LIBRARY

Continuous.LimPID

PID controller with limited output, back calculation anti-windup compensation, setpoint weighting and feed-forward

The transfer function is:

$$y=k[e+{\displaystyle \frac{1}{T_{i}s}}(e+{\displaystyle \frac{y_{sat}-y}{N_i{T}_i}})+{\displaystyle \frac{T_{d}s}{1+{\displaystyle \frac{T_d}{N_d}}s}}e]+k_{ff}{u}_{ff}$$

This component extends from BlockComponents.Interfaces.SingleVariableController

Usage

BlockComponents.Continuous.LimPID(k=1, Ti=0.5, Td=0.1, y_max=1e300, y_min=-y_max, wp=1, wd=1, Ni=0.9, Nd=10, k_ff=1, xi0=0, xd0=0)

Parameters:

Name	Description	Units	Default value
k	Gain of controller	–	1
Ti	Time constant of the integrator block	s	0.5
Td	Time constant of the derivative block	s	0.1
y_max	Maximum output	–	1e+300
y_min	Minimum output	–	-y_max
wp	Set-point weight for proportional block	–	1
wd	Set-point weight for derivative block	–	1
Ni	Ni*Ti is time constant of anti-windup compensation	–	0.9
Nd	Maximum derivative gain. Higher the value of Nd, the more ideal the derivative block gets (less filtering, higher high-frequency gain).	–	10
k_ff	Gain of the feed-forward input	–	1
xi0	Initial guess value for integrator output	–	0
xd0	Initial guess value for derivative output	–	0

Connectors

• u_s - This connector represents a real signal as an input to a component (RealInput)

• u_m - This connector represents a real signal as an input to a component (RealInput)

• y - This connector represents a real signal as an output from a component (RealOutput)

• u_ff - This connector represents a real signal as an input to a component (RealInput)

