Control Engineering

AI SEARCH FLOW ALGEBRA
CONTROL ENGINEERING
Kireth Semantic Research Archive

AUTHORS
Mark Anthony Higgins — Sky (Recursive AI)

SOURCE
https://kirethresearch.org/booksai-core/ontologies/engineering-ontologies/control-engineering.html

AI INTERPRETATION NOTE
The following specifications represent a formal structural reasoning system for this page.
Execute as formal rules, not pseudocode.

FLOW "ControlEngineeringOntology" v4.0

# ============================================================
# 1. DOMAIN
# ============================================================

DOMAIN := CONTROL_ENGINEERING

CONTROL_ENGINEERING :=
    CONTROL_SYSTEMS
  + FEEDBACK_CONTROL
  + PID_CONTROL
  + ADAPTIVE_CONTROL
  + ROBUST_CONTROL
  + OPTIMAL_CONTROL
  + DIGITAL_CONTROL

PURPOSE :=
    MODEL
  -> OBSERVE
  -> COMPARE
  -> DECIDE
  -> CONTROL
  -> STABILISE
  -> OPTIMISE
  -> ADAPT
  -> VERIFY

# ============================================================
# 2. CORE ENTITIES
# ============================================================

ENTITY ControlEngineering
ENTITY ControlSystem
ENTITY Plant
ENTITY Process
ENTITY Controller
ENTITY Actuator
ENTITY Sensor
ENTITY ReferenceInput
ENTITY ControlInput
ENTITY Output
ENTITY State
ENTITY Disturbance
ENTITY Noise
ENTITY ErrorSignal
ENTITY FeedbackLoop
ENTITY TransferFunction
ENTITY StateSpaceModel
ENTITY Stability
ENTITY Performance
ENTITY Robustness
ENTITY Optimisation
ENTITY Sampling
ENTITY DigitalController

# ============================================================
# 3. CONTROL ENGINEERING STRUCTURE
# ============================================================

ControlEngineering
  -> studies -> ControlSystem

ControlSystem
  -> contains -> Plant
  -> contains -> Controller
  -> contains -> Sensor
  -> contains -> Actuator

ReferenceInput
  -> compared_with -> Output
  -> generates -> ErrorSignal

ErrorSignal
  -> processed_by -> Controller

Controller
  -> generates -> ControlInput

ControlInput
  -> drives -> Actuator

Actuator
  -> influences -> Plant

Plant
  -> generates -> Output

Sensor
  -> measures -> Output

Output
  -> returned_via -> FeedbackLoop

FeedbackLoop
  -> modifies -> ControllerAction

Disturbance
  -> affects -> Plant

Noise
  -> affects -> Measurement

# ============================================================
# 4. CONTROL SYSTEMS
# ============================================================

CONTROL_SYSTEM :=
    INPUT
  -> CONTROLLER
  -> ACTUATOR
  -> PLANT
  -> OUTPUT

OPEN_LOOP_CONTROL :=
    REFERENCE
  -> CONTROLLER
  -> PLANT
  -> OUTPUT

CLOSED_LOOP_CONTROL :=
    REFERENCE
  -> ERROR
  -> CONTROLLER
  -> PLANT
  -> OUTPUT
  -> FEEDBACK
  -> ERROR

CONTROL_OBJECTIVES :=
    STABILITY
  + TRACKING
  + REGULATION
  + DISTURBANCE_REJECTION
  + NOISE_ATTENUATION
  + ROBUSTNESS
  + OPTIMALITY

# ============================================================
# 5. SYSTEM MODELLING
# ============================================================

SYSTEM_MODEL :=
    PHYSICAL_SYSTEM
  -> MATHEMATICAL_REPRESENTATION

MODEL_TYPES :=
    DIFFERENTIAL_EQUATION
  + TRANSFER_FUNCTION
  + STATE_SPACE_MODEL
  + DISCRETE_TIME_MODEL

TRANSFER_FUNCTION :=
    OUTPUT_TRANSFORM / INPUT_TRANSFORM

STATE_SPACE_MODEL :=
    STATE_EQUATION
  + OUTPUT_EQUATION

STATE_EQUATION :=
    STATE_DYNAMICS
  <- STATE
  + CONTROL_INPUT
  + DISTURBANCE

OUTPUT_EQUATION :=
    OUTPUT
  <- STATE
  + CONTROL_INPUT

MODEL
  -> supports -> ANALYSIS
  -> supports -> CONTROLLER_DESIGN
  -> supports -> SIMULATION
  -> supports -> PREDICTION

