au 0.10.0

Automatic control systems library
Documentation 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161

//! # PID (Proportional-integral-derivative) controller
//!
//! Common industrial controllers.
//! * real PID
//! * ideal PID
//! * automatic calculation of the corrisponding transfer function

use crate::{polynomial::Poly, transfer_function::continuous::Tf};

use num_traits::Float;

/// Proportional-Integral-Derivative controller
#[derive(Debug)]
pub struct Pid<T: Float> {
    /// Proportional action coefficient
    kp: T,
    /// Integral time
    ti: T,
    /// Derivative time
    td: T,
    /// Constant for additional pole
    n: Option<T>,
}

/// Implementation of Pid methods
impl<T: Float> Pid<T> {
    /// Create a new ideal PID controller
    ///
    /// # Arguments
    ///
    /// * `kp` - Proportional action coefficient
    /// * `ti` - Integral time
    /// * `td` - Derivative time
    ///
    /// # Example
    /// ```
    /// use au::controller::pid::Pid;
    /// let pid = Pid::new_ideal(4., 6., 0.1);
    /// ```
    pub fn new_ideal(kp: T, ti: T, td: T) -> Self {
        Self {
            kp,
            ti,
            td,
            n: None,
        }
    }

    /// Create a new real PID controller
    ///
    /// # Arguments
    ///
    /// * `kp` - Proportional action coefficient
    /// * `ti` - Integral time
    /// * `td` - Derivative time
    /// * `n` - Constant for additional pole
    ///
    /// # Example
    /// ```
    /// use au::controller::pid::Pid;
    /// let pid = Pid::new(4., 6., 12., 0.1);
    /// ```
    pub fn new(kp: T, ti: T, td: T, n: T) -> Self {
        Self {
            kp,
            ti,
            td,
            n: Some(n),
        }
    }

    /// Calculate the transfer function of the PID controller
    ///
    /// # Real PID
    /// ```text
    ///          1         Td
    /// Kp (1 + ---- + ---------- s) =
    ///         Ti*s   1 + Td/N*s
    ///
    ///      N + (Ti*N +Td)s + Ti*Td(1 + N)s^2
    /// = Kp ----------------------------------
    ///             Ti*N*s + Ti*Td*s^2
    /// ```
    /// # Ideal PID
    ///
    /// ```text
    ///    1 + Ti*s + Ti*Td*s^2
    /// Kp --------------------
    ///           Ti*s
    /// ```
    ///
    /// # Example
    /// ```
    /// #[macro_use] extern crate au;
    /// use au::{controller::pid::Pid, Tf};
    /// let pid = Pid::new_ideal(2., 2., 0.5);
    /// let tf = Tf::new(poly![1., 2., 1.], poly![0., 1.]);
    /// assert_eq!(tf, pid.tf());
    /// ```
    pub fn tf(&self) -> Tf<T> {
        self.n
            .map_or_else(|| self.tf_from_ideal_pid(), |n| self.tf_from_real_pid(n))
    }

    /// Calculate the transfer function of a real PID controller
    ///
    /// # Arguments
    ///
    /// * `n` - Constant for additional pole
    fn tf_from_real_pid(&self, n: T) -> Tf<T> {
        let a0 = self.kp * n;
        let a1 = self.kp * (self.ti * n + self.td);
        let a2 = self.kp * self.ti * self.td * (T::one() + n);
        let b0 = T::zero();
        let b1 = self.ti * n;
        let b2 = self.ti * self.td;
        Tf::new(
            Poly::new_from_coeffs(&[a0, a1, a2]),
            Poly::new_from_coeffs(&[b0, b1, b2]),
        )
    }

    /// Calculate the transfer function of an ideal PID controller
    fn tf_from_ideal_pid(&self) -> Tf<T> {
        Tf::new(
            Poly::new_from_coeffs(&[T::one(), self.ti, self.ti * self.td]),
            Poly::new_from_coeffs(&[T::zero(), self.ti / self.kp]),
        )
    }
}

#[cfg(test)]
mod pid_tests {
    use super::*;
    use crate::units::ToDecibel;
    use num_complex::Complex64;

    #[test]
    fn ideal_pid_creation() {
        let pid = Pid::new_ideal(10., 5., 2.);
        let tf = pid.tf();
        let c = tf.eval(&Complex64::new(0., 1.));
        assert_eq!(Complex64::new(10., 18.), c);
    }

    #[test]
    fn real_pid_creation() {
        // Example 15.1
        let g = Tf::new(
            Poly::new_from_coeffs(&[1.]),
            Poly::new_from_roots(&[-1., -1., -1.]),
        );
        let pid = Pid::new(2., 2., 0.5, 5.);
        let r = pid.tf();
        assert_eq!(Some(vec![-10., 0.]), r.real_poles());
        let l = &g * &r;
        let critical_freq = 0.8;
        let c = l.eval(&Complex64::new(0., critical_freq));
        assert_abs_diff_eq!(0., c.norm().to_db(), epsilon = 0.1);
    }
}