CSCC85 Lecture 4: Control Systems “Control”: monitor/sense/measure, respond/act to achieve goals … A control system is a system which sends outputs to affect the physical system given inputs. Control systems are typically used to: deal with unstable systems deal with noise deal with disturbance Examples of control systems are: aircraft autopilot car cruise control flight control system (modern jet fighters are inherently unstable and can’t fly without a sophisticated control system ) Control systems attempt to change the system to the desired state by using reference value = measurement + error Typical setup The controller determines the correct inputs to send to the plant The plant represents the system being controlled. It receives inputs from user(s) as well as control signals, and its output can be measured. The plant is comprised of: o Actuators, which causes action and influence the system o Model of the system o Sensors Modeling - use physics 𝑥 = 𝐹 𝑥, 𝑢 (change in state variables over time) 𝑥 𝑦 𝑥 = 𝑣𝑥 𝑣𝑦 𝑎 (vector of state variables) 𝑥 = 𝐴𝑥 + 𝐵𝑢 (a linear model) 𝑢 = 𝐵 −1 𝑥 − 𝐴𝑥𝑟𝑒𝑓 (vector of inputs to the system) Proportional-Integral-Derivative (PID) controller Good all-purpose controller given input, 𝑒𝑟𝑟 𝑡 = 𝑟𝑒𝑓 − 𝑜𝑢𝑡𝑝𝑢𝑡 𝑡 response (as magnitude of error increase, controller input need to increase): 𝑢 = 𝑘1 ∗ 𝑒𝑟𝑟 𝑡 + 𝑘 2 ∗𝜕𝑒𝑟𝑟 𝑡 𝜕𝑡 + 𝑘3 ∗ 𝑒𝑟𝑟 𝑡 𝜕𝑡 Neural Nets for control Single neuron Neural networks are comprised of various neuron nodes combining multiple inputs using different weights to approximate some unknown function y = g(x). residual error: the difference between the output of neural net and y 𝛿 𝑜𝑢𝑡𝑝𝑢𝑡, 𝑦𝑖 Output of the neural net is compared to expected output The weight of neural net is adjusted slowly to decrease residual error Examples of f: sigmoid(), tanh(), etc. Single Layer: multiple neurons Greater number of neurons with different weights allows a greater range of functions to be approximated with increased accuracy error happens at output: 𝛿𝑒𝑟𝑟 𝛿𝑤 𝑖𝑗 There are also: Multiple Layers, Convolutional networks / deep learning… Example: Google used deep learning to trained their neural network to recognize challenging cat pictures out of 20, 000 distinct items by teaching the network using 10 million cat pictures. Direct NN control The neural network is trained to provide control signals directly to the plant. Reinforcement learning control A control system based on behaviorist psychology. The system attempts to maximize some cumulative reward using optimization. Model predictive control A control system which anticipates future events and can take action accordingly.
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