control-sys 0.1.0

A Control System library implemented in Rust to design and analyze control systems.
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

# control-sys, a control system library written in Rust

![GitHub Actions Workflow Status](https://img.shields.io/github/actions/workflow/status/rdesarz/control-sys-rs/rust.yml)

**control-sys** is a control system library written in Rust. It implements tools to represent and analyze LTI systems using state-space model.

## Examples

### Continuous state space model

A continuous state space model can be defined with `ContinuousStateSpaceModel`. As an example, a state-space model representing a DC motor can be defined this way. We are using `nalgebra` to represent the matrices: 

```rust
use nalgebra as na;
use control_sys::model;

// DC motor parameters
let b = 0.1f64;
let j = 0.01f64;
let k = 0.01f64;
let l = 0.5f64;
let r = 1.0f64;

let mat_ac = na::dmatrix![
        -b / j, k / j;
        -k / l, -r / l;
    ];
let mat_bc = na::dmatrix![0.0; 
                          1.0 / l];
let mat_cc = na::dmatrix![1.0, 0.0];

let cont_model = model::ContinuousStateSpaceModel::from_matrices(&mat_ac, &mat_bc, &mat_cc, &na::dmatrix![]);
```

### Continuous to discrete model conversion

A `DiscreteStateSpaceModel` can be built from a continuous one. You then need to specify the sampling step `ts`: 

```rust
use nalgebra as na;
use control_sys::model;

// DC motor parameters
let b = 0.1f64;
let j = 0.01f64;
let k = 0.01f64;
let l = 0.5f64;
let r = 1.0f64;

let mat_ac = na::dmatrix![
        -b / j, k / j;
        -k / l, -r / l;
    ];
let mat_bc = na::dmatrix![0.0; 
                          1.0 / l];
let mat_cc = na::dmatrix![1.0, 0.0];

let cont_model = model::ContinuousStateSpaceModel::from_matrices(&mat_ac, &mat_bc, &mat_cc, &na::dmatrix![]);

let discrete_model = 
    model::DiscreteStateSpaceModel::from_continuous_ss_forward_euler(&cont_model, 0.05);
```

### Step response 

You can compute the step response of a system. For a discrete system, the simulation steps are given by the sampling step of the discretization:

```rust
use nalgebra as na;
use control_sys::{model, simulator};

// DC motor parameters
let b = 0.1f64;
let j = 0.01f64;
let k = 0.01f64;
let l = 0.5f64;
let r = 1.0f64;

let mat_ac = na::dmatrix![
        -b / j, k / j;
        -k / l, -r / l;
    ];
let mat_bc = na::dmatrix![0.0; 
                          1.0 / l];
let mat_cc = na::dmatrix![1.0, 0.0];

let cont_model = model::ContinuousStateSpaceModel::from_matrices(&mat_ac, &mat_bc, &mat_cc, &na::dmatrix![]);

let discrete_model = 
    model::DiscreteStateSpaceModel::from_continuous_ss_forward_euler(&cont_model, 0.05);

// where model implements the traits `StateSpaceModel` and `Discrete`
let duration = 10.0; // [s]
let (response, input, states) = simulator::step_for_discrete_ss(
        &discrete_model,
        duration,
    );
```

You can also compute the step response for a continuous model. You will need to provide the sampling step and the model will be discretized before computing the step response:

```rust
use nalgebra as na;
use control_sys::{model, simulator};

// DC motor parameters
let b = 0.1f64;
let j = 0.01f64;
let k = 0.01f64;
let l = 0.5f64;
let r = 1.0f64;

let mat_ac = na::dmatrix![
        -b / j, k / j;
        -k / l, -r / l;
    ];
let mat_bc = na::dmatrix![0.0; 
                          1.0 / l];
let mat_cc = na::dmatrix![1.0, 0.0];

let cont_model = model::ContinuousStateSpaceModel::from_matrices(&mat_ac, &mat_bc, &mat_cc, &na::dmatrix![]);

// where model is a continuous state space model
let sampling_dt = 0.05; // [s]
let duration = 10.0; // [s]
let (response, input, states) = simulator::step_for_continuous_ss(
        &cont_model,
        sampling_dt,
        duration,
    );
```

### Controllability 

The controllability of a system can be evaluated using the `is_ss_controllable` method:

```rust
use nalgebra as na;
use control_sys::{model, analysis};

let ss_model = model::DiscreteStateSpaceModel::from_matrices(
        &nalgebra::dmatrix![1.0, -2.0; 
                            2.0, 1.0],
        &nalgebra::dmatrix![1.0;
                            2.0],
        &nalgebra::dmatrix![],
        &nalgebra::dmatrix![],
        0.05,
    );

let (is_controllable, controllability_matrix) = analysis::is_ss_controllable(&ss_model);

if is_controllable
{
    println!("The system is controllable");
    println!("Its controllability matrix is: {}", controllability_matrix);
}
```