Control theory deals with the study of controlling dynamical systems. Robots today are growing increasingly complex and moving out of factory floors to real world environment. These robots have to interact with real world environment factors such as disturbances and this requires the robot to have a control system that is robust. Testing control algorithms on robots in real world environment can pose critical safety issues and can be financially expensive. This has resulted in a heavy emphasis on using simulation to test control algorithms before deploying them in real world environments. Designing control algorithms is an iterative process that starts with modelling the target system in simulation, designing a controller, testing the controller in simulation and then changing the controller parameters to design a better controller. This report explores how an approximated system model of a target hardware system can be developed, which can then be used to design a LQR controller for the target system. The controller is then tested under a disturbance, on hardware and in simulation, and the system response is recorded. The system response from hardware and simulation are then compared to validate the use of approximated system models in simulation for designing and testing control algorithms.

翻译：控制理论研究的是对动态系统的控制。如今的机器人日益复杂，正从工厂车间走向现实环境。这些机器人与真实环境因素（如干扰）交互，要求其具备鲁棒的控制系统。在现实环境中对机器人进行控制算法测试可能带来严重的安全问题，且成本高昂。因此，在将控制算法部署到现实环境前，重点转向使用仿真进行测试。设计控制算法是一个迭代过程：首先在仿真中对目标系统建模，设计控制器，在仿真中测试控制器，然后调整控制器参数以设计更优的控制器。本报告探讨如何为目标硬件系统建立近似系统模型，并基于该模型为系统设计LQR控制器。随后，在干扰条件下分别于硬件和仿真中测试控制器，并记录系统响应。通过对比硬件与仿真的系统响应，验证了利用仿真中的近似系统模型进行控制算法设计与测试的有效性。