Put resistors, capacitors, diodes, transistors, op-amps, logic gates, a PID, sensors (NTC, LM35, LDR, tachometer, pressure, ultrasonic) and actuators (DC motor, heater, servo, fan, tank with valve) in one schematic. Simulate over time with a scope, check whether the whole system and each sensor are stable, and get the transfer function, root locus and Bode margins.
Yes: connect a reference, a PID, a DC motor and a tachometer; you get the speed, torque and stability analysis.
The subsystem table shows the own poles of every sensor and of the whole loop.
A real system mixes domains: a sensor measures temperature, a comparator or a PID decides, a transistor or an H-bridge drives a motor, and the motor changes what the sensor measures. This tool simulates it all together over time. This guide explains the ideas behind it (differential equations, time constants, poles and feedback loops) with a verified example.
Elements that store energy, such as a capacitor (charge), an inductor (current), a spinning mass (speed) or a tank (level), have a state variable that changes according to a differential equation. The simulator writes those equations for the whole circuit and integrates them step by step. In an electric circuit, the equations come from Kirchhoff's laws and from each component: i = C·dv/dt in a capacitor, v = L·di/dt in an inductor.
A 5 V source charges a 10 µF capacitor through a 10 kΩ resistor, starting from zero.
The simulator gives v = 3.161 V and i = 183.9 µA at t = 0.1 s, the pole at −10 (τ = 100 ms) and the same G(s). With a square-wave source, you see the capacitor charge and discharge every half period.
Linearizing the system at an instant, the tool computes its poles. If they all have negative real parts, any disturbance dies out: the system is stable. The further left, the faster; a pair of complex poles means oscillation, as in an underdamped RLC circuit. In a control loop, a controller (PID, ON/OFF) compares the sensor's measurement with the reference and acts. Too much gain or a delay in the loop can make it unstable, and the tool has examples of both cases.
Diodes, transistors in cutoff or saturation, comparators with hysteresis and ON/OFF controllers are not linear. The simulator treats them as they really behave over time. That is why the linearized poles may say "stable" while the simulation oscillates, as in an ON/OFF thermostat; the tool warns you when that happens.
C. K. Alexander and M. N. O. Sadiku, Fundamentals of Electric Circuits (McGraw-Hill); K. Ogata, System Dynamics (Pearson). Simuveliq is not affiliated with these authors or publishers.
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