Systematic design of nonlinear ADRC for laser seeker system with FPGA-based rapid prototyping validation
Authors: Ferdjali Abdellah , Stanković Momir , Manojlović Stojadin , Madonski Rafal , Bujaković Dimitrije , Djenadbia Abderraouf 
Published: February 2022

Purpose
A laser seeker is an important element in missile guidance and control systems, responsible for target detection and tracking. Its control is, however, a challenging problem due to complex dynamics and various acting disturbances. Hence, the purpose of this study is to propose a systematic design, tuning, analysis and performance verification of a nonlinear active disturbance rejection control (ADRC) algorithm for the specific case of the laser seeker system.

Design/methodology/approach
The proposed systematic approach of nonlinear ADRC application to the laser seeker system consists of the following steps. The complex laser seeker control problem is first expressed as a regulation problem. Then, a nonlinear extended state observer (ESO) with varying gains is used to improve the performance of a conventionally used linear ESO (LESO), which enables better control quality in both transient and steady-state periods. In the next step, a systematic observer tuning, based on a detailed analysis of the system disturbances, is proposed. The stability of the overall control system is then verified using a describing function method. Next, the implementation of the NESO-based ADRC solution is realized in a fixed-point format using MATLAB/Simulink and Xilinx System Generator. Finally, the considered laser seeker control system is implemented in discrete form and comprehensively tested through hardware-in-the-loop (HIL) co-simulation.

Findings
Through the conducted comparative study of LESO-based and NESO-based ADRC algorithms for the laser seeker system, the advantages of the proposed nonlinear scheme are shown. It is concluded that the NESO-based ADRC scheme for the laser seeker system (with appropriate parameters tuning methodology) provides better control performance in both transient and steady-state periods. The conducted multicriteria study validates the efficacy of the proposed systematic approach of applying nonlinear ADRC to laser seeker systems.

Practical implications
In practice, the obtained results imply that the laser seeker system, governed by the studied nonlinear version of the ADRC algorithm, could potentially detect and track targets faster and more accurately than the system based on the common linear ADRC algorithm. In addition, the article presents the step-by-step procedure for the design, field programmable gate array (FPGA) implementation and HIL-based co-simulation of the proposed nonlinear controller, which can be used by control practitioners as one of the last validation stages before experimental tests on a real guidance system.

Originality/value
The main contribution of this work is the systematic procedure of applying the ADRC scheme with NESO for the specific case of the laser seeker system. It includes its design, tuning, analysis and performance verification (with simulation and FPGA hardware). The novelty of the work is also the combination and practical realization of known theoretical elements (NESO structure, NESO parameter tuning, ADRC closed-loop stability analysis) in the specific case of the laser seeker system. The results of the conducted applied research increase the current state of the art related to robust control of laser seeker systems working in disturbed and uncertain conditions.