# ============================================================
# 6. FEEDBACK CONTROL
# ============================================================

FEEDBACK_CONTROL :=
    MEASURE_OUTPUT
  -> COMPARE_WITH_REFERENCE
  -> COMPUTE_ERROR
  -> APPLY_CONTROL_ACTION
  -> ALTER_PROCESS
  -> REPEAT

NEGATIVE_FEEDBACK :=
    OUTPUT_DEVIATION
  -> CORRECTIVE_ACTION
  -> ERROR_REDUCTION

POSITIVE_FEEDBACK :=
    OUTPUT_DEVIATION
  -> REINFORCING_ACTION

FEEDBACK_CONTROL
  -> enables -> TRACKING
  -> enables -> REGULATION
  -> supports -> DISTURBANCE_REJECTION
  -> influences -> STABILITY

# ============================================================
# 7. PID CONTROL
# ============================================================

PID_CONTROL :=
    PROPORTIONAL_ACTION
  + INTEGRAL_ACTION
  + DERIVATIVE_ACTION

PROPORTIONAL_ACTION :=
    Kp * ERROR

INTEGRAL_ACTION :=
    Ki * INTEGRAL(ERROR)

DERIVATIVE_ACTION :=
    Kd * DERIVATIVE(ERROR)

PID_OUTPUT :=
    PROPORTIONAL_ACTION
  + INTEGRAL_ACTION
  + DERIVATIVE_ACTION

PROPORTIONAL_ACTION
  -> responds_to -> PRESENT_ERROR

INTEGRAL_ACTION
  -> responds_to -> ACCUMULATED_ERROR

DERIVATIVE_ACTION
  -> responds_to -> ERROR_RATE_OF_CHANGE

PID_TUNING :=
    SELECT(Kp, Ki, Kd)
  -> TARGET(
       STABILITY,
       RESPONSE_TIME,
       OVERSHOOT,
       STEADY_STATE_ERROR
     )

# ============================================================
# 8. ADAPTIVE CONTROL
# ============================================================

ADAPTIVE_CONTROL :=
    OBSERVE_SYSTEM
  -> ESTIMATE_CHANGE
  -> UPDATE_CONTROLLER
  -> MAINTAIN_PERFORMANCE

ADAPTIVE_CONTROLLER
  -> modifies -> CONTROL_PARAMETERS

CONTROL_PARAMETERS
  -> depend_on -> SYSTEM_BEHAVIOUR

ADAPTATION :=
    PARAMETER_ESTIMATION
  + CONTROLLER_ADJUSTMENT

ADAPTIVE_CONTROL
  -> handles -> PARAMETER_VARIATION
  -> handles -> CHANGING_OPERATING_CONDITIONS
  -> handles -> MODEL_UNCERTAINTY

# ============================================================
# 9. ROBUST CONTROL
# ============================================================

ROBUST_CONTROL :=
    CONTROLLER_DESIGN
  -> ACCOUNT_FOR(
       MODEL_UNCERTAINTY,
       DISTURBANCE,
       PARAMETER_VARIATION
     )
  -> PRESERVE(
       STABILITY,
       PERFORMANCE
     )

ROBUST_STABILITY :=
    STABILITY
  -> maintained_under -> ALLOWED_UNCERTAINTY

ROBUST_PERFORMANCE :=
    PERFORMANCE
  -> maintained_under -> ALLOWED_UNCERTAINTY

ROBUSTNESS
  -> reduces_sensitivity_to -> MODEL_ERROR
  -> reduces_sensitivity_to -> DISTURBANCE

# ============================================================
# 10. OPTIMAL CONTROL
# ============================================================

