control parameter and yത = rxതଵ/m + kଵxതଶ + kୢxതଷ = uതୌ − xതሶଵ. Equation (7) is
rewritten as
( ) ( )1 1 2
1 1 1 2 3 1 2
1 1
1 1
d
u x dt y k
m r
r
x x k x k x k
m r m
η µ
η µ
= − − +
= − + + − +
∫ &%
(8)
By setting xതଶ = ηଶ, equation (8) can be rewritten as
3
1
du k x
r
µ= − +% (9)
There is a new control parameter μ in equation (9), which can make the plant asymptotically
stable.
3.5 Error Dynamic
In order to generate the error dynamic equation, let εଵ = xଵ − xതଵ and εଶ = xଶ − xതଶ = xଶ − ηଶ.
( )
1 1 1
1 1 2 H H
x x
r
x k x u ru u y
m
ε = −
= − − + + − −
&& &
%
(10)
where u = −kୢxതଷ/r + μ. We rewrite equation (10) as
( ) ( )
1 1 1 2 1 1 2 3
1 1 1 2 2 3 3
1 1 2
1
d
d d
r r
x k x ru x k x k x
m m
r
x x k x x k x r k x
m r
r
k r
m
ε
µ
ε ε µ
= − − + + + +
= − − − − + + − +
= − − +
& %
(11)
Similarly,
( )2 2 2 1 1 2
1 3 1 1 2 3 1 2
1
1 1
1 1 1
1
d d
x x u y k
m r
r
x k x x k x k x k
m r r m
m
ε η η
µ η
ε µ
= − = − − −
= + − − + + −
= −
& && %
(12)
10. Po-Jen Cheng & Han-Pang Huang
International Journal of Robotics and Automation (IJRA), Volume (6) : Issue (3) : 2015 57
By combining equations (11) and (12), we can obtain the MMC error dynamic equation as
1
2
1
( )
1 0 1
r r
H
ε
ε µ
ε
− −
= ∇ + −
&
&
(13)
where H(ε) = (εଵ
ଶ
/m + kଵεଶ
ଶ)/2 is the error energy function. The ∇H(ε) is a column gradient
vector.
3.6 Asymptotic Stability
By setting the new control input μ = 0 in equation (13), the differential equation is given as
( ) ( )
1 1 1 2 2
1 1 1 2 1 2 1
2
1
( ) /
/ / /
/
d
H m k
dt
r m k m k m
r m
ε ε ε ε ε
ε ε ε ε ε
ε
= +
= − − +
= −
& &
(14)
Through observing equation (14), we know the MMC control system is asymptotically stable.
However, the goal of adding a new controller μ is to force the system output y(t) to close the
model output yത(t). Define a new energy function Hୱ(ε) using the shaped Hamiltonian approach as
( )
2
1 2
2 2 2
1 1 2 1 2
( ) ( ) / 2
/ 2 / 2
sH H c
m k c
ε ε ε
ε ε ε
= +
= + +
(15)
where parameter cଵ is a constant.
In order to prove the stability, the energy function Hୱ(ε) has to satisfy the following Lyapunov
criteria.
Criterion 1: The energy function Hୱ(ε) equals to zero at ε = 0.
(0) 0sH = (16)
Criterion 2: According to equation (15), the energy function satisfies Hୱ(ε) > 0 for every input
because the parameters m and kଵ are positive. So, satisfying the fulfillment of this criterion
depends on parameter cଵ. The following criterion 3 is used for decision.
Criterion 3: The time derivative of Hୱ(ε) is negative, i.e.,
ୢ
ୢ୲
Hୱ(ε) < 0.
