Choose gains to place closed-loop poles.
With u=-Kx, closed-loop dynamics are A-BK; choose K (Ackermann or place) so poles are at desired locations meeting specs. Requires state measurement or estimation. Reference tracking adds feedforward gain or integral state.
Placing poles at -4±4j gives about 4% overshoot with fast settling.
State feedback sets the closed-loop poles directly, which gives precise control of speed and damping for multi-variable systems.
Choose gains to place closed-loop poles.
State feedback sets the closed-loop poles directly, which gives precise control of speed and damping for multi-variable systems.
Choosing the state feedback gains so the closed-loop matrix has the eigenvalues you specify.
The feedback uses the state vector, so unmeasured states must be estimated with an observer or measured directly.
Typical applications include placing the poles of a two-tank system to get a critically damped response, designing a gain matrix for a robot arm with several states and tuning a drone attitude controller by choosing pole locations.
Study "Controllability and observability" first (topic 60 of 101 in Signals, Control & Comms). It covers the groundwork this topic builds on.
Place poles for ζ and ω_n. Control effort vs speed. Integral augmentation.
Placing poles at -4±4j gives about 4% overshoot with fast settling.
The next topic is "Observers", which builds directly on this one.
It is classed as Intermediate in Signals, Control & Comms (topic 61 of 101). It is an intermediate topic. Work through the beginner topics in Signals, Control & Comms first.
Want to practise? Open the interactive course for quick checks, quizzes, simulations and progress tracking.