Robust design of sliding mode control for airship trajectory tracking with uncertainty and disturbance estimation

The robotic airship can provide a promising aerostatic platform for many potential applications.These applications require a precise autonomous trajectory tracking control for airship.Airship has a nonlinear and uncertain dynamics.It is prone to wind disturbances that offer a challenge for a trajectory tracking control design.This paper addresses the airship trajectory tracking problem having time varying reference path.A lumped parameter estimation approach under model uncertainties and wind disturbances is opted against distributed parameters.It uses extended Kalman filter(EKF)for uncertainty and disturbance estimation.The estimated parameters are used by sliding mode controller(SMC)for ultimate control of airship trajectory tracking.This comprehensive algorithm,EKF based SMC(ESMC),is used as a robust solution to track airship trajectory.The proposed estimator provides the estimates of wind disturbances as well as model uncertainty due to the mass matrix variations and aerodynamic model inaccuracies.The stability and convergence of the proposed method are investigated using the Lyapunov stability analysis.The simulation results show that the proposed method efficiently tracks the desired trajectory.The method solves the stability,convergence,and chattering problem of SMC under model uncertainties and wind disturbances.

Analyzing the Effects of Tool Holder Stiffness on Chatter Vibration Reduction in Turning

This paper investigates the effects of tool holder materials on chatter vibration in turning operations.The study uses a complex dynamic turning model with two degrees of freedom for the orthogonal cutting system.Tool holders made from different materials,including Al 5083,Al 6082,Al 7012,and a standard 4140 material,were subjected to chatter vibration to investigate their process damping capabilities.The study found that the standard tool holder 4140 allows for higher stable depths of cut and produces similar process damping values compared to the other tool holders.Finite element analyses(FEA)were performed to verify the experimental results,and the modal and FEA analyses produced very similar results.The study concludes that future research should investigate the effects of tool holders made from high alloy steel alloys on process damping.Overall,this paper provides important insights into the effects of tool hold-er materials on chatter vibration and process damping in turning operations,which can help in the design of more effi-cient and effective cutting systems.

Experimental Study on Entropy Features in Machining Vibrations of A Thin-Walled Tubular Workpiece

In machining processes,chatter vibrations are always regarded as one of the major limitations for production quality and efficiency.Accurate and timely monitoring of chatter is helpful to maintain stable machining operations.At present,most chatter monitoring methods are based on the energy level at specified chatter frequencies or frequency bands.However,the spectral features of chatter could change during machining operations due to complexity and time-varying dynamics of the physical machining process.The purpose of this paper is to investigate the time-varying chatter features in turning of thin-walled tubular workpieces from the perspective of entropy.The airborne acoustics was selected as the source of information for machining condition monitoring.First,corresponding to the distinguishing surface topographies relevant to machining conditions,the features of the sound signal emitted during turning of the thin-walled cylindrical workpieces were extracted using the spectral analysis and wavelet packet transform,respectively.It was shown that the dominant vibration frequency as well as the energy distribution could shift with the transition of the machining status.After that,two relative entropy indicators based on the spectrum and the wavelet packet energy were constructed to identify chattering events in turning of the thin-walled tubes.The experimental results demonstrate that the proposed indicators could accurately reflect the transition of machining conditions with high sensitivity and robustness in comparison with the traditional FFT-based methods.The achievement of this study lays the foundations of the online chatter monitoring and control technique for turning of the thin-walled tubular workpieces.

