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StateSpaceTest.md

StateSpaceTest ​

Test component for StateSpace block demonstrating basic functionality.

Creates a simple test system with:

  • A step input signal

  • A second-order state space system

  • Integration of the output for verification

The state space system represents a second-order system with:

  • States: position and velocity

  • Single input: force/acceleration

  • Single output: position

  • Operating point offset to test that feature

Usage ​

BlockComponents.StateSpaceTest()

Behavior ​

[connect(step+y(t),getindex(statespace+u(t),1))connect(getindex(statespace+y(t),1),integrator+u(t))connect(integrator+y(t),terminator+u(t))step.y(t)=ifelse(t≥step.start_time,step.height+step.offset,step.offset)state_space.Δu(t)=broadcast(−,state_space.u(t),state_space.u0)state_space.Δy(t)=broadcast(−,state_space.y(t),state_space.y0)dstate_space.x(t)dt=broadcast(+,state_space.Astate_space.x(t),state_space.Bstate_space.Δu(t))state_space.Δy(t)=broadcast(+,state_space.Cstate_space.x(t),state_space.Dstate_space.Δu(t))dintegrator.x(t)dt=integrator.kintegrator.u(t)integrator.y(t)=integrator.x(t)]

Source ​

dyad
"""
Test component for StateSpace block demonstrating basic functionality.

Creates a simple test system with:
- A step input signal
- A second-order state space system
- Integration of the output for verification

The state space system represents a second-order system with:
- States: position and velocity
- Single input: force/acceleration
- Single output: position
- Operating point offset to test that feature
"""
component StateSpaceTest
  "Step input signal starting at time 1.0 with amplitude 2.0"
  step = BlockComponents.Step(height = 2.0, start_time = 1.0)
  """
  Second-order state space system
  Represents: d²x/dt² + 2*damping*freq*dx/dt + freq²*x = freq²*u
  In state space form with x1=position, x2=velocity:
  dx1/dt = x2
  dx2/dt = -freq²*x1 - 2*damping*freq*x2 + freq²*u
  y = x1 (output position)
  """
  state_space = BlockComponents.StateSpace(nx = 2, nu = 1, ny = 1, A = reshape([0.0, 1.0, -4.0, -2.0], 2, 2), B = reshape([0.0, 4.0], 2, 1), C = reshape([1.0, 0.0], 1, 2), D = reshape([0.0], 1, 1), x0 = [0.5, 0.0], u0 = [0.5], y0 = [0.1]) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 180, "y1": 0, "x2": 280, "y2": 100, "rot": 0}
      }
    }
  }
  "Integrator to accumulate the output for testing"
  integrator = BlockComponents.Integrator(k = 1.0, x0 = 0.0) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 360, "y1": 0, "x2": 460, "y2": 100, "rot": 0}
      }
    }
  }
  "Terminator for the integrated signal"
  terminator = BlockComponents.Terminator() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 540, "y1": 0, "x2": 640, "y2": 100, "rot": 0}
      }
    }
  }
relations
  "Connect step input to state space system"
  connect(step.y, state_space.u[1])
  "Connect state space output to integrator"
  connect(state_space.y[1], integrator.u)
  "Connect integrator output to terminator"
  connect(integrator.y, terminator.u) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
metadata {
  "Dyad": {
    "icons": {"default": "dyad://BlockComponents/Example.svg"},
    "tests": {
      "case1": {
        "stop": 5,
        "rtol": {"integrator.y": 0.0001},
        "expect": {
          "signals": ["integrator.y"],
          "initial": {"integrator.y": 0},
          "final": {"integrator.y": -18.288754189661404}
        }
      }
    }
  }
}
end
Flattened Source
dyad
"""
Test component for StateSpace block demonstrating basic functionality.

Creates a simple test system with:
- A step input signal
- A second-order state space system
- Integration of the output for verification

The state space system represents a second-order system with:
- States: position and velocity
- Single input: force/acceleration
- Single output: position
- Operating point offset to test that feature
"""
component StateSpaceTest
  "Step input signal starting at time 1.0 with amplitude 2.0"
  step = BlockComponents.Step(height = 2.0, start_time = 1.0)
  """
  Second-order state space system
  Represents: d²x/dt² + 2*damping*freq*dx/dt + freq²*x = freq²*u
  In state space form with x1=position, x2=velocity:
  dx1/dt = x2
  dx2/dt = -freq²*x1 - 2*damping*freq*x2 + freq²*u
  y = x1 (output position)
  """
  state_space = BlockComponents.StateSpace(nx = 2, nu = 1, ny = 1, A = reshape([0.0, 1.0, -4.0, -2.0], 2, 2), B = reshape([0.0, 4.0], 2, 1), C = reshape([1.0, 0.0], 1, 2), D = reshape([0.0], 1, 1), x0 = [0.5, 0.0], u0 = [0.5], y0 = [0.1]) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 180, "y1": 0, "x2": 280, "y2": 100, "rot": 0}
      }
    }
  }
  "Integrator to accumulate the output for testing"
  integrator = BlockComponents.Integrator(k = 1.0, x0 = 0.0) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 360, "y1": 0, "x2": 460, "y2": 100, "rot": 0}
      }
    }
  }
  "Terminator for the integrated signal"
  terminator = BlockComponents.Terminator() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 540, "y1": 0, "x2": 640, "y2": 100, "rot": 0}
      }
    }
  }
relations
  "Connect step input to state space system"
  connect(step.y, state_space.u[1])
  "Connect state space output to integrator"
  connect(state_space.y[1], integrator.u)
  "Connect integrator output to terminator"
  connect(integrator.y, terminator.u) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
metadata {
  "Dyad": {
    "icons": {"default": "dyad://BlockComponents/Example.svg"},
    "tests": {
      "case1": {
        "stop": 5,
        "rtol": {"integrator.y": 0.0001},
        "expect": {
          "signals": ["integrator.y"],
          "initial": {"integrator.y": 0},
          "final": {"integrator.y": -18.288754189661404}
        }
      }
    }
  }
}
end


Test Cases ​

Test Case case1 ​

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