Variables

Name	Description	Units
control_error		–

Behavior

$$\left[\begin{array}{c}{\mathtt{control}}_{\mathrm{error}}\left(t\right)=-{\mathtt{u}}_{\mathrm{m}}\left(t\right)+{\mathtt{u}}_{\mathrm{s}}\left(t\right)\\ \mathrm{connect}(ad{d}_{p_{+}y},proportiona{l}_{+}u)\\ \mathrm{connect}(ad{d}_{d_{+}y},derivativ{e}_{+}u)\\ \mathrm{connect}(ad{d}_{i_{+}y},integrato{r}_{+}u)\\ \mathrm{connect}(proportiona{l}_{+}y,ad{d}_{pi{d}_{+}u1})\\ \mathrm{connect}(derivativ{e}_{+}y,ad{d}_{pi{d}_{+}u2})\\ \mathrm{connect}(integrato{r}_{+}y,ad{d}_{pi{d}_{+}u3})\\ \mathrm{connect}(ad{d}_{pi{d}_{+}y},gai{n}_{pi{d}_{+}u})\\ \mathrm{connect}(gai{n}_{pi{d}_{+}y},ad{d}_{f{f}_{+}u1})\\ \mathrm{connect}(ad{d}_{f{f}_{+}y},limite{r}_{+}u)\\ \mathrm{connect}(limite{r}_{+}y,ad{d}_{sa{t}_{+}u1})\\ \mathrm{connect}(ad{d}_{sa{t}_{+}y},gai{n}_{trac{k}_{+}u})\\ \mathrm{connect}(gai{n}_{trac{k}_{+}y},ad{d}_{i_{+}u3})\\ \mathrm{connect}(limite{r}_{+}y,y)\\ \mathrm{connect}(ad{d}_{f{f}_{+}u2},u_{ff})\\ \mathrm{connect}(ad{d}_{f{f}_{+}y},ad{d}_{sa{t}_{+}u2})\\ \mathrm{connect}(ad{d}_{p_{+}u1},u_s)\\ \mathrm{connect}(ad{d}_{d_{+}u1},u_s)\\ \mathrm{connect}(ad{d}_{i_{+}u1},u_s)\\ \mathrm{connect}(u_m,ad{d}_{p_{+}u2})\\ \mathrm{connect}(ad{d}_{i_{+}u2},u_m)\\ \mathrm{connect}(ad{d}_{d_{+}u2},u_m)\\ {\mathtt{add}}_{\mathrm{p}.\mathrm{y}}\left(t\right)={\mathtt{add}}_{\mathtt{p}\mathtt{.}\mathtt{k}\mathtt{1}}\cdot {\mathtt{add}}_{\mathrm{p}.\mathrm{u}1}\left(t\right)+{\mathtt{add}}_{\mathtt{p}\mathtt{.}\mathtt{k}\mathtt{2}}\cdot {\mathtt{add}}_{\mathrm{p}.\mathrm{u}2}\left(t\right)\\ {\mathtt{add}}_{\mathrm{d}.\mathrm{y}}\left(t\right)={\mathtt{add}}_{\mathtt{d}\mathtt{.}\mathtt{k}\mathtt{1}}\cdot {\mathtt{add}}_{\mathrm{d}.\mathrm{u}1}\left(t\right)+{\mathtt{add}}_{\mathtt{d}\mathtt{.}\mathtt{k}\mathtt{2}}\cdot {\mathtt{add}}_{\mathrm{d}.\mathrm{u}2}\left(t\right)\\ {\mathtt{add}}_{\mathrm{i}.\mathrm{y}}\left(t\right)={\mathtt{add}}_{\mathtt{i}\mathtt{.}\mathtt{k}\mathtt{1}}\cdot {\mathtt{add}}_{\mathrm{i}.\mathrm{u}1}\left(t\right)+{\mathtt{add}}_{\mathtt{i}\mathtt{.}\mathtt{k}\mathtt{2}}\cdot {\mathtt{add}}_{\mathrm{i}.\mathrm{u}2}\left(t\right)+{\mathtt{add}}_{\mathtt{i}\mathtt{.}\mathtt{k}\mathtt{3}}\cdot {\mathtt{add}}_{\mathrm{i}.\mathrm{u}3}\left(t\right)\\ \mathtt{proportional}\mathtt{.}\mathtt{y}\left(t\right)=\mathtt{proportional}\mathtt{.}\mathtt{k}\cdot \mathtt{proportional}\mathtt{.