Describe systems with first-order equations x'=Ax+Bu.
State-space: ẋ=Ax+Bu, y=Cx+Du models multi-input multi-output, time-varying and nonlinear (after linearisation) systems. Transfer function G(s)=C(sI-A)⁻¹B+D; eigenvalues of A are poles. Realisations are not unique (similarity transforms). Foundation for modern control.
A two-mass system has four states: positions and velocities.
State-space models describe multi-input multi-output systems in a compact form, which suits modern control design and simulation.
Describe systems with first-order equations x'=Ax+Bu.
State-space models describe multi-input multi-output systems in a compact form, which suits modern control design and simulation.
The set of variables that describe the internal condition of the system, so that the future depends only on the state and inputs.
A describes the internal dynamics, B the effect of inputs, C how states appear at the output, and D the direct input to output path.
Typical applications include modelling a drone with position, velocity and attitude states, writing the equations of a two-tank process for a controller and designing a controller for a robot with several joints.
Study "Lead and lag compensators" first (topic 58 of 101 in Signals, Control & Comms). It covers the groundwork this topic builds on.
State variables. Canonical forms. Matrix exponential e^{At}.
A two-mass system has four states: positions and velocities.
The next topic is "Controllability and observability", which builds directly on this one.
It is classed as Intermediate in Signals, Control & Comms (topic 59 of 101). It is an intermediate topic. Work through the beginner topics in Signals, Control & Comms first.
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