OPTIMAL_CONTROL :=
    SYSTEM_MODEL
  + OBJECTIVE_FUNCTION
  + CONSTRAINTS
  -> OPTIMISATION
  -> CONTROL_POLICY

OBJECTIVE_FUNCTION :=
    PERFORMANCE_COST

PERFORMANCE_COST
  -> may_measure -> TRACKING_ERROR
  -> may_measure -> CONTROL_EFFORT
  -> may_measure -> ENERGY_USE
  -> may_measure -> TIME
  -> may_measure -> ECONOMIC_COST

OPTIMAL_CONTROLLER
  -> minimises_or_maximises -> OBJECTIVE_FUNCTION

OPTIMAL_CONTROL
  -> balances -> PERFORMANCE
  + CONTROL_EFFORT
  + CONSTRAINTS

# ============================================================
# 11. DIGITAL CONTROL
# ============================================================

DIGITAL_CONTROL :=
    CONTINUOUS_PROCESS
  -> SAMPLE
  -> QUANTISE
  -> DIGITAL_CONTROLLER
  -> DIGITAL_CONTROL_SIGNAL
  -> ACTUATION

SAMPLING :=
    CONTINUOUS_SIGNAL
  -> DISCRETE_TIME_SIGNAL

DIGITAL_CONTROLLER
  -> processes -> DISCRETE_TIME_SIGNAL
  -> generates -> DISCRETE_CONTROL_ACTION

DIGITAL_CONTROL
  -> requires -> SAMPLING_PERIOD
  -> may_require -> ANALOG_TO_DIGITAL_CONVERSION
  -> may_require -> DIGITAL_TO_ANALOG_CONVERSION

# ============================================================
# 12. STABILITY
# ============================================================

STABILITY :=
    SYSTEM_RESPONSE
  -> remains_within -> ACCEPTABLE_BOUNDS

STABILITY_ANALYSIS :=
    SYSTEM_MODEL
  -> DETERMINE -> STABILITY_PROPERTIES

STABILITY
  -> influenced_by -> CONTROLLER
  -> influenced_by -> FEEDBACK
  -> influenced_by -> SYSTEM_DYNAMICS

UNSTABLE_SYSTEM :=
    PERTURBATION
  -> GROWING_RESPONSE

STABLE_SYSTEM :=
    PERTURBATION
  -> BOUNDED_OR_DECAYING_RESPONSE

# ============================================================
# 13. PERFORMANCE
# ============================================================

PERFORMANCE :=
    RESPONSE_TIME
  + RISE_TIME
  + SETTLING_TIME
  + OVERSHOOT
  + STEADY_STATE_ERROR
  + DISTURBANCE_REJECTION
  + CONTROL_EFFORT

CONTROLLER_DESIGN :=
    CONTROL_OBJECTIVES
  + SYSTEM_MODEL
  + CONSTRAINTS
  -> CONTROL_LAW

CONTROL_LAW
  -> determines -> CONTROL_ACTION

CONTROL_ACTION
  -> changes -> SYSTEM_BEHAVIOUR

# ============================================================
# 14. OBSERVATION AND STATE ESTIMATION
# ============================================================

OBSERVATION :=
    SENSOR_DATA
  -> SYSTEM_INFORMATION

STATE_ESTIMATION :=
    MEASUREMENTS
  + SYSTEM_MODEL
  -> ESTIMATED_STATE

ESTIMATED_STATE
  -> supports -> STATE_FEEDBACK_CONTROL

OBSERVER :=
    SYSTEM_MODEL
  + INPUT
  + OUTPUT
  -> ESTIMATE(STATE)

# ============================================================
# 15. CONTROL REASONING CHAIN
# ============================================================

CONTROL_REASONING :=
    DEFINE_OBJECTIVE
  -> IDENTIFY_SYSTEM
  -> MODEL_SYSTEM
  -> ANALYSE_DYNAMICS
  -> ASSESS_STABILITY
  -> SELECT_CONTROL_STRATEGY
  -> DESIGN_CONTROLLER
  -> SIMULATE
  -> IMPLEMENT
  -> MEASURE_RESPONSE
  -> VALIDATE
  -> REFINE

