Block Diagram Examples

Control system diagrams with transfer functions, feedback loops, and export to LaTeX/Simulink.

PID Controller

Classic proportional-integral-derivative controller with feedback.

DSL Code

diagram "PID Controller"

  shape ref as @box label: "Reference"
  shape sum as @junction label: "+/-"
  shape pid as @transfer-fn label: "PID"
  shape plant as @transfer-fn label: "Plant\nG(s)"
  shape output as @box label: "Output"

  ref -> sum label: "r(t)"
  sum -> pid label: "e(t)"
  pid -> plant label: "u(t)"
  plant -> output label: "y(t)"
  output -> sum label: "feedback"

Generated SVG

Generated SVG

Transfer Function

$$C(s) = K_p + \frac{K_i}{s} + K_d s$$

Where:

• $K_p$ = Proportional gain
• $K_i$ = Integral gain
• $K_d$ = Derivative gain

Control Law

$$u(t) = K_p e(t) + K_i \int_0^t e(\tau) d\tau + K_d \frac{de(t)}{dt}$$

Use Cases

• Temperature control
• Motor speed control
• Robotic arm positioning
• Flight control systems

Feedback System

Generic feedback control system with forward and feedback paths.

DSL Code

diagram "Feedback Control System" direction: LR

  # Forward path
  shape input as @box label: "Input\nR(s)"
  shape error as @summing-junction label: "Σ"
  shape controller as @transfer-fn label: "Controller\nC(s)"
  shape plant as @transfer-fn label: "Plant\nG(s)"
  shape output as @box label: "Output\nY(s)"

  # Feedback path
  shape sensor as @transfer-fn label: "Sensor\nH(s)"

  # Disturbance
  shape disturbance as @box label: "Disturbance\nD(s)"
  shape dist_sum as @summing-junction label: "Σ"

  # Forward connections
  input -> error label: "+"
  error -> controller
  controller -> dist_sum label: "+"
  disturbance -> dist_sum label: "+"
  dist_sum -> plant
  plant -> output

  # Feedback path
  output -> sensor
  sensor -> error label: "-"

Generated SVG

Generated SVG

Closed-Loop Transfer Function

$$\frac{Y(s)}{R(s)} = \frac{C(s)G(s)}{1 + C(s)G(s)H(s)}$$

Open-Loop vs Closed-Loop

Open-Loop (no feedback):

• Simple design
• No self-correction
• Sensitive to disturbances

Closed-Loop (with feedback):

• Self-correcting
• Reduced sensitivity
• Improved stability

Transfer Function Chain

Series connection of multiple transfer functions.

DSL Code

diagram "Multi-Stage Amplifier" direction: LR

  shape input as @box label: "Input"
  shape stage1 as @transfer-fn label: "Stage 1\nA₁(s)"
  shape stage2 as @transfer-fn label: "Stage 2\nA₂(s)"
  shape stage3 as @transfer-fn label: "Stage 3\nA₃(s)"
  shape output as @box label: "Output"

  input -> stage1
  stage1 -> stage2
  stage2 -> stage3
  stage3 -> output

Generated SVG

Generated SVG

Overall Transfer Function

For series connection: $$H(s) = A_1(s) \cdot A_2(s) \cdot A_3(s)$$

Example: $$H(s) = \frac{10}{s+1} \cdot \frac{5}{s+10} \cdot \frac{2}{s+100}$$

State-Space Representation

Modern control representation using state variables.

DSL Code

diagram "State-Space System" direction: TB

  # Input
  shape u as @box label: "Input\nu(t)"

  # State equations
  shape B as @gain label: "B"
  shape integrator as @transfer-fn label: "1/s"
  shape A as @gain label: "A"
  shape C as @gain label: "C"
  shape D as @gain label: "D"

  # Output
  shape y as @box label: "Output\ny(t)"

  # State feedback
  shape sum1 as @summing-junction label: "Σ"
  shape sum2 as @summing-junction label: "Σ"

  # Connections
  u -> B
  B -> sum1 label: "+"
  sum1 -> integrator label: "ẋ(t)"
  integrator -> A label: "x(t)"
  A -> sum1 label: "+"
  integrator -> C
  C -> sum2 label: "+"
  u -> D
  D -> sum2 label: "+"
  sum2 -> y

Generated SVG

Generated SVG

State-Space Equations

$$\dot{x}(t) = Ax(t) + Bu(t)$$ $$y(t) = Cx(t) + Du(t)$$

Where:

• $x(t)$ = State vector
• $u(t)$ = Input vector
• $y(t)$ = Output vector
• $A$ = System matrix
• $B$ = Input matrix
• $C$ = Output matrix
• $D$ = Feedthrough matrix

Parallel Paths

Multiple parallel signal paths that combine.