Machining dynamics and chatters in micro-milling:A critical review on the state-of-the-art and future perspectives

Micro-milling technology is widely applied in micro manufacturing,particularly for the fabrication of miniature and micro components.However,the chatters and machining dynamics related issues in micro-milling are often the main challenges restricting its machining quality and productivity.Many research works have rendered that the machining dynamics and chatters in micro-milling are more complex compared with the conventional macro-milling process,likely because of the size effect and rigidity of the micro-milling system including the tooling,workpiece,process variables,materials involved,and the high-speed milling machines,and further their collective dynamic effects.Therefore,in this paper,the state of the art focusing on micro-milling chatters and dynamics related issues over the past years are comprehensively and critically reviewed to provide some insights for potential researchers and practitioners.Firstly,typical applications and the problems caused by the machining dynamics and chatters in micro-milling have been put forward in this paper.Then,the research on the underlying micro-cutting mechanics and dynamics,stability analysis,chatters detection,and chatter suppression are summarized critically.Furthermore,the underlying scientific and technological challenges are discussed particularly against typical precision engineering applications.Finally,the possible future directions and trends in research and development of micro-milling have been discussed.

Design of High Precision CNC Vertical Lathe Turning Tool Holder

A large aspect ratio vibration reducing tool holder based on passive damping vibration reduction technology is designed to solve the vibration problem that occurs in deep hole machining of vertical lathes.A dynamic model of passive damping vibration reduction tool holder was established,and the optimal damping ratio,optimal frequency ratio,and maximum relative amplitude were derived.Modal analysis of the passive damping vibrationreduction tool holder was conducted using software.The results showed that the maximum response amplitude of the passive damping vibration reduction tool holder decreased significantly compared to the original one.

立铣加工颤振稳定性时域求解与分析研究(英文)

In this paper, the instantaneous undeformed chip thickness is modeled to include the dynamic modulation caused by the tool vibration while the dynamic regenerative effects are taken into account. The numerical method is used to solve the differential equations goveming the dynamics of the milling system. Several chatter detection criteria are applied synthetically to the simulated signals and the stability diagram is obtained in time-domain. The simulation results in time-domain show a good agreement with the analytical prediction, which is validated by the cutting experiments. By simulating the chatter stability lobes in the time-domain and analyzing the influences of different spindle speeds on the vibration amplitudes of the tool under a Fixed chip-load condition, conclusions could be drawn as follows： In rough milling, higher machining efficiency can be achieved by selecting a spindle speed corresponding to the axial depth of cut in accordance with the simulated chatter stability lobes, and in Fmish milling, lower surface roughness can be achieved by selecting a spindle speed well beyond the resonant frequency of machining system.

Grinding Chatter Detection and Identication Based on BEMD and LSSVM

Grinding chatter is a self?induced vibration which is unfavorable to precision machining processes. This paper proposes a forecasting method for grinding state identification based on bivarition empirical mode decomposition(BEMD) and least squares support vector machine(LSSVM), which allows the monitoring of grinding chatter over time. BEMD is a promising technique in signal processing research which involves the decomposition of two?dimen?sional signals into a series of bivarition intrinsic mode functions(BIMFs). BEMD and the extraction criterion of its true BIMFs are investigated by processing a complex?value simulation chatter signal. Then the feature vectors which are employed as an amplification for the chatter premonition are discussed. Furthermore, the methodology is tested and validated by experimental data collected from a CNC guideway grinder KD4020 X16 in Hangzhou Hangji Machine Tool Co., Ltd. The results illustrate that the BEMD is a superior method in terms of processing non?stationary and nonlinear signals. Meanwhile, the peak to peak, real?time standard deviation and instantaneous energy are proven to be e ec?tive feature vectors which reflect the di erent grinding states. Finally, a LSSVM model is established for grinding status classification based on feature vectors, giving a prediction accuracy rate of 96%.

FUZZY GLOBAL SLIDING MODE CONTROL BASED ON GENETIC ALGORITHM AND ITS APPLICATION FOR FLIGHT SIMULATOR SERVO SYSTEM

To alleviate the chattering problem, a new type of fuzzy global sliding mode controller （FGSMC） is presented. In this controller, the switching gain is estimated by fuzzy logic system based on the reachable conditions of sliding mode controller（SMC）, and genetic algorithm （GA） is used to optimize scaling factor of the switching gain, thus the switch chattering of SMC can be alleviated. Moreover, global sliding mode is realized by designing an exponential dynamic sliding surface. Simulation and real-time application for flight simulator servo system with Lugre friction are given to indicate that the proposed controller can guarantee high robust performance all the time and can alleviate chattering phenomenon effectively.