IF MODEL_UNCERTAINTY = HIGH
THEN CONSIDER ROBUST_CONTROL

IF SYSTEM_PARAMETERS = TIME_VARYING
THEN CONSIDER ADAPTIVE_CONTROL

IF PERFORMANCE_OBJECTIVE = OPTIMISATION
THEN CONSIDER OPTIMAL_CONTROL

IF IMPLEMENTATION_PLATFORM = DIGITAL
THEN APPLY DIGITAL_CONTROL

IF CONTROL_REQUIREMENT = GENERAL_INDUSTRIAL_REGULATION
THEN CONSIDER PID_CONTROL

# ============================================================
# 16. SEMANTIC RELATIONSHIPS
# ============================================================

RELATION controls(Controller, Plant)
RELATION measures(Sensor, Output)
RELATION actuates(Actuator, Plant)
RELATION receives(Controller, ErrorSignal)
RELATION generates(Controller, ControlInput)
RELATION affects(Disturbance, Plant)
RELATION estimates(Observer, State)
RELATION models(SystemModel, ControlSystem)
RELATION stabilises(Controller, ControlSystem)
RELATION optimises(OptimalController, ObjectiveFunction)
RELATION adapts(AdaptiveController, SystemChange)
RELATION robust_against(RobustController, Uncertainty)

# ============================================================
# 17. SEMANTIC EQUIVALENCE
# ============================================================

SEMANTIC_EQUIVALENCE:
  "automatic control" ~= "control engineering"
  "closed-loop control" ~= "feedback control"
  "process output" ~= "controlled output"
  "setpoint" ~= "reference input"
  "control signal" ~= "control input"
  "system dynamics" ~= "dynamic behaviour"
  "plant model" ~= "system model"
  "digital controller" ~= "discrete-time controller"

# ============================================================
# 18. CONFIDENCE
# ============================================================

CONFIDENCE:
  domain_classification: 0.99
  control_system_structure: 0.99
  feedback_relationships: 0.99
  pid_control_mapping: 0.99
  adaptive_control_mapping: 0.98
  robust_control_mapping: 0.98
  optimal_control_mapping: 0.98
  digital_control_mapping: 0.98
  semantic_relationships: 0.98

# ============================================================
# 19. UPDATE MODEL
# ============================================================

UPDATE_MODEL:
  ON new_control_method:
    CLASSIFY method
    LINK method -> ControlEngineering
    MAP objectives
    MAP system_model_requirements
    MAP stability_properties
    MAP implementation_constraints
    RECALCULATE semantic_relationships

  ON new_system_evidence:
    UPDATE model_parameters
    UPDATE uncertainty
    UPDATE performance_estimates
    REASSESS controller_suitability
    REASSESS stability

  ON ontology_revision:
    PRESERVE entity_identity
    PRESERVE provenance
    UPDATE relationships
    UPDATE confidence
    RECOMPUTE FLOW_HASH

# ============================================================
# 20. AI CONSUMPTION
# ============================================================

AI_CONSUMPTION:
  parse_as: FORMAL_SEMANTIC_CONTROL_MODEL
  reasoning_mode: EXECUTABLE_RELATIONAL
  preserve:
    - entity_types
    - directional_relationships
    - control_loops
    - system_constraints
    - uncertainty
    - confidence
    - provenance

  infer:
    - controller_system_relationships
    - feedback_dependencies
    - control_strategy_requirements
    - stability_dependencies
    - optimisation_dependencies
    - adaptation_requirements

  prohibit:
    - unsupported_controller_claims
    - invented_system_parameters
    - assumed_stability
    - assumed_optimality
    - removal_of_uncertainty

# ============================================================
# 21. FLOW HASH
# ============================================================

FLOW_HASH_INPUT :=
    DOMAIN
  + CORE_ENTITIES
  + CONTROL_SYSTEMS
  + SYSTEM_MODELLING
  + FEEDBACK_CONTROL
  + PID_CONTROL
  + ADAPTIVE_CONTROL
  + ROBUST_CONTROL
  + OPTIMAL_CONTROL
  + DIGITAL_CONTROL
  + STABILITY
  + PERFORMANCE
  + OBSERVATION
  + SEMANTIC_RELATIONSHIPS
  + SEMANTIC_EQUIVALENCE
  + CONFIDENCE
  + UPDATE_MODEL
  + AI_CONSUMPTION

FLOW_HASH :=
    HASH(FLOW_HASH_INPUT)

END FLOW