( ) ( )
1 1 1 2 2 1 2 2
1 1 1 2 1 2 1 1 2 1
2
1 1 2 2 1 12 1
1
( )
1 1 1
1
s
d
H k c
dt m
r
k r k c
m m m m
r
r c k c
m m
ε ε ε ε ε ε ε
ε ε ε µ ε ε µ ε ε µ
ε ε µ ε ε µ
= + +
= − − + + − + −
= − + + − +
& & &
(17)
11. Po-Jen Cheng & Han-Pang Huang
International Journal of Robotics and Automation (IJRA), Volume (6) : Issue (3) : 2015 58
It is clear that when the goal of the MMC controller is achieved, the system is asymptotically
stable. The stability condition requires kଵ + cଵ = 0, and rμ + cଵεଶ = 0. Therefore, cଵ = −kଵ and
μ = kଵ(xଶ − xതଶ)/r is subject to equation (13). Based on those conditions, the system stability can
be checked by the following equations
1 1 1 2
1
r
k r
m
r
m
ε ε ε µ
ε
= − − +
= −
&
(18)
( )1
2 1 1 2 2
1 1 k
x x
m m r
ε ε µ ε= − = − −& (19)
For system stability, the control law u is chosen as
( )3 3 1 2 2
1 1
d du k x k x k x x
r r
µ = − + = − − − % (20)
4. SIMULATIONS
The MMC is applied to APVSEA, and the simulation is conducted using ADAMS and
Matlab/Simulink. In order to simplify the simulation processing, the APVSEA was built, as shown
in figure 13. The car is regarded as a wall if velocity u = 0. Therefore, the human force is an
external force for this simplified simulation model. In other words, the velocity can move the
absolute position of the whole system. But if human force is applied to the block, only the relative
position can be changed. The MMC controller was established using Simulink, it receives the
datum from ADAMS and feedback velocity command u.
Figure 14 is the APVSEA velocity simulation results, where the blue curve is the reference
model’s velocity. The simulation input force is 10 × sin (3t) Newton based on kୢ = 50N/m. The
green curve represents the APVSEA output velocity under the MMC. From the simulation results,
the MMC has a good tracking response. It means the MMC controller can change the plant output
response to match to the reference model’s response well.
FIGURE 13: The APVSEA Simplify Simulation Model.
12. Po-Jen Cheng & Han-Pang Huang
International Journal of Robotics and Automation (IJRA), Volume (6) : Issue (3) : 2015 59
FIGURE 14: The Velocity Response of Mass Block in MMC.
Different stiffness coefficients of spring kୢ (140N/m, 50N/m, 0N/m, -50N/m, -140N/m) are tested
and analyzed in the simulations, as shown in figure 15. It is worth noting that the simulation with
0N/m stiffness indicates that the response is subject to the condition of the plant without any
controller. When the kୢ parameter is changed and the same force (3.6N) is applied to the plant,
the displacements of the spring under those parameters are different. It means that the stiffness
of APVSEA has been changed, and the APVSEA model is matching to the reference model.
FIGURE 15: The displacement of the spring with different kd parameters.
The above simulation results show MMC can vary the stiffness of APVSEA well. Since the
simulation condition is ideal, the model matching ability still depends on the actuator power or
hardware condition in practical case.
13. Po-Jen Cheng & Han-Pang Huang
International Journal of Robotics and Automation (IJRA), Volume (6) : Issue (3) : 2015 60
5. EXPERIMENTS
Although the APVSEA is an elastic system, it is still insufficient for all applications. However, we
can change the APVSEA stiffness using MMC in advance. Through this approach, the user can
apply different forces with the same displacement based on different designed stiffness. If the
stiffness of the spring is higher, the applied force will be bigger at the same displacement and
vice versa.
Figure 16 shows that the stiffness of the APVSEA can be changed by MMC. In the MMC
experiments, the user was instructed to apply force to the APVSEA and rotate it to a constant
angle. The APVSEA stiffness was changed by MMC, and the user applied forces were
simultaneously measured with a potentiometer. In this experiment, the model matching ability
which is used to vary the stiffness of APVSEA can be proven. Because the stiffness will affect the
displacement of the spring, high/low stiffness generates a smaller/larger displacement.
FIGURE 16: Rotate Output Link to Constant Angle.
Figure 17 shows the control structure of the MMC experiment. First, the user applied force to act
on the APVSEA system and the feedback displacement of the spring is fed into the MMC.
