Fuzzy logic-based adaptive gravitational search algorithm for optimal tuning of fuzzy-controlled servo systems

This study proposes an adaptive gravitational search algorithm (AGSA) which carries out adaptation of depreciation law of the gravitational constant and of a parameter in the weighted sum of all forces exerted from the other agents to the iteration index. The adaptation is ensured by a simple single input-two output (SITO) fuzzy block in the algorithm's structure. SITO fuzzy block operates in the iteration domain, the iteration index is the input variable and the gravitational constant and the parameter in the weighted sum of all forces are the output variables. AGSA's convergence is guaranteed by a theorem derived from Popov's hyperstability analysis results. AGSA is embedded in an original design and tuning method for Takagi-Sugeno proportional-integral fuzzy controllers (T-S PI-FCs) dedicated to servo systems modelled by second-order models with an integral component and variable parameters. AGSA solves a minimisation-type optimisation problem based on an objective function which depends on the sensitivity function with respect to process gain variations, therefore a reduced process gain sensitivity is offered. AGSA is validated by a case study that optimally tunes a T-S PI-FC for position control of a laboratory servo system. Representative experimental results are presented.