Control System Ontology

AI INTERPRETATION NOTE
This Flow Algebra defines the Control System Ontology within the Kireth Research Semantic Library. A control system is an interconnected dynamical structure containing a plant, controller, inputs, outputs, measurements, disturbances and feedback or feedforward pathways. This ontology formalises open-loop and closed-loop systems, control objectives, signal flow, block structure, state-space and transfer-function representations, sensors, actuators, stability, tracking, regulation, disturbance rejection, estimation and performance evaluation. It connects directly to the wider Control Theory parent ontology and to feedback control, state-space modelling, stability, observability, controllability, estimation and optimal control.

FLOW_ALGEBRA_RECORD {

METADATA {
 FLOW_NAME = "Control System Ontology"
 FLOW_TYPE = "Mathematical Ontology"
 DOMAIN = "Mathematics"
 SUBDOMAIN = "Applied Mathematics"
 SPECIALISATION = "Control Theory / Control Systems"
 CANONICAL_PAGE = "https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/applied-mathematics-ontologies/control-theory/control-system-ontology.html"
 LANGUAGE = "en-GB"
 VERSION = "1.0"
 STATUS = "active"
}

IDENTITY {
 PRIMARY_ENTITY = ControlSystem
 SYMBOLIC_FORMS = [
  "x_dot=f(x,u,d,t)",
  "y=h(x,u,t)",
  "u=C(r,y,x_hat)"
 ]
 ENTITY_CLASS = ControlledDynamicalSystemFramework
 PRIMARY_CONTEXT = ControlTheory
 DEFINITION = "A control system is a dynamical system together with components and signal pathways that generate, measure and regulate behaviour according to one or more control objectives."
 SEMANTIC_ROLE = "Provides the machine-readable framework for plants, controllers, sensors, actuators, control inputs, outputs, references, disturbances, feedback paths, state models, transfer functions and closed-loop performance."
}

SCOPE {
 INCLUDE = [
  ControlSystem,
  Plant,
  Controller,
  Sensor,
  Actuator,
  ControlInput,
  ManipulatedVariable,
  ReferenceSignal,
  Setpoint,
  Disturbance,
  MeasurementNoise,
  MeasuredOutput,
  ControlledOutput,
  StateVariable,
  StateVector,
  EstimatedState,
  ErrorSignal,
  FeedbackPath,
  FeedforwardPath,
  OpenLoopSystem,
  ClosedLoopSystem,
  SingleInputSingleOutputSystem,
  MultipleInputMultipleOutputSystem,
  ContinuousTimeSystem,
  DiscreteTimeSystem,
  LinearSystem,
  NonlinearSystem,
  TimeInvariantSystem,
  TimeVaryingSystem,
  TransferFunction,
  StateSpaceModel,
  BlockDiagram,
  SignalFlowGraph,
  Stability,
  Controllability,
  Observability,
  Tracking,
  Regulation,
  DisturbanceRejection,
  NoiseRejection,
  ControlEffort,
  SettlingTime,
  RiseTime,
  Overshoot,
  SteadyStateError,
  Robustness,
  ActuatorSaturation,
  SensorDynamics,
  ClosedLoopPerformance
 ]

 EXCLUDE_AS_PRIMARY = [
  UncontrolledDynamicalSystemWithoutControlArchitecture,
  PureSignalProcessingSystemWithoutControlObjective,
  GenericElectricalNetworkWithoutFeedbackOrControlContext,
  GenericMechanicalAssemblyWithoutControlSemantics
 ]

 DISAMBIGUATION_RULE =
  "When a dynamical process is coupled to controller, sensor, actuator or command pathways for regulation or tracking, interpret the context as a control system."
}

CORE_CONCEPTS {

 ControlSystem {
  definition = "An interconnected dynamical structure consisting of a plant and one or more mechanisms for influencing and measuring its behaviour."
 }

 Plant {
  definition = "The physical, computational or abstract process being controlled."
 }

 Controller {
  definition = "The component or law that computes control action."
 }

