# Controls Bootcamp - Steve Brunton ## Overview - Controls are of two types: - Passive Control: Control introduced in system due to design. Does not need additional energy to function. e.g. Truck shape introducing drag to keep it from lifting - Active Control: Control introduced in system by use of external energy. Types: - Open Loop: No feedback in system which results in continuous inputs. - Closed Loop: Introduces feedback system using sensors which can be used for minute control which varies based on output of the system. --- - Why Feedback is needed? - **Uncertainity**: System often has uncertainity which renders preplanned input useless. - **Instability**: System might be unstable due to external noise. Feedback can result in better control. - **Disturbance** tends to pass through system dynamics and can be measured to improve control over it. - **Efficient:** Introducing feedback results in overall lower energy consumption due to applied force being proportional to present error, thus reduces overall lower energy. --- ## Important Topics - Linear Systems - Stability and Eigen Values - Linearizing Around a Fixed Point - Controllability - Controllabiltiy, Reachability and Eigen Value Placement - Controllability and the Discrete-Time Impulse Response - Degree of Controllability and Gramians - Controllability and PBH Test - Cayley-Hamilton Theorem - Reachability and Controllabilty with Cayley Hamilton - Inverted Pendulum on a Cart - Pole Placement for the Inverted Pendulum on a Cart - Linear Quadratic Regulator(LQR) Control for the Inverted Pendulum on a Cart - Motivation for Full-State Estimation - Observability - Full-State Estimation - The Kalman Filter - Linear Quadratic Gaussian (LQG) - Robust Control - Equivalent Representations of Linear Systems ## Resources - Reference Playlist: [Control Bootcamp](https://www.youtube.com/playlist?list=PLMrJAkhIeNNR20Mz-VpzgfQs5zrYi085m)