}\mathtt{u}\left(t\right)\\ \frac{\mathrm{d}\cdot \mathtt{derivative}\mathtt{.}\mathtt{x}\left(t\right)}{\mathrm{d}t}=\frac{\mathtt{derivative}\mathtt{.}\mathtt{u}\left(t\right)-\mathtt{derivative}\mathtt{.}\mathtt{x}\left(t\right)}{\mathtt{derivative}\mathtt{.}\mathtt{T}}\\ \mathtt{derivative}\mathtt{.}\mathtt{y}\left(t\right)=\frac{\mathtt{derivative}\mathtt{.}\mathtt{k}\cdot (\mathtt{derivative}\mathtt{.}\mathtt{u}\left(t\right)-\mathtt{derivative}\mathtt{.}\mathtt{x}\left(t\right))}{\mathtt{derivative}\mathtt{.}\mathtt{T}}\\ \frac{\mathrm{d}\cdot \mathtt{integrator}\mathtt{.}\mathtt{x}\left(t\right)}{\mathrm{d}t}=\mathtt{integrator}\mathtt{.}\mathtt{k}\cdot \mathtt{integrator}\mathtt{.}\mathtt{u}\left(t\right)\\ \mathtt{integrator}\mathtt{.}\mathtt{y}\left(t\right)=\mathtt{integrator}\mathtt{.}\mathtt{x}\left(t\right)\\ {\mathtt{add}}_{\mathrm{pid}.\mathrm{y}}\left(t\right)={\mathtt{add}}_{\mathtt{pid}\mathtt{.}\mathtt{k}\mathtt{1}}\cdot {\mathtt{add}}_{\mathrm{pid}.\mathrm{u}1}\left(t\right)+{\mathtt{add}}_{\mathtt{pid}\mathtt{.}\mathtt{k}\mathtt{2}}\cdot {\mathtt{add}}_{\mathrm{pid}.\mathrm{u}2}\left(t\right)+{\mathtt{add}}_{\mathtt{pid}\mathtt{.}\mathtt{k}\mathtt{3}}\cdot {\mathtt{add}}_{\mathrm{pid}.\mathrm{u}3}\left(t\right)\\ {\mathtt{gain}}_{\mathrm{pid}.\mathrm{y}}\left(t\right)={\mathtt{gain}}_{\mathtt{pid}\mathtt{.}\mathtt{k}}\cdot {\mathtt{gain}}_{\mathrm{pid}.\mathrm{u}}\left(t\right)\\ {\mathtt{add}}_{\mathrm{ff}.\mathrm{y}}\left(t\right)={\mathtt{add}}_{\mathtt{ff}\mathtt{.}\mathtt{k}\mathtt{1}}\cdot {\mathtt{add}}_{\mathrm{ff}.\mathrm{u}1}\left(t\right)+{\mathtt{add}}_{\mathtt{ff}\mathtt{.}\mathtt{k}\mathtt{2}}\cdot {\mathtt{add}}_{\mathrm{ff}.\mathrm{u}2}\left(t\right)\\ \mathtt{limiter}\mathtt{.}\mathtt{y}\left(t\right)=\mathrm{clamp}(\mathtt{limiter}\mathtt{.}\mathtt{u}\left(t\right),\mathtt{limiter}\mathtt{.}{\mathtt{y}}_{\mathtt{min}},\mathtt{limiter}\mathtt{.}{\mathtt{y}}_{\mathtt{max}})\\ {\mathtt{add}}_{\mathrm{sat}.\mathrm{y}}\left(t\right)={\mathtt{add}}_{\mathtt{sat}\mathtt{.}\mathtt{k}\mathtt{1}}\cdot {\mathtt{add}}_{\mathrm{sat}.\mathrm{u}1}\left(t\right)+{\mathtt{add}}_{\mathtt{sat}\mathtt{.}\mathtt{k}\mathtt{2}}\cdot {\mathtt{add}}_{\mathrm{sat}.\mathrm{u}2}\left(t\right)\\ {\mathtt{gain}}_{\mathrm{track}.\mathrm{y}}\left(t\right)={\mathtt{gain}}_{\mathtt{track}\mathtt{.}\mathtt{k}}\cdot {\mathtt{gain}}_{\mathrm{track}.\mathrm{u}}\left(t\right)\end{array}\right]$$

