To Örebro University

The technique of mitigating chatter phenomenon in an effective manner is an important issue from the viewpoint of superior quality machining process with quality production. In this paper, an innovative solution to control chatter vibration actively in the milling process is presented. The mathematical modelling associated with the milling technique is presented in the primary phase of the paper. In this paper, an innovative technique of discrete time sliding mode control(DSMC) is blended with Type 2 fuzzy logic system. Superior mitigation of chatter is the outcome of developed active controller. The Lyapunov scheme is implemented to validate the stability criteria of the proposed controller. The embedded nonlinearity in the cutting forces and damper friction are compensated in an effective manner by the utilization of Type-2 fuzzy technique. The vibration attenuation ability of DSMC-Type-2 fuzzy (DSMC-T2) is compared with the Discrete time PID (D-PID) and DSMC-Type-1 fuzzy (DSMC-T1) for validating the effectiveness of the controller. Finally, the numerical analysis is carried out to validate that DSMC-T2 is superior to D-PID and DSMC-T1 in the minimization of the milling chatter.

In order to achieve a high-quality machining process with superior productivity, it is very important to tackle the phenomenon of chatter in an effective manner. The problems like tool wear and improper surface finish affect the milling process and are caused by self-induced vibration termed as chatter. A strategy to control chatter vibration actively in the milling process is presented. The mathematical modeling of the process is carried out initially. In this paper, an innovative technique of discrete time sliding mode control (DSMC) is blended with the type-2 fuzzy logic system. The proposed active controller results in a significantly high mitigation of vibration. The DSMC is linked to the time-varying gain which is an innovative approach to mitigate chattering. The theorem is laid down which validates that the system states are bounded in the case of DSMC-type-2 fuzzy. Stability analysis is carried out using Lyapunov candidate. The nonlinearities linked with the cutting forces and damper friction are handled effectively by using the type-2 fuzzy logic system. The performance of the DSMC-type-2 fuzzy concept is compared with the discrete time PID (D-PID) and discrete time sliding mode control for validating the effectiveness of the controller. The better performance of DSMC-type-2 fuzzy over D-PID and DSMC-T1 fuzzy in the minimization of milling chatter are validated by a numerical analysis approach.

In terms of vibrations along bidirectional earthquake forces, several problems are faced when modelling and controlling the structure of a building, such as lateral-torsional vibration, uncertainties surrounding the rigidity and the difficulty of estimating damping forces.In this paper, we use a fuzzy logic model to identify and compensate the uncertainty which does not require an exact model of the building structure. To attenuate bidirectional vibration, a novel discrete-time sliding mode control is proposed. This sliding mode control has time-varying gain and is combined with fuzzy sliding mode control in order to reduce the chattering of the sliding mode control. We prove that the closed-loop system is uniformly stable using Lyapunov stability analysis. We compare our fuzzy sliding mode control with the traditional controllers: proportional?integral?derivative and sliding mode control. Experimental results show significant vibration attenuation with our fuzzy sliding mode control and horizontal-torsional actuators. The proposed control system is the most efficient at mitigating bidirectional and torsional vibrations.

In this paper, the uncertainty property is represented by Z-number as the coefficients and variables of the fuzzy equation. This modification for the fuzzy equation is suitable for nonlinear system modeling with uncertain parameters. Here, we use fuzzy equations as the models for the uncertain nonlinear systems. The modeling of the uncertain nonlinear systems is to find the coefficients of the fuzzy equation. However, it is very difficult to obtain Z-number coefficients of the fuzzy equations.

Taking into consideration the modeling case at par with uncertain nonlinear systems, the implementation of neural network technique is contributed in the complex way of dealing the appropriate coefficients of the fuzzy equations. We use the neural network method to approximate Z-number coefficients of the fuzzy equations.

