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：控制理论研究的是动态系统的控制问题。当今的机器人日益复杂，正从工厂车间迈向真实环境。这些机器人与外界环境因素（如扰动）进行交互，这就要求机器人具备鲁棒的控制系统。在真实环境中测试机器人控制算法可能带来严重的安问题，且经济成本高昂。因此，在将控制算法部署到真实环境之前，人们高度重视利用仿真进行测试。设计控制算法是一个迭代过程：首先对目标系统进行建模仿真，接着设计控制器，然后在仿真中测试控制器，最后调整控制器参数以改进设计。本报告探讨如何为目标硬件系统开发近似系统模型，并利用该模型设计LQR控制器。随后在扰动条件下，分别在硬件和仿真中测试该控制器，并记录系统响应。最后，通过对比硬件与仿真中的系统响应，验证利用仿真中的近似系统模型来设计和测试控制算法的可行性。