Receptance Coupling for Tool Point Dynamics Prediction on Machine Tools

Chatter has been a primary obstacle to the successful implementation of high speed machining.The frequency response function（FRF） of the tool point is crucial for identification of chatter free cutting conditions.In order to quickly acquire the FRF of the different components combinations of machine tool,the assembly of machine tool was always decomposed into several parts,where the fluted portion of tool,however,was always treated as a uniform beam,and the associated discrepancy was ignored.This paper presents a new method to predict the dynamic response of the machine-spindle-holder-tool assembly using the receptance coupling substructure analysis technique,where the assembly is divided into three parts：machine-spindle,holder and tool shank,and tool＇s fluted portion.Impact testing is used to measure the receptance of machine-spindle,the Timoshenko beam model is employed to analyze the dynamics of holder and tool shank,and the finite element method（FEM） is used to calculate the receptance of the tool＇s fluted portion.The approximation of the fluted portion cross section using an equivalent diameter is also addressed.All the individual receptances are coupled by using substructure method.The predicted assembly receptance is experimentally verified for three different tool overhang lengths.The results also show that the equivalent diameter beam model reaches an acceptable accuracy.The proposed approach is helpful to predict the tool point dynamics rapidly in industry.

Prediction of Dynamic Cutting Force and Regenerative Chatter Stability in Inserted Cutters Milling

Currently, the modeling of cutting process mainly focuses on two aspects: one is the setup of the universal cutting force model that can be adapted to a broader cutting condition; the other is the setup of the exact cutting force model that can accurately reflect a true cutting process. However, there is little research on the prediction of chatter stablity in milling. Based on the generalized mathematical model of inserted cutters introduced by ENGIN, an improved geometrical, mechanical and dynamic model for the vast variety of inserted cutters widely used in engineering applications is presented, in which the average directional cutting force coefficients are obtained by means of a numerical approach, thus leading to an analytical determination of stability lobes diagram (SLD) on the axial depth of cut. A new kind of SLD on the radial depth of cut is also created to satisfy the special requirement of inserted cutter milling. The corresponding algorithms used for predicting cutting forces, vibrations, dimensional surface finish and stability lobes in inserted cutter milling under different cutting conditions are put forward. Thereafter, a dynamic simulation module of inserted cutter milling is implemented by using hybrid program of Matlab with Visual Basic. Verification tests are conducted on a vertical machine center for Aluminum alloy LC4 by using two different types of inserted cutters, and the effectiveness of the model and the algorithm is verified by the good agreement of simulation result with that of cutting tests under different cutting conditions. The proposed model can predict the cutting process accurately under a variety of cutting conditions, and a high efficient and chatter-free milling operation can be achieved by a cutting condition optimization in industry applications.

Modeling and Analytical Solution of Chatter Stability for T-slot Milling

T-slot milling is one of the most common milling processes in industry. Despite recent advances in machining technology, productivity of T-slot milling is usually limited due to the process limitations such as high cutting forces and stability. If cutting conditions are not selected properly the process may result in the poor surface finish of the workpiece and the potential damage to the machine tool. Currently, the predication of chatter stability and determination of optimal cutting conditions based on the modeling of T-slot milling process is an effective way to improve the material removal rate（MRR） of a T-slot milling operation. Based on the geometrical model of the T-slot cutter, the dynamic cutting force model was presented in which the average directional cutting force coefficients were obtained by means of numerical approach, and leads to an analytical determination of stability lobes diagram（SLD） on the axial depth of cut. A new kind of SLD on the radial depth of cut was also created to satisfy the special requirement of T-slot milling. Thereafter, a dynamic simulation model of T-slot milling was implemented using Matlab software. In order to verify the effectiveness of the approach, the transfer functions of a typical cutting system in a vertical CNC machining center were measured in both feed and normal directions by an instrumented hammer and accelerators. Dynamic simulations were conducted to obtain the predicated SLD under specified cutting conditions with both the proposed model and CutPro~. Meanwhile, a set of cutting trials were conducted to reveal whether the cutting process under specified cutting conditions is stable or not. Both the simulation comparison and experimental verification demonstrated that the satisfactory coincidence between the simulated, the predicted and the experimental results. The chatter-free T-slot milling with higher MRR can be achieved under the cutting conditions determined according to the SLD simulation.

