iir: document

This commit is contained in:
Robert Jördens 2020-11-22 22:58:17 +01:00
parent c91e395d12
commit 6808d32e0f
1 changed files with 90 additions and 22 deletions

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@ -3,15 +3,10 @@ use serde::{Deserialize, Serialize};
use core::f32;
pub type IIRState = [f32; 5];
#[derive(Copy, Clone, Deserialize, Serialize)]
pub struct IIR {
pub ba: IIRState,
pub y_offset: f32,
pub y_min: f32,
pub y_max: f32,
}
// These are implemented here because core::f32 doesn't have them (yet).
// They are naive and don't handle inf/nan.
// `compiler-intrinsics`/llvm should have better (robust, universal, and
// faster) implementations.
fn abs(x: f32) -> f32 {
if x >= 0. {
@ -45,17 +40,72 @@ fn min(x: f32, y: f32) -> f32 {
}
}
// Multiply-accumulate vectors `x` and `a`.
//
// A.k.a. dot product.
// Rust/LLVM optimize this nicely.
fn macc<T>(y0: T, x: &[T], a: &[T]) -> T
where
T: Add<Output = T> + Mul<Output = T> + Copy,
{
x.iter()
.zip(a.iter())
.map(|(&i, &j)| i * j)
.zip(a)
.map(|(&x, &a)| x * a)
.fold(y0, |y, xa| y + xa)
}
/// IIR state and coefficients type.
///
/// To represent the IIR state (input and output memory) during the filter update
/// this contains the three inputs (x0, x1, x2) and the two outputs (y1, y2)
/// concatenated.
/// To represent the IIR coefficients, this contains the feed-forward
/// coefficients (b0, b1, b2) followd by the feed-back coefficients (a1, a2),
/// all normalized such that a0 = 1.
pub type IIRState = [f32; 5];
/// IIR configuration.
///
/// Contains the coeeficients `ba`, the output offset `y_offset`, and the
/// output limits `y_min` and `y_max`.
///
/// This implementation achieves several important properties:
///
/// * Its transfer function is universal in the sense that any biquadratic
/// transfer function can be implemented (high-passes, gain limits, second
/// order integrators with inherent anti-windup, notches etc) without code
/// changes preserving all features.
/// * It inherits a universal implementation of "integrator anti-windup", also
/// and especially in the presence of set-point changes and in the presence
/// of proportional or derivative gain without any back-off that would reduce
/// steady-state output range.
/// * It has universal derivative-kick (undesired, unlimited, and un-physical
/// amplification of set-point changes by the derivative term) avoidance.
/// * An offset at the input of an IIR filter (a.k.a. "set-point") is
/// equivalent to an offset at the output. They are related by the
/// overall (DC feed-forward) gain of the filter.
/// * It stores only previous outputs and inputs. These have direct and
/// invariant interpretation (independent of gains and offsets).
/// Therefore it can trivially implement bump-less transfer.
/// * Cascading multiple IIR filters allows stable and robust
/// implementation of transfer functions beyond bequadratic terms.
#[derive(Copy, Clone, Deserialize, Serialize)]
pub struct IIR {
pub ba: IIRState,
pub y_offset: f32,
pub y_min: f32,
pub y_max: f32,
}
impl IIR {
/// Configures IIR filter coefficients for proportional-integral behavior
/// with gain limit.
///
/// # Arguments
///
/// * `kp` - Proportional gain. Also defines gain sign.
/// * `ki` - Integral gain at Nyquist. Sign taken from `kp`.
/// * `g` - Gain limit.
pub fn set_pi(&mut self, kp: f32, ki: f32, g: f32) -> Result<(), &str> {
let ki = copysign(ki, kp);
let g = copysign(g, kp);
@ -75,33 +125,51 @@ impl IIR {
}
(a1, b0, b1)
};
self.ba[0] = b0;
self.ba[1] = b1;
self.ba[2] = 0.;
self.ba[3] = a1;
self.ba[4] = 0.;
self.ba.copy_from_slice(&[b0, b1, 0., a1, 0.]);
Ok(())
}
/// Compute the overall (DC feed-forward) gain.
pub fn get_k(&self) -> f32 {
self.ba[..3].iter().sum()
}
/// Compute input-referred (`x`) offset from output (`y`) offset.
pub fn get_x_offset(&self) -> Result<f32, &str> {
let b: f32 = self.ba[..3].iter().sum();
if abs(b) < f32::EPSILON {
Err("b is zero")
let k = self.get_k();
if abs(k) < f32::EPSILON {
Err("k is zero")
} else {
Ok(self.y_offset / b)
Ok(self.y_offset / k)
}
}
/// Convert input (`x`) offset to equivalent output (`y`) offset and apply.
///
/// # Arguments
/// * `xo`: Input (`x`) offset.
pub fn set_x_offset(&mut self, xo: f32) {
let b: f32 = self.ba[..3].iter().sum();
self.y_offset = xo * b;
self.y_offset = xo * self.get_k();
}
/// Feed a new input value into the filter, update the filter state, and
/// return the new output. Only the state `xy` is modified.
///
/// # Arguments
/// * `xy` - Current filter state.
/// * `x0` - New input.
pub fn update(&self, xy: &mut IIRState, x0: f32) -> f32 {
// `xy` contains x0 x1 y0 y1 y2
// Increment time x1 x2 y1 y2 y3
// Rotate y3 x1 x2 y1 y2
xy.rotate_right(1);
// Store x0 x0 x1 x2 y1 y2
xy[0] = x0;
// Compute y0 by multiply-accumulate
let y0 = macc(self.y_offset, xy, &self.ba);
// Limit y0
let y0 = max(self.y_min, min(self.y_max, y0));
// Store y0 x0 x1 y0 y1 y2
xy[xy.len() / 2] = y0;
y0
}