Optimal Robust Motion Controller Design Using Multiobjective Genetic Algorithm

Algorithm 1

Multiobjective DE algorithm.

(1) Select central polynomials 𝐶_in(𝑠),𝐶_𝑜ut(𝑠) and weights 𝑊(𝑠),𝑉(𝑠).

(2) Select controllers’ structure 𝐾,𝐶 and parameters 𝜎,𝜂.

   deg𝐾=deg𝐶_in−deg𝑃₀,

   deg𝑅_𝐾=deg𝐿_𝐾,

   deg𝐶=deg𝐶_out−(deg𝐶_in+deg𝑃_𝑚+deg𝑃^′),

   deg𝑅_𝐶=deg𝐿_𝐶.

(3) Parameters’ selection of the DE-optimization algorithm.

  (Number of parents-NP, differential weight-F, crossover probability-CR, mutation strategy)

(4)   while (min𝑓(𝜔²,𝑋))

(5)   DE selects value of parameters 𝜎,𝜂.

(6)   Solve polynomial equations (14), (16).

(7)   Derive convex polynomials 𝜋(𝜔²,𝑋).

(8)   Find current Pareto-front of the 𝑓(𝜔²,𝑋).

(9)   end while