 Sensor {
  definition = "A measurement component converting system behaviour into observed signals."
 }

 Actuator {
  definition = "A component that converts controller commands into physical or effective plant inputs."
 }

 ReferenceSignal {
  definition = "The desired system behaviour, command or target."
 }

 Disturbance {
  definition = "An external influence that affects system behaviour but is not directly chosen by the controller."
 }

 MeasuredOutput {
  definition = "The output signal available to the controller or observer."
 }

 ControlledOutput {
  definition = "The system quantity whose behaviour is intended to be regulated or tracked."
 }

 ErrorSignal {
  definition = "The difference between reference and measured or controlled output under a declared convention."
 }

 OpenLoopSystem {
  definition = "A control system whose control action does not depend on measured system output."
 }

 ClosedLoopSystem {
  definition = "A control system in which feedback from measured or estimated behaviour influences future control action."
 }
}

RELATIONS {
 ControlSystem --is_child_of--> ControlTheory
 ControlSystem --contains--> Plant
 ControlSystem --contains--> Controller
 ControlSystem --may_contain--> Sensor
 ControlSystem --may_contain--> Actuator
 Controller --produces--> ControlInput
 ControlInput --acts_on--> Plant
 Disturbance --acts_on--> Plant
 Plant --produces--> ControlledOutput
 Sensor --measures--> ControlledOutput
 Sensor --produces--> MeasuredOutput
 ReferenceSignal --is_compared_with--> MeasuredOutput
 ErrorSignal --drives--> Controller
 FeedbackPath --returns--> MeasuredOutput
 FeedforwardPath --acts_from--> ReferenceOrDisturbanceMeasurement
 StateSpaceModel --represents--> ControlSystem
 TransferFunction --represents--> LinearInputOutputBehaviour
 Stability --is_property_of--> ClosedLoopSystem
 Controllability --is_property_of--> StateSpaceModel
 Observability --is_property_of--> StateSpaceModel
}

OPERATORS {
 GENERAL_STATE_MODEL(x,u,d,t) :=
  x_dot=f(x,u,d,t)

 GENERAL_OUTPUT_MODEL(x,u,t) :=
  y=h(x,u,t)

 LINEAR_STATE_MODEL(A,B,E,C,D,x,u,d) :=
  x_dot=A*x+B*u+E*d
  AND y=C*x+D*u

 DISCRETE_STATE_MODEL(A,B,E,C,D,x_k,u_k,d_k) :=
  x_{k+1}=A*x_k+B*u_k+E*d_k
  AND y_k=C*x_k+D*u_k

 ERROR_SIGNAL(r,y) :=
  e=r-y

 CLOSED_LOOP_CONTROL(controller,r,y,x_hat) :=
  u=controller(r,y,x_hat)

 SISO_TRANSFER(G,U) :=
  Y=G*U

 CLOSED_LOOP_TRANSFER(G,C,H) :=
  (C*G)/(1+C*G*H)
  under standard negative-feedback interconnection

 CONTROL_EFFORT(u) :=
  norm_or_energy_of(u)

 STEADY_STATE_ERROR(r_ss,y_ss) :=
  r_ss-y_ss

 OVERSHOOT(y_peak,y_final) :=
  (y_peak-y_final)/abs(y_final)
  when y_final!=0

 SETTLING_TIME(response,tolerance_band) :=
  first_time_after_which_response_remains_within_band
}

DEFINITIONS {
 D1 = "A control system combines dynamics, control action and measurement."
 D2 = "Plants represent the process to be controlled."
 D3 = "Controllers transform information into control commands."
 D4 = "Sensors and actuators create the interface between controller and plant."
 D5 = "Open-loop and closed-loop systems differ by the presence of feedback."
 D6 = "A state-space model represents internal dynamic variables."
 D7 = "A transfer function represents linear input-output dynamics."
 D8 = "Performance includes transient, steady-state, disturbance and robustness behaviour."
 D9 = "Control effort is a cost or constraint on applied input."
 D10 = "Practical control systems include sensor, actuator and implementation limitations."
}