Source

"""
PID controller with limited output, back calculation anti-windup compensation, setpoint weighting and feed-forward

The transfer function is:

math y = k \left[e + \dfrac{1}{T_is}\left(e + \dfrac{y_{sat} - y}{N_iT_i}\right) + \dfrac{T_ds}{1 + {\dfrac{T_d}{N_d}s}}e \right] + k_{ff}u_

"""
component LimPID
  extends BlockComponents.Interfaces.SingleVariableController
  u_ff = RealInput() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "input", "x1": 450, "y1": -100, "x2": 550, "y2": 0, "rot": 90}
      },
      "tags": []
    }
  }
  add_p = BlockComponents.Math.Add(k1 = wp, k2 = -1) {
    "Dyad": {
      "placement": {
        "icon": {"iconName": "input", "x1": 100, "y1": 100, "x2": 200, "y2": 200, "rot": 0},
        "diagram": {"iconName": "input", "x1": 100, "y1": 90, "x2": 200, "y2": 190, "rot": 0}
      },
      "tags": []
    }
  }
  add_d = BlockComponents.Math.Add(k1 = wd, k2 = -1) {
    "Dyad": {
      "placement": {"icon": {"iconName": "input", "x1": 100, "y1": 300, "x2": 200, "y2": 400}}
    }
  }
  add_i = BlockComponents.Math.Add3(k2 = -1) {
    "Dyad": {
      "placement": {"icon": {"iconName": "input", "x1": 100, "y1": 500, "x2": 200, "y2": 600}}
    }
  }
  proportional = BlockComponents.Math.Gain(k = 1) {
    "Dyad": {
      "placement": {
        "icon": {"iconName": "input", "x1": 300, "y1": 100, "x2": 400, "y2": 200, "rot": 0},
        "diagram": {"iconName": "input", "x1": 300, "y1": 90, "x2": 400, "y2": 190, "rot": 0}
      },
      "tags": []
    }
  }
  derivative = Derivative(k = Td, T = max(Td / Nd, 1e-14), x0 = xd0) {
    "Dyad": {
      "placement": {"icon": {"iconName": "input", "x1": 300, "y1": 300, "x2": 400, "y2": 400}}
    }
  }
  integrator = Integrator(k = 1 / Ti, x0 = xi0) {
    "Dyad": {
      "placement": {"icon": {"iconName": "input", "x1": 300, "y1": 500, "x2": 400, "y2": 600}}
    }
  }
  add_pid = BlockComponents.Math.Add3() {
    "Dyad": {
      "placement": {
        "icon": {"iconName": "input", "x1": 500, "y1": 300, "x2": 600, "y2": 400, "rot": 0},
        "diagram": {"iconName": "input", "x1": 500, "y1": 120, "x2": 600, "y2": 220, "rot": 0}
      },
      "tags": []
    }
  }
  gain_pid = BlockComponents.Math.Gain(k = k) {
    "Dyad": {
      "placement": {
        "icon": {"iconName": "input", "x1": 700, "y1": 300, "x2": 800, "y2": 400, "rot": 0},
        "diagram": {"iconName": "input", "x1": 550, "y1": 310, "x2": 650, "y2": 410, "rot": 0}
      },
      "tags": []
    }
  }
  add_ff = BlockComponents.Math.Add(k2 = k_ff) {
    "Dyad": {
      "placement": {
        "icon": {"iconName": "input", "x1": 900, "y1": 300, "x2": 1000, "y2": 400, "rot": 0},
        "diagram": {"iconName": "input", "x1": 710, "y1": 340, "x2": 810, "y2": 440, "rot": 0}
      },
      "tags": []
    }
  }
  limiter = BlockComponents.Nonlinear.Limiter(y_max = y_max, y_min = y_min) {
    "Dyad": {
      "placement": {
        "icon": {"iconName": "input", "x1": 1100, "y1": 300, "x2": 1200, "y2": 400, "rot": 0},
        "diagram": {"iconName": "input", "x1": 850, "y1": 340, "x2": 950, "y2": 440, "rot": 0}
      },
      "tags": []
    }
  }
  add_sat = BlockComponents.Math.Add(k1 = 1, k2 = -1) {
    "Dyad": {
      "placement": {
        "icon": {"iconName": "input", "x1": 1100, "y1": 500, "x2": 1200, "y2": 600, "rot": 90},
        "diagram": {"iconName": "input", "x1": 800, "y1": 590, "x2": 900, "y2": 690, "rot": 90}
      },
      "tags": []
    }
  }
  gain_track = BlockComponents.Math.Gain(k = 1 / (k * Ni)) {
    "Dyad": {
      "placement": {
        "icon": {"iconName": "input", "x1": 500, "y1": 700, "x2": 600, "y2": 800, "rot": 180}
      }
    }
  }
  variable control_error::Real
  "Gain of controller"
  parameter k::Real = 1
  "Time constant of the integrator block"
  parameter Ti::Time = 0.5
  "Time constant of the derivative block"
  parameter Td::Time = 0.1
  "Maximum output"
  parameter y_max::Real = 1e300
  "Minimum output"
  parameter y_min::Real = -y_max
  "Set-point weight for proportional block"
  parameter wp::Real = 1
  "Set-point weight for derivative block"
  parameter wd::Real = 1
