Genetic Algorithm Based Improved Sub-Optimal Model Reduction in Nyquist   Plane for Optimal Tuning Rule Extraction of PID and PI{\lambda}D{\mu}   Controllers via Genetic Programming
  Genetic Algorithm (GA) has been used in this paper for a new Nyquist based sub-optimal model reduction and optimal time domain tuning of PID and fractional order (FO) PI{\lambda}D{\mu} controllers. Comparative studies show that the new model reduction technique outperforms the conventional H2-norm based reduced order modeling techniques. Optimum tuning rule has been developed next with a test-bench of higher order processes via Genetic Programming (GP) with minimum value of weighted integral error index and control signal. From the Pareto optimal front which is a trade-off between the complexity of the formulae and control performance, an efficient set of tuning rules has been generated for time domain optimal PID and PI{\lambda}D{\mu} controllers. 
Saptarshi Das, Indranil Pan, Shantanu Das, and Amitava Gupta
cs.SY