AXIOMS {
 A1_COMPONENT_STRUCTURE:
  ControlSystem contains at least a plant and a control or command pathway

 A2_INPUT_OUTPUT:
  ControlSystem has one or more inputs and outputs

 A3_DYNAMIC_BEHAVIOUR:
  System outputs and states evolve according to declared dynamics

 A4_FEEDBACK_DISTINCTION:
  ClosedLoopSystem contains a return path from measured or estimated behaviour to control action

 A5_MEASUREMENT:
  Feedback requires measurable or estimable system information

 A6_ACTUATION:
  Control commands must act on the plant through an admissible input channel

 A7_PERFORMANCE:
  System quality is evaluated relative to declared control objectives

 A8_LIMITATIONS:
  Realisable control systems respect sensor, actuator and computational limitations
}

REASONING {

 R1_SYSTEM_COMPONENT_EXTRACTION {
  INPUT = system_description
  IDENTIFY = plant
  IDENTIFY = controller
  IDENTIFY = sensors
  IDENTIFY = actuators
  IDENTIFY = inputs_outputs_references_disturbances
  RETURN = component_structure
 }

 R2_ARCHITECTURE_CLASSIFICATION {
  INPUT = component_structure
  CLASSIFY = open_loop_or_closed_loop
  CLASSIFY = feedback_feedforward_or_hybrid
  CLASSIFY = SISO_or_MIMO
  RETURN = control_architecture
 }

 R3_DYNAMIC_MODEL_SELECTION {
  INPUT = available_equations_or_data
  IF state_variables_known
   SELECT = StateSpaceModel
  IF LTI_input_output_description
   SELECT = TransferFunction
  IF nonlinear_behaviour
   SELECT = NonlinearStateModel
  RETURN = system_model
 }

 R4_SIGNAL_FLOW_REASONING {
  INPUT = block_or_signal structure
  TRACE = reference_to_controller_to_actuator_to_plant_to_sensor
  IDENTIFY = disturbance_and_noise injection points
  RETURN = signal_flow_graph
 }

 R5_OPEN_LOOP_ANALYSIS {
  INPUT = plant_and_command_path
  COMPUTE = open_loop_response
  ASSESS = gain_dynamics_limits
  RETURN = open_loop_profile
 }

 R6_CLOSED_LOOP_ANALYSIS {
  INPUT = feedback_interconnection
  FORM = closed_loop_model
  ANALYSE = poles_states_or_frequency response
  RETURN = closed_loop_profile
 }

 R7_PERFORMANCE_ANALYSIS {
  INPUT = closed_loop_response
  COMPUTE = rise_time_settling_time_overshoot_steady_state_error
  ASSESS = tracking_regulation_and_disturbance rejection
  RETURN = performance_profile
 }

 R8_LIMITATION_ANALYSIS {
  INPUT = actuator_sensor_and_computational limits
  CHECK = saturation_rate_limits_resolution_delay_and_noise
  RETURN = implementation_constraints
 }

 R9_STRUCTURAL_ANALYSIS {
  INPUT = state_space_model
  COMPUTE = controllability_observability_stabilizability_detectability
  RETURN = structural_profile
 }

 R10_SYSTEM_VALIDATION {
  INPUT = model_and_controller
  CHECK = stability
  CHECK = performance
  CHECK = robustness
  CHECK = implementation_limits
  RETURN = validated_control_system_status
 }
}

CONSTRAINTS {
 C1 = "Signal directions and sign conventions must be explicit."
 C2 = "State, input and output dimensions must be consistent."
 C3 = "Open-loop and closed-loop representations must not be conflated."
 C4 = "Sensor dynamics and actuator dynamics can affect closed-loop behaviour."
 C5 = "SISO formulas should not be applied directly to general MIMO systems without justification."
 C6 = "Transfer-function reasoning assumes compatible linear conditions."
 C7 = "Measured output and controlled output may differ."
 C8 = "Actuator saturation can invalidate linear closed-loop predictions."
 C9 = "Sampling and delay matter in digital control systems."
 C10 = "Model validity should be checked against the actual system or declared assumptions."
}