  "`Ni*Ti` is time constant of anti-windup compensation"
  parameter Ni::Real = 0.9
  "Maximum derivative gain. Higher the value of `Nd`, the more ideal the derivative block gets (less filtering, higher high-frequency gain)."
  parameter Nd::Real = 10
  "Gain of the feed-forward input"
  parameter k_ff::Real = 1
  "Initial guess value for integrator output"
  parameter xi0::Real = 0
  "Initial guess value for derivative output"
  parameter xd0::Real = 0
relations
  connect(add_p.y, proportional.u) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  connect(add_d.y, derivative.u) {"Dyad": {"edges": [{"S": 1, "E": 2}]}}
  connect(add_i.y, integrator.u) {"Dyad": {"edges": [{"S": 1, "E": 2}]}}
  connect(proportional.y, add_pid.u1) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  connect(derivative.y, add_pid.u2) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 452.5, "y": 350}, {"x": 452.5, "y": 170}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  connect(integrator.y, add_pid.u3) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 490, "y": 550}, {"x": 490, "y": 200}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  connect(add_pid.y, gain_pid.u) {
    "Dyad": {
      "edges": [
        {
          "S": 1,
          "M": [
            {"x": 650, "y": 170},
            {"x": 650, "y": 260},
            {"x": 510, "y": 260},
            {"x": 510, "y": 360}
          ],
          "E": 2
        }
      ],
      "renderStyle": "standard"
    }
  }
  connect(gain_pid.y, add_ff.u1) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  connect(add_ff.y, limiter.u) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  connect(limiter.y, add_sat.u1) {
    "Dyad": {
      "edges": [
        {
          "S": 1,
          "M": [{"x": 970, "y": 390}, {"x": 970, "y": 500}, {"x": 880, "y": 500}],
          "E": 2
        }
      ],
      "renderStyle": "standard"
    }
  }
  connect(add_sat.y, gain_track.u) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 850, "y": 750}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  connect(gain_track.y, add_i.u3) {
    "Dyad": {"edges": [{"S": 1, "M": [{"x": 75, "y": 750}, {"x": 75, "y": 580}], "E": 2}]}
  }
  control_error = u_s - u_m
  connect(limiter.y, y) {
    "Dyad": {
      "edges": [
        {
          "S": 1,
          "M": [{"x": 970, "y": 390}, {"x": 970, "y": 500}, {"x": 1050, "y": 500}],
          "E": 2
        }
      ],
      "renderStyle": "standard"
    }
  }
  connect(add_ff.u2, u_ff) {
    "Dyad": {
      "edges": [
        {
          "S": 1,
          "M": [{"x": 670, "y": 420}, {"x": 670, "y": 80}, {"x": 500, "y": 80}],
          "E": 2
        }
      ],
      "renderStyle": "standard"
    }
  }
  connect(add_ff.y, add_sat.u2) {
    "Dyad": {
      "edges": [
        {
          "S": 1,
          "M": [{"x": 830, "y": 390}, {"x": 830, "y": 545}, {"x": 820, "y": 545}],
          "E": 2
        }
      ],
      "renderStyle": "standard"
    }
  }
  connect(add_p.u1, u_s) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 20, "y": 110}, {"x": 20, "y": 270}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  connect(add_d.u1, u_s) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 20, "y": 320}, {"x": 20, "y": 270}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  connect(add_i.u1, u_s) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 20, "y": 520}, {"x": 20, "y": 270}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  connect(u_m, add_p.u2) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 50, "y": 730}, {"x": 50, "y": 170}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  connect(add_i.u2, u_m) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 50, "y": 550}, {"x": 50, "y": 730}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  connect(add_d.u2, u_m) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 50, "y": 380}, {"x": 50, "y": 730}], "E": 2}],
      "renderStyle": "standard"
    }
  }
metadata {
  "Dyad": {
    "labels": [{"label": "$(instance)", "x": 500, "y": 1100, "rot": 0}],
    "icons": {"default": "dyad://BlockComponents/LimPID.svg"}
  }
}
end

