Practical implementable controller design with guaranteed asymptotic stability for nonlinear systems

• Published in: Computers & chemical engineering 2022-07, Vol.163, p.107827, Article 107827
• Main Authors: Rajhans, Chinmay, Gupta, Sowmya
• Format: Article
• Language: English
• Subjects: Asymptotic stability; Computation time analysis; Linear quadratic regulator; Model predictive control; Practical controller design
• ISSN: 0098-1354; 1873-4375
• DOI: 10.1016/j.compchemeng.2022.107827

•One novel linear quadratic Gaussian regulator based approach for the terminal set characterization for the discrete time model predictive control formulation is proposed.•Efficacy of the controller is demonstrated using benchmark four tank system.•Computation time per iteration is much lesser than the chosen sampling time for the proposed approach as against infeasible computation times for the approaches from the literature.•Design is suitable for practical implementation in real time for a chosen sampling time on an ordinary computer, eliminating need of supercomputing facility.•Novel terminal set characterization approach and controller design method is applicable to a system with any state and input dimension. Establishing the stability of model predictive control formulation is challenging. Using a combination of the terminal cost term and the terminal inequality constraint i.e. terminal set results in nominal asymptotic stability. Larger terminal set results in shorter minimum prediction horizon length required for feasibility from identical initial condition. Current work presents novel linear quadratic Gaussian regulator based approach for the terminal set characterization for the discrete time model predictive control scheme. Proposed approach provides large degrees of freedom in the form of additive matrices as tuning parameters for enlarging the terminal sets as against a single scalar for the literature approaches. Efficacy of the novel approach is demonstrated using a benchmark four tank system. It was observed that the average computation time reduces to significantly when compared to the approaches from the literature for identical initial conditions. This makes the controller design suitable for practical implementation.