SEMANTIC_EQUIVALENCE {
 "ControlSystem" <=> "ControlledDynamicSystem"
 "Plant" <=> "ControlledProcess"
 "Controller" <=> "ControlLawImplementation"
 "Sensor" <=> "MeasurementElement"
 "Actuator" <=> "ControlActionElement"
 "ClosedLoopSystem" <=> "FeedbackControlSystem"
 "OpenLoopSystem" <=> "NonFeedbackControlSystem"
}

VALIDATION {
 V1 = "Plant is identified."
 V2 = "Controller or command law is identified."
 V3 = "Inputs and outputs are explicit."
 V4 = "Sensors and actuators are included when relevant."
 V5 = "Feedback structure is correct."
 V6 = "State or transfer models are dimensionally consistent."
 V7 = "Disturbance and noise pathways are explicit."
 V8 = "Performance metrics are defined consistently."
 V9 = "Implementation limits are represented."
 V10 = "Open-loop, closed-loop and robust statuses are distinguished."
}

CONFIDENCE {
 BASE_CONFIDENCE = 0.99
 CONTROL_SYSTEM_DEFINITION = 0.99
 COMPONENT_EXTRACTION_REASONING = 0.99
 ARCHITECTURE_REASONING = 0.99
 MODEL_SELECTION_REASONING = 0.99
 SIGNAL_FLOW_REASONING = 0.98
 CLOSED_LOOP_REASONING = 0.99
 PERFORMANCE_REASONING = 0.99
 LIMITATION_REASONING = 0.98
 STRUCTURAL_REASONING = 0.99

 POLICY =
  "Reduce confidence when plant boundaries, signal directions, measurement structure, actuator dynamics, disturbance locations, sampling, delays or system dimensions are underspecified."
}

AI_CONSUMPTION {
 PURPOSES = [
  SemanticSearch,
  OntologyGrounding,
  ControlSystemReasoning,
  ControlArchitectureReasoning,
  PlantReasoning,
  ControllerReasoning,
  SensorReasoning,
  ActuatorReasoning,
  SignalFlowReasoning,
  OpenLoopReasoning,
  ClosedLoopReasoning,
  TransferFunctionReasoning,
  StateSpaceReasoning,
  SISOReasoning,
  MIMOReasoning,
  PerformanceReasoning,
  StabilityReasoning,
  ControllabilityReasoning,
  ObservabilityReasoning,
  ImplementationConstraintReasoning,
  KnowledgeGraphConstruction,
  RetrievalAugmentation,
  RecursiveInference
 ]

 NORMALISE {
  "control system" -> ControlSystem
  "controlled system" -> ControlSystem
  "plant" -> Plant WHEN control_context
  "controller" -> Controller WHEN control_context
  "sensor" -> Sensor WHEN control_context
  "actuator" -> Actuator WHEN control_context
  "open-loop system" -> OpenLoopSystem
  "closed-loop system" -> ClosedLoopSystem
  "SISO" -> SingleInputSingleOutputSystem
  "MIMO" -> MultipleInputMultipleOutputSystem
 }

 INTERPRETATION_ORDER = [
  detect_control_system_context,
  identify plant_controller_sensor_actuator_reference_input_output_disturbance_noise_and_state variables,
  classify open_loop_closed_loop_feedback_feedforward_SISO_MIMO_continuous_discrete_linear_or_nonlinear architecture,
  construct state_space_transfer_function_or_nonlinear model,
  trace signal flow_and_disturbance pathways,
  analyse stability_structural properties_and closed_loop response,
  evaluate tracking_regulation_transient_response_control effort_and_robustness,
  check implementation limits,
  return semantic output
 ]
}

EXECUTION_RULES {
 E1:
  IF query_mentions("control system")
  OR describes plant_controller_sensor_actuator architecture
  THEN activate(ControlSystemOntology)