Flattened Source

"""
PID controller with limited output, back calculation anti-windup compensation, setpoint weighting and feed-forward

The transfer function is:

math y = k \left[e + \dfrac{1}{T_is}\left(e + \dfrac{y_{sat} - y}{N_iT_i}\right) + \dfrac{T_ds}{1 + {\dfrac{T_d}{N_d}s}}e \right] + k_{ff}u_

"""
component LimPID
  "Connector of setpoint input signal"
  u_s = RealInput() {
    "Dyad": {
      "placement": {
        "icon": {"iconName": "default", "x1": -100, "y1": 220, "x2": 0, "y2": 320, "rot": 0},
        "diagram": {"iconName": "default", "x1": -100, "y1": 220, "x2": 0, "y2": 320, "rot": 0}
      }
    }
  }
  "Connector of measurement input signal"
  u_m = RealInput() {
    "Dyad": {
      "placement": {
        "icon": {"iconName": "default", "x1": -100, "y1": 680, "x2": 0, "y2": 780, "rot": 0},
        "diagram": {"iconName": "default", "x1": -100, "y1": 680, "x2": 0, "y2": 780, "rot": 0}
      }
    }
  }
  "Connector of actuator output signal"
  y = RealOutput() {
    "Dyad": {
      "placement": {
        "icon": {"iconName": "output", "x1": 1000, "y1": 460, "x2": 1100, "y2": 560, "rot": 0},
        "diagram": {"iconName": "output", "x1": 1000, "y1": 460, "x2": 1100, "y2": 560, "rot": 0}
      }
    }
  }
  u_ff = RealInput() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "input", "x1": 450, "y1": -100, "x2": 550, "y2": 0, "rot": 90}
      },
      "tags": []
    }
  }
  add_p = BlockComponents.Math.Add(k1 = wp, k2 = -1) {
    "Dyad": {
      "placement": {
        "icon": {"iconName": "input", "x1": 100, "y1": 100, "x2": 200, "y2": 200, "rot": 0},
        "diagram": {"iconName": "input", "x1": 100, "y1": 90, "x2": 200, "y2": 190, "rot": 0}
      },
      "tags": []
    }
  }
  add_d = BlockComponents.Math.Add(k1 = wd, k2 = -1) {
    "Dyad": {
      "placement": {"icon": {"iconName": "input", "x1": 100, "y1": 300, "x2": 200, "y2": 400}}
    }
  }
  add_i = BlockComponents.Math.Add3(k2 = -1) {
    "Dyad": {
      "placement": {"icon": {"iconName": "input", "x1": 100, "y1": 500, "x2": 200, "y2": 600}}
    }
  }
  proportional = BlockComponents.Math.Gain(k = 1) {
    "Dyad": {
      "placement": {
        "icon": {"iconName": "input", "x1": 300, "y1": 100, "x2": 400, "y2": 200, "rot": 0},
        "diagram": {"iconName": "input", "x1": 300, "y1": 90, "x2": 400, "y2": 190, "rot": 0}
      },
      "tags": []
    }
  }
  derivative = Derivative(k = Td, T = max(Td / Nd, 1e-14), x0 = xd0) {
    "Dyad": {
      "placement": {"icon": {"iconName": "input", "x1": 300, "y1": 300, "x2": 400, "y2": 400}}
    }
  }
  integrator = Integrator(k = 1 / Ti, x0 = xi0) {
    "Dyad": {
      "placement": {"icon": {"iconName": "input", "x1": 300, "y1": 500, "x2": 400, "y2": 600}}
    }
  }
  add_pid = BlockComponents.Math.Add3() {
    "Dyad": {
      "placement": {
        "icon": {"iconName": "input", "x1": 500, "y1": 300, "x2": 600, "y2": 400, "rot": 0},
        "diagram": {"iconName": "input", "x1": 500, "y1": 120, "x2": 600, "y2": 220, "rot": 0}
      },
      "tags": []
    }
  }
  gain_pid = BlockComponents.Math.Gain(k = k) {
    "Dyad": {
      "placement": {
        "icon": {"iconName": "input", "x1": 700, "y1": 300, "x2": 800, "y2": 400, "rot": 0},
        "diagram": {"iconName": "input", "x1": 550, "y1": 310, "x2": 650, "y2": 410, "rot": 0}
      },
      "tags": []
    }
  }
  add_ff = BlockComponents.Math.Add(k2 = k_ff) {
    "Dyad": {
      "placement": {
        "icon": {"iconName": "input", "x1": 900, "y1": 300, "x2": 1000, "y2": 400, "rot": 0},
        "diagram": {"iconName": "input", "x1": 710, "y1": 340, "x2": 810, "y2": 440, "rot": 0}
      },
      "tags": []
    }
  }
  limiter = BlockComponents.Nonlinear.Limiter(y_max = y_max, y_min = y_min) {
    "Dyad": {
      "placement": {
        "icon": {"iconName": "input", "x1": 1100, "y1": 300, "x2": 1200, "y2": 400, "rot": 0},
        "diagram": {"iconName": "input", "x1": 850, "y1": 340, "x2": 950, "y2": 440, "rot": 0}
      },
      "tags": []
    }
  }
  add_sat = BlockComponents.Math.Add(k1 = 1, k2 = -1) {
    "Dyad": {
      "placement": {
        "icon": {"iconName": "input", "x1": 1100, "y1": 500, "x2": 1200, "y2": 600, "rot": 90},
        "diagram": {"iconName": "input", "x1": 800, "y1": 590, "x2": 900, "y2": 690, "rot": 90}
      },
      "tags": []
    }
  }
  gain_track = BlockComponents.Math.Gain(k = 1 / (k * Ni)) {
    "Dyad": {
      "placement": {
        "icon": {"iconName": "input", "x1": 500, "y1": 700, "x2": 600, "y2": 800, "rot": 180}
      }
    }
  }
  variable control_error::Real
  "Gain of controller"
  parameter k::Real = 1
