Application of Model Order Reduction Techniques in PID controller Design

Doctoral Thesis / Dissertation from the year 2012 in the subject Engineering - General, Basics, grade: A, Anna University, language: English, abstract: The analysis and synthesis of higher order models are complicated and are not desirable on economic and computational considerations. To circumvent the difficulties, lower order model formulation techniques are utilized to find a lower dimensional approximant for the original higher order model. The obtained lower order model preserves the characteristics of the original higher order model. Firstly, the linear time invariant single input single output continuous systems are considered to investigate the efficiency of the proposed lower order model formulation approach. For this, the given linear time invariant higher order system represented in the form of transfer function is adopted to get adjunct lower order transfer function and its coefficients are tuned suitably with the help of modified particle swarm optimization along with transient and steady state gain adjustments. The lower order model is formed on an error based criterion. Moreover, the formulated second order models are used to design the continuous PID controllers. Secondly, the single input single output linear time invariant discrete systems are dealt for model order formulation with the help of proposed approach. Discrete PID controllers are designed by employing the proposed formulated lower order model and it retains the desired performance specifications. The lower order models minimize the computational complexities for the process of output stabilization compared with higher order models. The proposed approach is direct and simple in approach for linear time invariant discrete systems. Thirdly, certain procedures are proposed for designing the state feedback controller and state space observer of linear time invariant continuous and discrete systems. Further, the lower order model formulation approach for single input single output systems is extended to multi input multi output linear time invariant continuous and discrete systems. The analysis of the discrete system is carried out directly without applying any linear or bilinear transformations, which reduces computational complexities. This approach guarantees an absolutely stable lower order model if the considered higher order system is stable in nature. The proposed methodology extracts a second order model which has a better approximation compared to models obtained due to other methods. Algorithms are also presented for all the contributions provided in the thesis with illustrations and results.