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Lecture 5 - Feedforward • • • • • • •
Programmed control Path planning and nominal trajectory feedforward Feedforward of the disturbance Reference feedforward, 2-DOF architecture Non-causal inversion Input shaping, flexible system control Iterative update of feedforward
EE392m - Winter 2003
Control Engineering
5-1
Why Feedforward? • Feedback works even if we know little about the plant dynamics and disturbances • Was the case in many of the first control systems • Much attention to feedback - for historical reasons • Open-loop control/feedforward is increasingly used • Model-based design means we know something • The performance can be greatly improved by adding openloop control based on our system knowledge (models)
EE392m - Winter 2003
Control Engineering
5-2
Feedforward Feedforward controller
Plant
Plant
Feedback controller
– this Lecture 5
• Main premise of the feedforward control: – Lecture 4 PID a model of the plant is known – Lecture 6 Analysis • Model-based design of feedback control - – Lecture 7 Design the same premise • The difference: feedback control is less sensitive to modeling error Plant • Common use of the feedforward: cascade with feedback Feedforward Feedback controller EE392m - Winter 2003
Control Engineering
controller 5-3
Open-loop (programmed) control • Control u(t) found by solving an optimization problem. Constraints on control and state variables. • Used in space, missiles, aircraft FMS – Mission planning – Complemented by feedback corrections
• Sophisticated mathematical methods were developed in the 60s to overcome computing limitations. • Lecture 12 will get into more detail of control program optimization.
x& = f ( x, u, t ) J ( x, u, t ) → min x ∈ X, u ∈ U Optimal control: u = u* (t )
EE392m - Winter 2003
Control Engineering
5-4
Optimal control • Performance index and constraints • Programmed control – compute optimal control as a time function for particular initial (and final) conditions
• Optimal control synthesis – find optimal control for any initial conditions – at any point in time apply control that is optimal now, based on the current state. This is feedback control! – example: LQG for linear systems, gaussian noise, quadratic performance index. Analytically solvable problem. – simplified model, toy problems, conceptual building block
• MPC - will discuss in Lecture 12 EE392m - Winter 2003
Control Engineering
5-5
Path/trajectory planning • The disturbance caused by the change of the command r influences the feedback loop. • The error sensitivity to the reference R(s) is bandpass: |R(iω)|