Impact of Modal Parameters on Milling Process Chatter Stability Lobes

Modals of the machine/tool and machine/part system are the principal factors affecting the stability of a milling process. Based on the modeling of chatter stability of milling process,the influence of modal parameters on chatter stability lobes independently or jointly has been analyzed by simulation. Peak-to-valley specific value,lobe coefficient and the corresponding calculation formula have been put forward. General laws and steps of modal simplification for multimodality system have been summarized.

Continuous Sliding Mode Controller with Disturbance Observer for Hypersonic Vehicles

In this paper, a continuous sliding mode controller with disturbance observer is proposed for the tracking control of hypersonic vehicles to suppress the chattering. The finite time disturbance observer is involved to make that the continuous sliding mode controller has the property of disturbance rejection.Due to continuous terms replacing the discontinuous term of traditional sliding mode control, switching modes of velocity and altitude firstly arrive at small regions with respect to disturbance observation errors. Switching modes keep zero and velocity and altitude asymptotically converge to their reference commands after disturbance observation errors disappear. Simulation results have proved the proposed method can guarantee the tracking of velocity and altitude with continuous sliding mode control laws,and also has the fast convergence rate and robustness.

Harmonic Current′s Coupling Effect on the Main Motion of Temper Mill Set

The paper probes into a probable condition that causes temper mill chatter from aspect of electromechanical coupling of complex electromechanical system, and mainly studies the effect of temper mill electrical driving system harmonic current on the main motion of temper mill set. Aiming at the electrical driving system of CM04 temper mill, the effect of harmonic current is analyzed and evaluated according to different load. Combining the features of CM04 temper mill′s structure and its working state, the paper discusses in every detail how the harmonic current in main circuit, which can be regarded as a disturbance via feedback control circuit , influences main motion of temper mill set.

Backstepping sliding mode control for uncertain strict-feedback nonlinear systems using neural-network-based adaptive gain scheduling

A neural-network-based adaptive gain scheduling backstepping sliding mode control（NNAGS-BSMC） approach for a class of uncertain strict-feedback nonlinear system is proposed.First, the control problem of uncertain strict-feedback nonlinear systems is formulated. Second, the detailed design of NNAGSBSMC is described. The sliding mode control（SMC） law is designed to track a referenced output via backstepping technique.To decrease chattering result from SMC, a radial basis function neural network（RBFNN） is employed to construct the NNAGSBSMC to facilitate adaptive gain scheduling, in which the gains are scheduled adaptively via neural network（NN）, with sliding surface and its differential as NN inputs and the gains as NN outputs. Finally, the verification example is given to show the effectiveness and robustness of the proposed approach. Contrasting simulation results indicate that the NNAGS-BSMC decreases the chattering effectively and has better control performance against the BSMC.

Disturbance observer based time-varying sliding mode control for uncertain mechanical system

It is now well known that the time-varying sliding mode control （TVSMC） is characterized by its global robustness against matched model uncertainties and disturbances. The accurate tracking problem of the mechanical system in the presence of the parametric uncertainty and external disturbance is addressed in the TVSMC framework. Firstly, an exponential TVSMC algorithm is designed and the main features are analyzed. Especially, the control parameter is obtained by solving an optimal problem. Subsequently, the global chattering problem in TVSMC is considered. To reduce the static error resulting from the continuous TVSMC algorithm, a disturbance observer based time-varying sliding mode control （DOTVSMC） algorithm is presented. The detailed design principle and the stability of the closed-loop system under the composite controller are provided. Simulation results verify the effectiveness of the proposed algorithm.

