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The Ziegler–Nichols tuning (represented by the 'Classic PID' equations in the table above) creates a "quarter wave decay". This is an acceptable result for some purposes, but not optimal for all applications. This tuning rule is meant to give PID loops best disturbance rejection. [2]
PID Control in MATLAB/Simulink and Python with TCLab; What's All This P-I-D Stuff, Anyhow? Article in Electronic Design; Shows how to build a PID controller with basic electronic components (pg. 22) PID Without a PhD; PID Control with MATLAB and Simulink; PID with single Operational Amplifier; Proven Methods and Best Practices for PID Control
A phase-locked loop or phase lock loop (PLL) is a control system that generates an output signal whose phase is fixed relative to the phase of an input signal. Keeping the input and output phase in lockstep also implies keeping the input and output frequencies the same, thus a phase-locked loop can also track an input frequency.
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A fuzzy control system is a control system based on fuzzy logic –a mathematical system that analyzes analog input values in terms of logical variables that take on continuous values between 0 and 1, in contrast to classical or digital logic, which operates on discrete values of either 1 or 0 (true or false, respectively).
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In practice self-tuning is done through the use of specialised hardware or adaptive software algorithms. Giving software the ability to self-tune (adapt): Facilitates controlling critical processes of systems; Approaches optimum operation regimes; Facilitates design unification of control systems; Shortens the lead times of system testing and ...