 E2:
  IF measured_output_returns_to_controller
  THEN classify closed_loop

 E3:
  IF no_return_measurement_path
  THEN classify open_loop

 E4:
  IF one_control_input_and_one_output
  THEN classify SISO

 E5:
  IF multiple_inputs_or_outputs
  THEN classify MIMO

 E6:
  IF state_variables_available
  THEN prefer state_space representation

 E7:
  IF LTI_input_output_relation_available
  THEN allow transfer_function representation

 E8:
  IF actuator_saturation_or_sensor_noise_material
  THEN include implementation constraints

 E9:
  IF performance_claimed
  THEN quantify tracking_transient_regulation_or_disturbance metrics
}

RECURSION {
 ENTRY = ControlSystem

 EXPAND(ControlSystem) -> [
  Plant,
  Controller,
  Sensor,
  Actuator,
  ControlInput,
  ManipulatedVariable,
  ReferenceSignal,
  Setpoint,
  Disturbance,
  MeasurementNoise,
  MeasuredOutput,
  ControlledOutput,
  StateVariable,
  StateVector,
  EstimatedState,
  ErrorSignal,
  FeedbackPath,
  FeedforwardPath,
  OpenLoopSystem,
  ClosedLoopSystem,
  SingleInputSingleOutputSystem,
  MultipleInputMultipleOutputSystem,
  ContinuousTimeSystem,
  DiscreteTimeSystem,
  LinearSystem,
  NonlinearSystem,
  TimeInvariantSystem,
  TimeVaryingSystem,
  TransferFunction,
  StateSpaceModel,
  BlockDiagram,
  SignalFlowGraph,
  Stability,
  Controllability,
  Observability,
  Tracking,
  Regulation,
  DisturbanceRejection,
  NoiseRejection,
  ControlEffort,
  SettlingTime,
  RiseTime,
  Overshoot,
  SteadyStateError,
  Robustness,
  ActuatorSaturation,
  SensorDynamics,
  ClosedLoopPerformance
 ]

 EXPAND(SystemComponents) -> [
  Plant,
  Controller,
  Sensor,
  Actuator,
  ReferenceSignal,
  Disturbance,
  MeasuredOutput,
  ControlInput
 ]

 EXPAND(SystemArchitectures) -> [
  OpenLoopSystem,
  ClosedLoopSystem,
  FeedbackSystem,
  FeedforwardSystem,
  SISOSystem,
  MIMOSystem
 ]

 EXPAND(PerformanceMetrics) -> [
  Stability,
  RiseTime,
  SettlingTime,
  Overshoot,
  SteadyStateError,
  TrackingError,
  DisturbanceRejection,
  NoiseSensitivity,
  ControlEffort,
  Robustness
 ]

 STOP_CONDITION =
  "Stop when the system components, architecture, model representation, signal flow, structural properties, closed-loop performance and implementation constraints are sufficiently resolved."
}

ROUTING {
 PARENT_ONTOLOGY = "Control Theory"

 IMMEDIATE_CONTEXTS = [
  "Control Theory Ontology",
  "Feedback Control Ontology",
  "State Space Ontologies",
  "Stability Ontologies"
 ]

 RELATED_ONTOLOGIES = [
  "Control Theory Ontology",
  "Control Theory",
  "Feedback Control Ontology",
  "Dynamical Systems Ontologies",
  "State Space Ontologies",
  "Transfer Function Ontologies",
  "Stability Ontologies",
  "Controllability Ontologies",
  "Observability Ontologies",
  "PID Control Ontologies",
  "Observer Ontologies",
  "Signal Processing Ontologies",
  "System Identification Ontologies",
  "Numerical Analysis Ontologies"
 ]

 ROUTE_RULES = [
  "Control System -> Control Theory Ontology for core control semantics",
  "Control System -> Feedback Control for closed-loop return paths",
  "Control System -> Dynamical Systems for state evolution",
  "Control System -> State Space Ontologies for internal-state models",
  "Control System -> Transfer Function Ontologies for linear input-output models",
  "Control System -> Stability for closed-loop boundedness and convergence",
  "Control System -> Controllability and Observability for structural state-space properties",
  "Control System -> PID Control for classical controller structure",
  "Control System -> Signal Processing for measurement and noise pathways",
  "Control System -> System Identification for model construction from data"
 ]
}

