N-PID controller with feedforward og generalized maxwell-slip and static friction model for for friction compensation in machine tools

Increasing demand for accuracy and precision in machine tools application has placed greater pressure on researchers and machine developers for better products performance. Several factors that have been identified in literature that could affect machine performance are the active presence of disturbance forces such as cutting forces and friction forces. This research focuses only on the effect of friction forces as disturbance in a positioning system. “Spikes” on milled surface are normally observed in computer numerical control machine based on recent research and analysis. These “spikes” are known as quadrant glitches and is mainly due to the friction forces, which is an undesirable and nonlinear phenomenon that cannot be avoided during positioning process. The main objective of this research is the compensation of these friction forces to improve tracking performance of system by utilizing two different approaches, namely; non-model based method and friction model-based feedforward method. Two controllers, namely, proportional-integral-derivative (PID) controller and nonlinear PID (N-PID) controller, were designed, implemented and validated as non-model based technique to compensate friction forces on a XYZ-Stage, which is a fundamental block of a milling machine. In friction model-based method, two friction models, namely; static friction model and Generalized Maxwell-slip (GMS) model, were identified, modeled and applied as friction model-based feedforward. The system frequency response function was identified using a data acquisition unit, dSPACE 1104 with MATLAB software and H1 estimator, a nonlinear least square frequency domain identification method. Parameters for static friction and GMS model were identified using heuristic method and virgin curve respectively. PID and N-PID controllers were designed based on traditional loop shaping frequency domain approach and Popov stability criterion respectively. Numerical simulation and experimental validation for non-model based method showed that N-PID controller provided 25.0% improved performance in terms of quadrant glitches magnitude reduction than the PID controller. This is due to its automatic gain adjustment based on the chosen nonlinear function. For friction model-based feedforward method, the static friction model produced 95.9% reduction in tracking errors using PID controller and 95.8% reduction using the N-PID controller. For GMS friction model feedforward, the quadrant glitches magnitude was reduced by 33.3% using PID controller and 30.0% while using the N-PID controller. Finally, a combined feedforward of static and GMS friction models with the N-PID controller has resulted in the best performance that was a 96.5% reduction in tracking errors, and a 50.0% reduction in quadrant glitches magnitude. It is concluded that this combined approach would benefits to machine tools manufacturers and users as it improves the tracking performance as well as precision especially during circular motion and low tracking velocity

Super Twisting Sliding Mode Controllers And Kalman-Bucy Filter For Single Axis Positioning System

Demands for accuracy and precision in machine tools have generated great interests for development of high performance drive control system with excellent characteristics in reference tracking, chattering,and robustness against input disturbance and load variation. Recently, a nonlinear control approach named super twisting sliding mode controller (ST -SMC) becomes attractive for its ability to meet complex demands on system performance where classical controllers have failed to meet.ST-SMC provides good tracking quality and effectively proven disturbance rejection property. However,chattering still exist as an issue in application of ST-SMC. To-date, there exists a knowledge gap in in-depth analyses on optimal design of gains parameters in control laws of ST-SMC constituting trade-off between tracking accuracy and effect of chattering. This thesis presents optimal design of ST-SMC with enhanced smoothening functions for precise tracking performances and reduced chattering; validated on a single axis sliding unit with direct driven linear motor.In addition, a Kalman-Bucy filter (KBF) was designed and applied to estimate velocity signal for the control system thus eliminating effect of noise amplification normally associated with numerical differentiation of position signal. A Taguchi optimization method was applied to optimize the control laws gain parameters of ST-SMC based on three performance indexes, namely; root mean square of tracking error (RMSE), chattering amplitude reduction in frequency domain,and variations in RMSE values from exposure to input disturbance. The optimal values of the gain parameters L and W were 0.7 and 10 10-5 respectively; with a confidence level of 95%.Two variants of ST-SMC were formulated based on modifications of the control laws of original ST-SMC; where the signum function was replaced by either a hyperbolic tangent function or an arc-tangent smoothening function to a form hyperbolic ST-SMC (HST-SMC) and an arc-tangent STSMC (Arc-ST-SMC) respectively. Five controllers were designed and validated experimentally, namely; cascade P/PI controller, pseudo-SMC, optimized ST-SMC, HSTSMC, and Arc-ST-SMC. The control performances of each controller were analyzed with respect to tracking accuracy,chattering suppression, and robustness against input disturbance and system dynamics variation. The optimized ST-SMC produced the best overall control performance with 9.6% (RMSE),3.9% (disturbance rejection),and 13.4% (robustness) superior results compared to the other variants of SMC-based controllers. On the other hand, HST-SMC produced a comparable tracking performance to optimized STSMC with minimal difference of 7.3% (RMSE), 0.4% (disturbance rejection), and 0.7%(robustness).HST-SMC offers a fair trade-off in control performance between tracking accuracy, disturbance rejection and chattering attenuation. Arc-ST-SMC showed its strength with a significant 71.4% reduction in chattering effect.Finally, this thesis has demonstrated outstanding control performances of ST-SMC-based controllers that produced tracking accuracy that was 96.0% better than classical cascade P/PI controller