DSL Code

diagram "Parallel PID Controller" direction: LR

  shape error as @box label: "Error\ne(t)"

  # Parallel paths
  shape Kp as @gain label: "Kp"
  shape Ki as @transfer-fn label: "Ki/s"
  shape Kd as @transfer-fn label: "Kd·s"

  # Sum
  shape sum as @summing-junction label: "Σ"
  shape output as @box label: "Output\nu(t)"

  # Connections
  error -> Kp -> sum label: "+"
  error -> Ki -> sum label: "+"
  error -> Kd -> sum label: "+"
  sum -> output

Generated SVG

Generated SVG

Parallel Transfer Function

For parallel paths: $$H(s) = H_1(s) + H_2(s) + H_3(s)$$

PID example: $$C(s) = K_p + \frac{K_i}{s} + K_d s$$

Block Diagram Elements

Runiq provides specialized shapes for control systems:

Basic Blocks

Shape	Syntax	Use Case
Box	@box	Input/output, reference
Transfer Function	@transfer-fn	System dynamics $G(s)$
Gain	@gain	Constant multiplier $K$
Summing Junction	@summing-junction	Addition/subtraction $\Sigma$
Junction	@junction	Signal split point
Integrator	@transfer-fn	$\frac{1}{s}$ or $\int$
Differentiator	@transfer-fn	$s$ or $\frac{d}{dt}$

Common Transfer Functions

# First-order lag
shape tf1 as @transfer-fn label: "1/(τs+1)"

# Second-order system
shape tf2 as @transfer-fn label: "ωₙ²/(s²+2ζωₙs+ωₙ²)"

# Integrator
shape int as @transfer-fn label: "1/s"

# Differentiator
shape diff as @transfer-fn label: "s"

# Delay
shape delay as @transfer-fn label: "e^(-τs)"

# Lead-lag compensator
shape comp as @transfer-fn label: "(s+z)/(s+p)"

Complete Examples

Motor Speed Control

diagram "DC Motor Speed Control" direction: LR

  # Input
  shape ref as @box label: "Desired\nSpeed"

  # Controller
  shape error as @summing-junction label: "Σ"
  shape pid as @transfer-fn label: "PID\nController"

  # Motor model
  shape motor as @transfer-fn label: "Motor\nK/(Js+b)"

  # Tachometer (sensor)
  shape tacho as @gain label: "Kt"

  # Output
  shape speed as @box label: "Actual\nSpeed"

  # Connections
  ref -> error label: "+"
  error -> pid
  pid -> motor label: "Voltage"
  motor -> speed
  speed -> tacho
  tacho -> error label: "-"

Aircraft Pitch Control

diagram "Aircraft Pitch Control" direction: LR

  # Reference
  shape theta_ref as @box label: "θ_ref"

  # Autopilot
  shape error as @summing-junction label: "Σ"
  shape autopilot as @transfer-fn label: "Autopilot\nC(s)"

  # Elevator actuator
  shape actuator as @transfer-fn label: "Actuator\n1/(τs+1)"

  # Aircraft dynamics
  shape aircraft as @transfer-fn label: "Aircraft\nG(s)"

  # Pitch angle sensor
  shape gyro as @gain label: "Kg"

  # Output
  shape theta as @box label: "θ"

  # Disturbance (wind)
  shape wind as @box label: "Wind"
  shape wind_sum as @summing-junction label: "Σ"

  # Connections
  theta_ref -> error label: "+"
  error -> autopilot
  autopilot -> actuator
  actuator -> wind_sum label: "+"
  wind -> wind_sum label: "+"
  wind_sum -> aircraft
  aircraft -> theta
  theta -> gyro
  gyro -> error label: "-"

Export Options

LaTeX/TikZ

Generate publication-quality diagrams for papers:

\begin{tikzpicture}[auto, node distance=2cm]
  \node [input] (input) {$R(s)$};
  \node [sum, right of=input] (sum) {$\Sigma$};
  \node [block, right of=sum] (controller) {$C(s)$};
  \node [block, right of=controller] (plant) {$G(s)$};
  \node [output, right of=plant] (output) {$Y(s)$};

  \draw [->] (input) -- (sum);
  \draw [->] (sum) -- (controller);
  \draw [->] (controller) -- (plant);
  \draw [->] (plant) -- (output);
  \draw [->] (output) |- (sum) node[near end] {$-$};
\end{tikzpicture}

Simulink

Generate .mdl files for MATLAB Simulink:

• Drag-and-drop compatible
• Preserves transfer functions
• Ready for simulation
• Includes feedback loops

# Export to Simulink
runiq pid-controller.runiq --export simulink -o pid.mdl

# Open in MATLAB
matlab -r "open_system('pid.mdl')"

Analysis Methods

Frequency Response

Bode Plot: Magnitude and phase vs. frequency

• Gain margin
• Phase margin
• Crossover frequencies

Nyquist Plot: Polar plot in complex plane

• Stability analysis
• Encirclements of -1 point

Time Response

Step Response: System response to unit step

• Rise time
• Settling time
• Overshoot
• Steady-state error

Impulse Response: Response to delta function

• System characterization
• Natural frequencies

Best Practices

Signal Flow

• Use LR (left-right) direction for forward paths
• Use TB (top-bottom) for hierarchical systems
• Place feedback paths below forward paths

Transfer Function Labels

Use proper mathematical notation:

shape tf as @transfer-fn label: "K/(τs+1)"
shape tf2 as @transfer-fn label: "ωₙ²/(s²+2ζωₙs+ωₙ²)"

Support Unicode: τ, ω, ζ, θ, ϕ

Summing Junctions

Always label inputs with signs:

ref -> sum label: "+"
feedback -> sum label: "-"

Next Steps

• Electrical Circuits → - Analog schematics
• Digital Logic → - Gate-level design
• Flowcharts → - Process flows

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Download Examples

All example .runiq files are available in the GitHub repository.

git clone https://github.com/jgreywolf/runiq.git
cd runiq/examples/block-diagrams