Module control_theory 

Control theory: PID, state-space, LQR, Kalman filter, EKF, Bode analysis, root locus, Ziegler-Nichols auto-tuning, lead/lag compensator, poles/zeros.

Overview

This module provides classical and modern control theory building blocks:

• PidController — PID with anti-windup, derivative filter, output clamping
• StateSpaceModel — A, B, C, D matrices; step response; stability check
• LqrController — LQR via discrete algebraic Riccati equation (iterative)
• KalmanFilter — discrete Kalman filter: predict + update
• ExtendedKalmanFilter — EKF with Jacobian-based linearization
• BodeAnalysis — gain/phase at frequencies; gain/phase margins
• RootLocus — closed-loop poles vs gain K; breakaway points
• ZieglerNichols — auto-tune PID from ultimate gain/period
• LeadLagCompensator — lead/lag compensator transfer function
• PolesZeros — transfer function poles, zeros, DC gain, step response

Structs

BodeAnalysis

Bode analysis for a transfer function given numerator and denominator polynomials.

BodePoint

A single point on a Bode plot.

ExtendedKalmanFilter

Extended Kalman Filter (EKF) with Jacobian-based linearization.

KalmanFilter

Discrete Kalman filter.

LeadLagCompensator

Lead or lag compensator: C(s) = Kc * (s + z) / (s + p).

LqrController

Discrete Linear Quadratic Regulator (LQR) controller.

PidController

A PID controller with anti-windup, derivative filter, and output clamping.

PolesZeros

Transfer function representation via poles, zeros, and DC gain.

RootLocus

Root locus computation: closed-loop poles as a function of gain K.

RootLocusPoint

A point on the root locus.

StateSpaceModel

Discrete-time linear state-space model: x[k+1] = Ax[k] + Bu[k], y[k] = Cx[k] + Du[k].

ZieglerNichols

Ziegler-Nichols auto-tuning: compute PID gains from ultimate gain and period.

ZnGains

PID gains recommended by Ziegler-Nichols method.