Systematic Method For Cutting Forces Characterization For XY Milling Table Ballscrew Drive System

Inclusion of disturbances in the control system structure of XY table during simulation process is crucial in order to closely replicate the real system in the simulation structure. An example of the distinguished disturbances during cutting operation is cutting forces. It can affect the accuracy of actual position of x and y-axis movement during the cutting operation. Thus, it is important for control designer to include the cutting force disturbance before designing the controller for the XY table system. This paper is focused on the fundamental aspect on how to extract the useful cutting forces data from the raw cutting force data by showing the step by step procedure on how to implement the process. In addition, method on how to convert from the selected cutting forces disturbance data into the form of voltage so that the disturbances is possible to be injected into the system is also being touched and finally, the discussion on the relationship between machine spindle speed and the cutting force generated is also being addressed comprehensively

Assessment on tracking error performance of Cascade P/PI, NPID and N-Cascade controller for precise positioning of xy table ballscrew drive system

Abstract. At present, positioning plants in machine tools are looking for high degree of accuracy and robustness attributes for the purpose of compensating various disturbance forces. The objective of this paper is to assess the tracking performance of Cascade P/PI, Nonlinear PID (NPID) and Nonlinear cascade (N-Cascade) controller with the existence of disturbance forces in the form of cutting forces. Cutting force characteristics at different cutting parameters; such as spindle speed rotations is analysed using Fast Fourier Transform. The tracking performance of a Nonlinear cascade controller in presence of these cutting forces is compared with NPID controller and Cascade P/PI controller. Robustness of these controllers in compensating different cutting characteristics is compared based on reduction in the amplitudes of cutting force harmonics using Fast Fourier Transform. It is found that the Ncascade controller performs better than both NPID controller and Cascade P/PI controller. The average percentage error reduction between N-cascade controller and Cascade P/PI controller is about 65 % whereas the average percentage error reduction between cascade controller and NPID controller is about 82 % at spindle speed of 3000 rpm spindle speed rotation. The finalized design of N-cascade controller could be utilized further for machining application such as milling process. The implementation of N-cascade in machine tools applications will increase the quality of the end product and the productivity in industry by saving the machining time. It is suggested that the range of the spindle speed could be made wider to accommodate the needs for high speed machining.

Extensive Tracking Performance Analysis of Classical feedback control for XY Stage ballscrew drive system

Performance analysis in term of identifying the system's transient response, stability and system's dynamical behavior in control system design is undeniably a must process. There are several ways in which a system can be analyzed. An example of well known techniques are using time domain and frequency domain approach. This paper is focused on the fundamental aspect of analysis of classical feedback controller in frequency domain of XY milling table ballscrew drive system. The controller used for the system is the basic PID controller using Matlab SISOTOOL graphical user interface. For this case, the frequency response function (FRF) of the system is used instead of using estimated model of transfer function to represent the real system. Result in simulation shows that after proper tuning of the controller, the system has been successfully being controlled accordingly. In addition, the result also fulfill the set requirement of frequency domain analysis in terms of the required gain and phase margin, the required maximum peak sensitivity and complimentary sensitivity function and the required stability

Extensive Tracking Performance Analysis of Classical feedback control for XY Stage ballscrew drive system

Performance analysis in term of identifying the system's transient response, stability and system's dynamical behavior in control system design is undeniably a must process. There are several ways in which a system can be analyzed. An example of well known techniques are using time domain and frequency domain approach. This paper is focused on the fundamental aspect of analysis of classical feedback controller in frequency domain of XY milling table ballscrew drive system. The controller used for the system is the basic PID controller using Matlab SISOTOOL graphical user interface. For this case, the frequency response function (FRF) of the system is used instead of using estimated model of transfer function to represent the real system. Result in simulation shows that after proper tuning of the controller, the system has been successfully being controlled accordingly. In addition, the result also fulfill the set requirement of frequency domain analysis in terms of the required gain and phase margin, the required maximum peak sensitivity and complimentary sensitivity function and the required stability

