[wpimath] Add ImplicitModelFollower (#4056)

wpimath/src/main/java/edu/wpi/first/math/controller/ImplicitModelFollower.java

@@ -0,0 +1,138 @@
+// Copyright (c) FIRST and other WPILib contributors.
+// Open Source Software; you can modify and/or share it under the terms of
+// the WPILib BSD license file in the root directory of this project.
+
+package edu.wpi.first.math.controller;
+
+import edu.wpi.first.math.Matrix;
+import edu.wpi.first.math.Num;
+import edu.wpi.first.math.numbers.N1;
+import edu.wpi.first.math.system.Discretization;
+import edu.wpi.first.math.system.LinearSystem;
+import org.ejml.simple.SimpleMatrix;
+
+/**
+ * Contains the controller coefficients and logic for an implicit model follower.
+ *
+ * <p>Implicit model following lets us design a feedback controller that erases the dynamics of our
+ * system and makes it behave like some other system. This can be used to make a drivetrain more
+ * controllable during teleop driving by making it behave like a slower or more benign drivetrain.
+ *
+ * <p>For more on the underlying math, read appendix B.3 in
+ * https://file.tavsys.net/control/controls-engineering-in-frc.pdf.
+ */
+@SuppressWarnings("ClassTypeParameterName")
+public class ImplicitModelFollower<States extends Num, Inputs extends Num, Outputs extends Num> {
+  // Computed controller output
+  @SuppressWarnings("MemberName")
+  private Matrix<Inputs, N1> m_u;
+
+  // State space conversion gain
+  @SuppressWarnings("MemberName")
+  private Matrix<Inputs, States> m_A;
+
+  // Input space conversion gain
+  @SuppressWarnings("MemberName")
+  private Matrix<Inputs, Inputs> m_B;
+
+  /**
+   * Constructs a controller with the given coefficients and plant.
+   *
+   * @param plant The plant being controlled.
+   * @param plantRef The plant whose dynamics should be followed.
+   * @param dtSeconds Discretization timestep.
+   */
+  public ImplicitModelFollower(
+      LinearSystem<States, Inputs, Outputs> plant,
+      LinearSystem<States, Inputs, Outputs> plantRef,
+      double dtSeconds) {
+    this(plant.getA(), plant.getB(), plantRef.getA(), plantRef.getB(), dtSeconds);
+  }
+
+  /**
+   * Constructs a controller with the given coefficients and plant.
+   *
+   * @param A Continuous system matrix of the plant being controlled.
+   * @param B Continuous input matrix of the plant being controlled.
+   * @param Aref Continuous system matrix whose dynamics should be followed.
+   * @param Bref Continuous input matrix whose dynamics should be followed.
+   * @param dtSeconds Discretization timestep.
+   */
+  @SuppressWarnings("ParameterName")
+  public ImplicitModelFollower(
+      Matrix<States, States> A,
+      Matrix<States, Inputs> B,
+      Matrix<States, States> Aref,
+      Matrix<States, Inputs> Bref,
+      double dtSeconds) {
+    m_u = new Matrix<>(new SimpleMatrix(B.getNumCols(), 1));
+
+    // Discretize real dynamics
+    var discABPair = Discretization.discretizeAB(A, B, dtSeconds);
+    var discA = discABPair.getFirst();
+    var discB = discABPair.getSecond();
+
+    // Discretize desired dynamics
+    var discABrefPair = Discretization.discretizeAB(Aref, Bref, dtSeconds);
+    var discAref = discABrefPair.getFirst();
+    var discBref = discABrefPair.getSecond();
+
+    // Find u_imf that makes real model match reference model.
+    //
+    // x_k+1 = Ax_k + Bu_imf
+    // z_k+1 = Aref z_k + Bref u_k
+    //
+    // Let x_k = z_k.
+    //
+    // x_k+1 = z_k+1
+    // Ax_k + Bu_imf = Aref x_k + Bref u_k
+    // Bu_imf = Aref x_k - Ax_k + Bref u_k
+    // Bu_imf = (Aref - A)x_k + Bref u_k
+    // u_imf = B^+ ((Aref - A)x_k + Bref u_k)
+    // u_imf = -B^+ (A - Aref)x_k + B^+ Bref u_k
+
+    // The first term makes the open-loop poles that of the reference
+    // system, and the second term makes the input behave like that of the
+    // reference system.
+    m_A = discB.solve(discA.minus(discAref)).times(-1.0);
+    m_B = discB.solve(discBref);
+
+    reset();
+  }
+
+  /**
+   * Returns the control input vector u.
+   *
+   * @return The control input.
+   */
+  public Matrix<Inputs, N1> getU() {
+    return m_u;
+  }
+
+  /**
+   * Returns an element of the control input vector u.
+   *
+   * @param i Row of u.
+   * @return The row of the control input vector.
+   */
+  public double getU(int i) {
+    return m_u.get(i, 0);
+  }
+
+  /** Resets the controller. */
+  public void reset() {
+    m_u.fill(0.0);
+  }
+
+  /**
+   * Returns the next output of the controller.
+   *
+   * @param x The current state x.
+   * @param u The current input for the original model.
+   * @return The next controller output.
+   */
+  public Matrix<Inputs, N1> calculate(Matrix<States, N1> x, Matrix<Inputs, N1> u) {
+    m_u = m_A.times(x).plus(m_B.times(u));
+    return m_u;
+  }
+}