Complex order PIα+ jβDγ+ jθ design for surface roughness control in machining CNT Al-Mg hybrid composites

Abstract

Accurate machining control is indispensable for the smart factories of tomorrow. Variations in controller responses may cause unacceptable process deviations during machining leading to productivity losses and possible damage. In the present work, a complex order PIα+ jβDγ+ jθ (COPID) controller was designed to effectively control surface roughness generation while machining CNT Al-Mg hybrid composites. Performance of the designed complex order controller was compared against the conventional PID and fractional order PID (FOPID) controllers for the machined surface roughness system. Output signal responses indicate that the complex order controller attains the desired surface roughness set point with zero percent overshoot in almost same settling time (46 sec) as PID (41 sec) and FOPID (46 sec) controllers. The PID and FOPID output signals registered overshoots of 96.8 % and 36.7 % respectively. Similarly, in case of control signals (feed rate) the COPID controller successfully minimised peak overshoot to 4.6 %; as compared to 64.2 % and 96.5 % in case of the PID and FOPID controllers respectively. The COPID controller was also effective in reducing its peak time response metric (2.001 % for control signal and no peak time for output signal due to zero overshoot). In comparison, the PID and FOPID controllers recorded higher response peak times (7 sec / 26 sec for the PID ouput/control and 5 sec / 7.84 sec for FOPID output/control signal responses). Overshoot elimination in output signal (surface roughness) is crucial for consistency of the machined surface quality. Similarly, overshoot minimisation in control signal (feed rate) is critical because excessive feed rate can damage the cutting tool, work piece, machinery and is a potential safety hazard for the machine operator as well. Hence, the COPID controller can be safely and extensively applied in smart industrial control systems of the future.