System Identification of XY Table ballscrew drive using parametric and non parametric frequency domain estimation via deterministic approach

System Identification of a system is the very first part in design control procedure of mechatronics system. There are several ways in which a system can be identified. An example of well known techniques are using time domain and frequency domain approach. This paper is focused on the fundamental aspect of system identification of mechatronics system in which it includes the step by step procedure on how to perform system identification. The system for this case is XY milling table ballscrew drive. Both parametric and nonparametric procedure. In addition, comparison of estimated model transfer function obtained via non-linear least square (NLLS) and Linear least square estimator algorithm were also being addressed. It shows that the NLLS technique perform better than LLS technique for this case. LLS technique for this case. The result was judged based on result was judged based on result was judged based on the requirement during model validation procedure such as through heuristic approach (graphical observation) of best fit model with respect to the frequency response function (FRF) of the system

Evaluation On Tracking Performance Of PID, Gain Scheduling And Classical Cascade P/PI Controller On XY Table Ballscrew Drive System

Today, positioning systems in machine tools aim for high accuracy and robustness characteristics in order to accommodate against various disturbance forces. The objective of this paper is to evaluate the tracking performance of PID, Gain Scheduling and Cascade P/PI controller with the existence of disturbance forces in the form of cutting forces. Cutting force characteristics at different cutting parameters; such as spindle speed rotations is analysed using Fast Fourier Transform. The tracking performance of a classical cascade controller in presence of these cutting forces is compared to the PID controller and gain scheduling PID controller. Robustness of these controllers in compensating different cutting characteristics is compared based on reduction in the amplitudes of cutting force harmonics using Fast Fourier Transform. It is found that the cascade controller performs better than both PID controller and gain scheduling PID controller. The average percentage error reduction between cascade controller and Gain Scheduling controller is about 88% whereas the average percentage error reduction between cascade controller and Gain Scheduling controller is about 84% at spindle speed of 1000 rpm spindle speed rotation. The finalized design of cascade controller could be utilized further for machining application such as milling process. The implementation of cascade P/PI in machine tools applications will increase the quality of the end product and the productivity in industry by saving the machining time. It is suggested that the range of the spindle speed could be made wider to accommodate the needs for high speed machining

Design and Analysis of Self-tuned Nonlinear PID Controller for XY Table Ballscrew Drive System

Positioning systems in machine tools lately insists for high accuracy and self adjusting mechanism to be implemented into the system in order to sustain against various disturbance forces. The disturbance forces are in the form of both cutting forces and friction forces. The aim of this paper is to propose a controller namely Nonlinear Proportional Integral Derivative (NPID) to control the position of the system. The tracking error will be compensated by the NPID controller.The tracking performance of NPID controller is compared with conventional PID controller. The degree of robustness of both controllers is quantified based on reduction in the amplitudes of cutting force harmonics using Fast Fourier Transform. It is obvious that the average tracking performance result of NPID controller outweigh the PID controller about 8 % to 40 % better. The finalize design of NPID controller do provide brighter prospect for machining application such as milling process. The execution of NPID controller will offer flexibility since the controller are an adaptive type of controller in which it can automatically adjust for better value of gain based on the error generated from the system. Finally, it is recommended that in order to improvise further the NPID controller, control designer could embedded any type of add on features like dead zone compensator and tracking differentiator into the controller to improve the tracking performance

Optimization Of Super Twisting Sliding Mode Control Gains Using Taguchi Method

This paper focuses on optimization of super twisting controller gains using Taguchi method with objective to minimize tracking error and the chattering effect. Two gain parameters in super twisting algorithm, that is L and W were identified as two factors with three levels respectively. The optimization method applied a L9 orthogonal array and the performance index used was root mean square of tracking error and Fast Fourier Transform of control inputs. The optimized super twisting controller with traditional sliding surface and the continuous control action laws was validated on a single axis direct driven linear motor. Analyses of variance and main effect plots were performed on the effect of gains variation on performance index. Values of L and W were chosen as 0.00002 and 0.08 respectively and were confirmed through confirmation test based on calculated confidence interval. Experimental results with 95% confidence level identified gain L as the significant factor in minimizing chattering effect while both gains L and W were responsible in minimizing tracking error in optimum condition. Optimized algorithm achieved 9.3% of reduction in root mean square of tracking error and 38.4% of reduction in chattering experimentally