Second, the MMC controller calculates the motor reference and controls the motor to track the
reference using proportional-integral-derivative (PID) controller. uୌ is the user input force, xଶ is
the spring displacement, u is the motor velocity command input, θሶ୫ is the velocity feedback from
motor, and τ is the motor torque that drives the APVSEA.
FIGURE 17: The Flow Chart of MMC Experiment.
Figure 18 is the tracking result of the APVSEA output link in the MMC experiment; parameter kୢ
is -50N/mm. In the result, the green curve shows the model’s angle response, i.e., it is a
reference input for APVSEA. The red curve represents the APVSEA output link angle in MMC. As
shown in the results, MMC had a good angle tracking performance. In other words, APVSEA has
14. Po-Jen Cheng & Han-Pang Huang
International Journal of Robotics and Automation (IJRA), Volume (6) : Issue (3) : 2015 61
a good model matching ability using MMC, and it can imitate the designed model response very
well.
The blue curve represents the force acted on the moving plant and measured by the
potentiometer. The actuator of APVSEA is motor 01, and it realizes the MMC control algorithm.
The experiment results are shown in Figs. 18 and 19. The user applied force in the same way,
but the rotated direction of motor command referred by the MMC controller is different. Since the
stiffness parameter kୢ is -50N/mm, as in figure 18, this will cause the system’s stiffness to
decrease and the motor command to be clockwise. However, when the designer sets the
stiffness parameter kୢ to be 50N/mm, it will cause the whole system’s stiffness to increase and
the motor command to be counterclockwise (see figure 19).
FIGURE 18: kd is -50N/mm.
FIGURE 19: kd is 50N/mm.
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International Journal of Robotics and Automation (IJRA), Volume (6) : Issue (3) : 2015 62
FIGURE 20: The user applied different forces at different designed system’s stiffness.
As mentioned above, the user applies force to the same position depending on the system’s
stiffness—the higher the stiffness the bigger the force. Figure 20 shows the user applied force to
the output link. The blue curve, where parameter kୢ is zero, shows that the APVSEA is
unaffected by the MMC controller. In other words, this is the intrinsic response of the APVSEA.
When kୢ = 0N/mm, it needs approximately 600N when the user rotated the output link to a
constant angle. The stiffness which is shown by the green curve is 162N/mm because the
parameter spring is set to kୢ = 10N/mm. For the case of the green curve, the user needs to apply
nearly 1200 N to the output link. However, if the parameter is set to kୢ = -10N/mm, the system’s
stiffness will decrease. The user only needs to provide a force of 380N to rotate the output link to
a constant angle.
6. CONCLUSION
With the more widespread applications of robots, the SEA with a constant stiffness cannot satisfy
various applications in the future. There is a need to consider the safety ability with human-robot
interaction applications. Nevertheless, if the system varies the stiffness using mechanical
approach, it will increase the system’s volume and weight. Therefore, this paper proposes a non-
back drivable APVSEA system with MMC. The bond graph method can be used to integrate
motors and electrical circuits and can easily extend the model to a robotic arm, exoskeleton
system design, or human-robot interaction model. In order to change the system’s stiffness
actively, we designed the MMC to vary APVSEA’s stiffness. MMC can control the plant in order to
track the model’s performance. This paper offers complete MMC controller design steps using
bond graph by checking solvability, finding an inverse system, solving DDP, deriving error
dynamics, and performing an asymptotic analysis.
From the simulation and experiment results, the MMC controller can change the APVSEA
stiffness very well. The proposed MMC variable stiffness APVSEA system can be safely applied
to human-robot interaction.
7. FUTURE WORK
Model Matching Control had been developed using bond graph approach. It can be used to
change system’s stiffness. However, this approach can be applied to human robot safe
interaction. Decreasing or stopping robot’s working velocity is a common method for guaranteeing
human safe in the factory, but it will cause the robot has low working efficiency. Therefore, we
can modify robot’s stiffness without decreasing or stopping its working velocity for keeping human
safe. The benefit of this future work is human can co-work with robot in safety environment.
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International Journal of Robotics and Automation (IJRA), Volume (6) : Issue (3) : 2015 63
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