Neblux Knowledge Graph
Control Theory
A controller chooses actions from available information. Control theory asks what behavior those actions can produce and under which assumptions the resulting system meets its requirements.
Overview
For a continuous-time linear time-invariant model ẋ=Ax+Bu, y=Cx, state feedback u=−Kx gives ẋ=(A−BK)x when there is no reference or disturbance input. This assumes that the state is available. If only y is measured, state reconstruction is a separate question of observability. Reachability asks which states the input can produce; neither property is created merely by naming a controller. Nonlinear models and practical limits require their own analysis.
Why it matters
A faster response can demand more control effort. Åström and Murray compare two state-feedback designs for a linearized balancing system: the faster design needs a larger input force. An LQR formulation expresses such a trade-off by assigning weights to squared state deviations and inputs. Its conclusion belongs to the chosen model and cost, not to every physical balancing device.
What it builds on
Where it leads
Related concepts
- Feedback ControlconceptualFeedback control is the central mechanism studied by control theory, using error signals to drive corrective actions toward desired states
- Stability and InstabilityappliedControl theory provides rigorous stability criteria (Routh-Hurwitz, Nyquist, Lyapunov) to guarantee controlled systems remain bounded
- OptimizationappliedOptimal control (LQR, MPC) finds control inputs that minimize cost functions subject to dynamic system constraints
- EngineeringlogicalControl Theory provides conceptual grounding that helps explain Engineering in this knowledge graph.
- Robotics EngineeringlogicalControl Theory provides conceptual grounding that helps explain Robotics Engineering in this knowledge graph.