SecondOrderTest

Second-order system test with constant input.

Tests a second-order dynamic system by applying a constant input and verifying the expected step response. The second-order system is configured with a gain of 1.0, natural frequency of 1.0, and damping ratio of 0.5, which produces a slightly under-damped response. The system should eventually reach the steady-state output value matching the input constant.

Usage

SecondOrderTest()

Behavior

$$\begin{array}{rl}\mathtt{c}\mathtt{.}\mathtt{y}\left(t\right)& =\mathtt{pt}\mathtt{2.}\mathtt{u}\left(t\right)\\ \mathtt{c}\mathtt{.}\mathtt{y}\left(t\right)& =\mathtt{c}\mathtt{.}\mathtt{k}\\ \frac{\mathrm{d}\mathtt{pt}\mathtt{2.}\mathtt{x}\left(t\right)}{\mathrm{d}t}& =\mathtt{pt}\mathtt{2.}\mathtt{xd}\left(t\right)\\ \frac{\mathrm{d}\mathtt{pt}\mathtt{2.}\mathtt{xd}\left(t\right)}{\mathrm{d}t}& =(-2\mathtt{pt}\mathtt{2.}\mathtt{d}\mathtt{pt}\mathtt{2.}\mathtt{xd}\left(t\right)+(-\mathtt{pt}\mathtt{2.}\mathtt{x}\left(t\right)+\mathtt{pt}\mathtt{2.}\mathtt{k}\mathtt{pt}\mathtt{2.}\mathtt{u}\left(t\right))\mathtt{pt}\mathtt{2.}\mathtt{w})\mathtt{pt}\mathtt{2.}\mathtt{w}\\ \mathtt{pt}\mathtt{2.}\mathtt{y}\left(t\right)& =\mathtt{pt}\mathtt{2.}\mathtt{x}\left(t\right)\end{array}$$

Source

# Second-order system test with constant input.
#
# Tests a second-order dynamic system by applying a constant input and verifying the expected
# step response. The second-order system is configured with a gain of 1.0, natural frequency
# of 1.0, and damping ratio of 0.5, which produces a slightly under-damped response. The system
# should eventually reach the steady-state output value matching the input constant.
test component SecondOrderTest
  # Constant source block that provides a fixed value of 1 as input
  c = Constant(k=1)
  # Second-order transfer function block with specified dynamics parameters
  pt2 = SecondOrder(k=1.0, w=1.0, d=0.5)
relations
  # Connects the constant output to the input of the second-order system
  connect(c.y, pt2.u)
metadata {
  "Dyad": {
    "experiments": {},
    "tests": {
      "case1": {
        "stop": 10,
        "initial": {"pt2.xd": 0},
        "atol": {"pt2.y": 0.01},
        "expect": {"final": {"pt2.y": 1}, "signals": ["pt2.y"]}
      }
    }
  }
}
end

Flattened Source

# Second-order system test with constant input.
#
# Tests a second-order dynamic system by applying a constant input and verifying the expected
# step response. The second-order system is configured with a gain of 1.0, natural frequency
# of 1.0, and damping ratio of 0.5, which produces a slightly under-damped response. The system
# should eventually reach the steady-state output value matching the input constant.
test component SecondOrderTest
  # Constant source block that provides a fixed value of 1 as input
  c = Constant(k=1)
  # Second-order transfer function block with specified dynamics parameters
  pt2 = SecondOrder(k=1.0, w=1.0, d=0.5)
relations
  # Connects the constant output to the input of the second-order system
  connect(c.y, pt2.u)
metadata {
  "Dyad": {
    "experiments": {},
    "tests": {
      "case1": {
        "stop": 10,
        "initial": {"pt2.xd": 0},
        "atol": {"pt2.y": 0.01},
        "expect": {"final": {"pt2.y": 1}, "signals": ["pt2.y"]}
      }
    }
  }
}
end

Test Cases

Test Case case1

plt

Related

• Examples

• Experiments

• Analyses

• Tests

  • Constant

  • SecondOrder