  "Time constant of the integrator block"
  parameter Ti::Time = 0.5
  "Time constant of the derivative block"
  parameter Td::Time = 0.1
  "Maximum output"
  parameter y_max::Real = 1e300
  "Minimum output"
  parameter y_min::Real = -y_max
  "Set-point weight for proportional block"
  parameter wp::Real = 1
  "Set-point weight for derivative block"
  parameter wd::Real = 1
  "`Ni*Ti` is time constant of anti-windup compensation"
  parameter Ni::Real = 0.9
  "Maximum derivative gain. Higher the value of `Nd`, the more ideal the derivative block gets (less filtering, higher high-frequency gain)."
  parameter Nd::Real = 10
  "Gain of the feed-forward input"
  parameter k_ff::Real = 1
  "Initial guess value for integrator output"
  parameter xi0::Real = 0
  "Initial guess value for derivative output"
  parameter xd0::Real = 0
relations
  connect(add_p.y, proportional.u) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  connect(add_d.y, derivative.u) {"Dyad": {"edges": [{"S": 1, "E": 2}]}}
  connect(add_i.y, integrator.u) {"Dyad": {"edges": [{"S": 1, "E": 2}]}}
  connect(proportional.y, add_pid.u1) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  connect(derivative.y, add_pid.u2) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 452.5, "y": 350}, {"x": 452.5, "y": 170}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  connect(integrator.y, add_pid.u3) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 490, "y": 550}, {"x": 490, "y": 200}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  connect(add_pid.y, gain_pid.u) {
    "Dyad": {
      "edges": [
        {
          "S": 1,
          "M": [
            {"x": 650, "y": 170},
            {"x": 650, "y": 260},
            {"x": 510, "y": 260},
            {"x": 510, "y": 360}
          ],
          "E": 2
        }
      ],
      "renderStyle": "standard"
    }
  }
  connect(gain_pid.y, add_ff.u1) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  connect(add_ff.y, limiter.u) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  connect(limiter.y, add_sat.u1) {
    "Dyad": {
      "edges": [
        {
          "S": 1,
          "M": [{"x": 970, "y": 390}, {"x": 970, "y": 500}, {"x": 880, "y": 500}],
          "E": 2
        }
      ],
      "renderStyle": "standard"
    }
  }
  connect(add_sat.y, gain_track.u) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 850, "y": 750}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  connect(gain_track.y, add_i.u3) {
    "Dyad": {"edges": [{"S": 1, "M": [{"x": 75, "y": 750}, {"x": 75, "y": 580}], "E": 2}]}
  }
  control_error = u_s - u_m
  connect(limiter.y, y) {
    "Dyad": {
      "edges": [
        {
          "S": 1,
          "M": [{"x": 970, "y": 390}, {"x": 970, "y": 500}, {"x": 1050, "y": 500}],
          "E": 2
        }
      ],
      "renderStyle": "standard"
    }
  }
  connect(add_ff.u2, u_ff) {
    "Dyad": {
      "edges": [
        {
          "S": 1,
          "M": [{"x": 670, "y": 420}, {"x": 670, "y": 80}, {"x": 500, "y": 80}],
          "E": 2
        }
      ],
      "renderStyle": "standard"
    }
  }
  connect(add_ff.y, add_sat.u2) {
    "Dyad": {
      "edges": [
        {
          "S": 1,
          "M": [{"x": 830, "y": 390}, {"x": 830, "y": 545}, {"x": 820, "y": 545}],
          "E": 2
        }
      ],
      "renderStyle": "standard"
    }
  }
  connect(add_p.u1, u_s) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 20, "y": 110}, {"x": 20, "y": 270}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  connect(add_d.u1, u_s) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 20, "y": 320}, {"x": 20, "y": 270}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  connect(add_i.u1, u_s) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 20, "y": 520}, {"x": 20, "y": 270}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  connect(u_m, add_p.u2) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 50, "y": 730}, {"x": 50, "y": 170}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  connect(add_i.u2, u_m) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 50, "y": 550}, {"x": 50, "y": 730}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  connect(add_d.u2, u_m) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 50, "y": 380}, {"x": 50, "y": 730}], "E": 2}],
      "renderStyle": "standard"
    }
  }
metadata {
  "Dyad": {
    "labels": [{"label": "$(instance)", "x": 500, "y": 1100, "rot": 0}],
    "icons": {"default": "dyad://BlockComponents/LimPID.svg"}
  }
}
end

Test Cases

No test cases defined.

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