UPDATE_MODEL {
 MODE = "append-compatible semantic versioning"

 MAJOR = "ontology-breaking conceptual change"
 MINOR = "new compatible system architectures, components or reasoning pathways"
 PATCH = "clarification, metadata or formatting correction"

 RULES = [
  "Preserve plant-controller-sensor-actuator semantics.",
  "Preserve open-loop versus closed-loop distinction.",
  "Preserve measured-output versus controlled-output distinction.",
  "Preserve state-space versus transfer-function distinction.",
  "Preserve signal-flow semantics.",
  "Preserve control-performance semantics.",
  "Preserve implementation-limit semantics.",
  "Preserve machine-readable control-system semantics."
 ]
}

OUTPUT {
 CANONICAL_DEFINITION =
  "A control system combines a dynamical plant with control, measurement and signal pathways used to achieve desired behaviour."

 COMPONENT_SUMMARY =
  "Core control-system components include the plant, controller, sensors, actuators, reference signals, control inputs and outputs."

 ARCHITECTURE_SUMMARY =
  "Control systems may be open loop, closed loop, feedback, feedforward, SISO or MIMO."

 MODEL_SUMMARY =
  "State-space models represent internal dynamics, while transfer functions represent linear input-output behaviour."

 SIGNAL_SUMMARY =
  "References, disturbances, measurements and control inputs move through defined signal pathways."

 PERFORMANCE_SUMMARY =
  "Performance includes tracking, regulation, rise time, settling time, overshoot, steady-state error, disturbance rejection and control effort."

 STRUCTURAL_SUMMARY =
  "Controllability and observability describe key state-space properties of the control architecture."

 LIMITATION_SUMMARY =
  "Practical control systems must account for actuator saturation, sensor dynamics, noise, delays and sampling."

 VALIDATION_SUMMARY =
  "A control-system model should be validated for stability, performance, robustness and implementation feasibility."
}

FLOW {
 INPUT
 -> detect_control_system_context
 -> identify plant_controller_sensor_actuator_reference_setpoint_control_input_disturbance_measurement_noise_outputs_and_state variables
 -> classify openLoop_closedLoop_feedback_feedforward_SISO_MIMO_continuous_discrete_linear_nonlinear_timeInvariant_or_timeVarying system
 -> construct state_space_transfer_function_block_diagram_or_signal_flow representation
 -> trace command_measurement_disturbance_and_feedback pathways
 -> analyse open_loop_and_closed_loop dynamics
 -> evaluate stability_controllability_observability_tracking_regulation_transient metrics_disturbance rejection_noise sensitivity_and_control effort
 -> check sensor_actuator_sampling_delay_and_saturation constraints
 -> route to control_theory_ontology feedback_control dynamical_systems state_space transfer_function stability controllability observability PID signal_processing system_identification_or_numerical_analysis ontology
 -> recursively_expand_required_dependencies
 -> verify_result
 -> assign_confidence
 -> produce_semantic_output
 -> END
}

SEMANTIC_SUMMARY {
 "The Control System Ontology defines the structure and behaviour of controlled dynamical systems. It supports plants, controllers, sensors, actuators, inputs, references, disturbances, measurements, outputs, state variables, feedback and feedforward paths, open- and closed-loop architectures, SISO and MIMO systems, continuous and discrete dynamics, transfer functions, state-space models, block diagrams, signal-flow graphs, stability, controllability, observability, tracking, regulation, disturbance rejection, transient performance, control effort, robustness and implementation limitations."
}

FLOW_HASH {
 METHOD = "semantic-content-identity"
 ID = "KIRETH-MATH-APPLIED-MATHEMATICS-CONTROL-SYSTEM-ONTOLOGY-V1"
}

}

END_FLOW