APPLICATION OF WAVELET TRANSFORM ON DIAGNOSIS AND PREDICTION OF MILLING CHATTER

In order to avoid the accuracy deterioration or tool damage caused by milling chatter, it is necessary to have an efficient and reliable diagnosis system that can on-line predict/detect the occur-rence of chatter. The diagnosis/predicting system proposed is to on-line process and analysis the vi-bration signals of the milling machine measured by accelerometers. According to the analysis results, the system will be able to detect/predict the occurrence of the chatter. The diagnosis algorithm is, first, collecting both the normal signals and chatter signals from milling processes, and then, converting the signals through wavelet transform and fast Fourier transform （FFT）. Since the converted chatter sig-nals exhibit different characteristics from the normal signals, through defining the characteristic val-ues, such as root-mean-square value, max value, and ratio of peak value to root-mean-square value, etc, a diagnosis reference library that contains the distribution of these characteristic values is built for diagnosis. When a diagnosis is executing, the characteristic value of the measured signals is con-trasted with the diagnosis reference. The approach index which shows the possibility of occurrence of milling chatter will, then, be calculated through the diagnosis system. Cutting experiments are con-ducted to verify the proposed diagnosis system. The results show the success of early chatter detecting for the system.

Optimization of the Tuned Mass Damper for Chatter Suppression in Turning

The tuned mass damper（TMD） has been successfully applied to the vibration control in machining, while the most widely adopted tuning is equal peaks, which splits the magnitude of the frequency response function（FRF） into equal peaks. However, chatter is a special self-excited problem and a chatter-flee machining is determined by FRF at the cutting zone. A TMD tuning aiming at achieving the maximum chatter stability is studied, and it is formulated as an optimization problem of maximizing the minimum negative real part of FRF. By employing the steepest descend method, the optimum frequency and damping ratio of TMD are obtained, and they are compared against the equal peaks tuning. The advantage of the proposed tuning is demonstrated numerically by comparing the minimum point of the negative real part, and is further verified by damping a flexible mode from the fixture of a turning machine. A TMD is designed and placed on the fixture along the vibration of the target mode after performing modal analysis and mode shape visualization. Both of the above two ttmings are applied to modify the tool point FRF by tuning TMD respectively. Chatter stability chart of the turning shows that the proposed tuning can increase the critical depth of cut 37% more than the equal peaks. Cutting tests with an increasing depth of cut are conducted on the turning machine in order to distinguish the stability limit. The tool vibrations during the machining are compared to validate the simulation results. The proposed damping design and optimization routine are able to further increase the chatter suppression effect.

Chatter Suppression with Ultrasonic Elliptical Vibration Based on Energy Principle

A new method is proposed to suppress chatter, in which the ultrasonic elliptical vibration is added on the cutting tool edge. It results in the fact that the rake face of tool is separated from the chip and the direction of the frictional force between the rake face and the chip is reversed in each cycle of elliptical vibration cutting. The experimental investigations show that the chatter can be suppressed effectively by adding ultrasonic elliptical vibration on the cutting tool edge. In order to make clear the reason of chatter suppression, the mechanism of chatter suppression is analyzed theoretically from the viewpoint of energy.

Approximation law for discrete-time variable structure control systems

Two approximation laws of sliding mode for discrete-time variable structure control systems are proposed to overcome the limitations of the exponential approximation law and the variable rate approximation law. By applying the proposed approximation laws of sliding mode to discrete-time variable structure control systems, the stability of origin can be guaranteed, and the chattering along the switching surface caused by discrete-time variable structure control can be restrained effectively. In designing of approximation laws, the problem that the system control input is restricted is also considered, which is very important in practical systems. Finally a simulation example shows the effectiveness of the two approximation laws proposed.