Uncertain nonlinear systems can be modeled with fuzzy differential equations (FDEs) and the solutions of these equations are applied to analyze many engineering problems. However, it is very difficult to obtain solutions of FDEs. In this book chapter, the solutions of FDEs are approximated by utilizing the fuzzy Sumudu transform (FST) method. Here, the uncertainties are in the sense of fuzzy numbers and Z-numbers. Important theorems are laid down to illustrate the properties of FST. This new technique is compared with Average Euler method and Max-Min Euler method. The theoretical analysis and simulation results show that the FST method is effective in estimating the solutions of FDEs.

Automatic fault detection system is an important aspect of industrial process and can contribute significantly for minimizing equipment downtime thus makingit a cost effective process. In this paper, an innovative model-based faultdetection (FD) system in combination with interval type-2 (IT2) Takagi-Sugeno(T-S) fuzzy system is developed for the detection of the faults in the drillbit of the drilling system. The proposed methodology validates the stabilityof the fault detection system in the presence of system uncertainties. Numerical analysis is carried out to prove the effectiveness of the theoretical approach. The effective methodology can be implemented in real time for detecting faults during downhole drilling operations.

In the area of vibration control associated with structures, proportional-integral-derivative (PID) is considered to be an effective controller for the vibration attenuation scheme. Although the researchers prefer the use of PID controller but due to huge uncertainties in the structure, the control actions are not good. This paper depicts the application of combined PID control with Type-1 Fuzzy system for the compensation of the involved uncertainties. The main role of the Type-1 Fuzzy logic model is the identification of the uncertainties in the modeling equation and also to compensate it in an effective way. The methodology of Lyapunov stability criterion is implemented to validate the uniform stability of the closed-loop system. The synergistic combination of active mass damper (AMD), torsional actuator (TA), and Type-1 Fuzzy PID controller resulted in superior vibration attenuation which is validated by the experimental tests.

Proportional-derivative (PD) and proportional-integral-derivative (PID) controllers are popular control algorithms in industrial applications, especially in structural vibration control. In this paper, the designs of two dampers, namely the horizontal actuator and torsional actuator, are combined for the lateral and torsional vibrations of the structure. The standard PD and PID controllers are utilized for active vibration control. The sufficient conditions for asymptotic stability of these controllers are validated by utilizing the Lyapunov stability theorem. An active vibration control system with two floors equipped with a horizontal actuator and a torsional actuator is installed to carry out the experimental analysis. The experimental results show that bidirectional active control has been achieved.

In this paper, a novel discrete-time sliding mode control is proposed in order to attenuate structural vibration due to earthquake forces. The analysis is based on the lateral-torsional vibration under the bidirectional waves. The proposed fuzzy modeling based sliding mode control can reduce chattering due to its time-varying gain. In the modeling equation of the structural system, the uncertainty exists in terms of sti¤ness, damping forces and earthquake. Fuzzy logic model is used to identify and compensate the uncertainty associated with the modeling equation. We prove that the closed-loop system is uniformly stable using Lyapunov stability analysis. The experimental result reveals that discrete-time sliding mode controller offers significant vibration attenuation with active mass damper and torsional actuator.

Chatter is an obstacle for achieving high-quality machining process and high production rate in industries. Chatter is an unstable self-exciting phenomenon that leads to tool wear, poor surface finish, and downgrade the milling operations. A novel active control strategy to attenuate the chatter vibration is proposed. PD/PID controllers in combination with Type-2 Fuzzy logic were utilized as a control strategy. The main control actions were generated by PD/PID controllers, whereas the Type-2 Fuzzy logic system was used to compensate the involved nonlinearities. The Lyapunov stability analysis was utilized to validate the stability of Fuzzy PD/PID controllers. The theoretical concepts and results are proved using numerical simulations. Although PD/PID controllers have been used for chatter control in machining process, the importance of stability along with the implementation of Type-2 Fuzzy logic system for nonlinearity compensation was the main contribution. In addition, active control using an Active Vibration Damper placed in an effective position is entirely a new approach with promising practical results.