Simulator model

BHTune's built-in simulator uses one generic first-order-plus-dead-time (FOPDT) model. It is intended to make the tuning workflow reproducible and safe to exercise without a live DCS, PLC, or OPC DA gateway. The six process categories currently available in the form do not select six different physical models. They select process-specific MRFT tuning correlations and defaults while sharing the same simulated process equation.

Transfer function

The continuous-time transfer function is:

G(s) = K * exp(-theta*s) / (tau*s + 1)

where:

Symbol	Meaning
K	Process gain: the steady-state PV change per unit MV change
tau	Time constant, in seconds: how quickly the PV responds after the dead time
theta	Dead time, in seconds: how long the PV waits before responding to an MV change

Using an initial operating point, the equivalent differential equation is:

tau * dPV/dt = -(PV - PV0) + K * (MV - MV0)

PV0 and MV0 are the configured initial process value and manipulated value. The process starts at this operating point before the MRFT relay changes the MV.

Discrete simulation

The simulator advances once for each PV read. During one simulated interval, the MV is treated as constant, so the process uses the exact zero-order-hold solution of the first-order lag:

decay = exp(-delta_t / tau)

PV_next = PV * decay
        + (1 - decay) * (PV0 - K * MV0 + K * MV_delayed)

This is a closed-form update, not a numerical ODE approximation. delta_t is the configured simulator poll interval. In Demo mode it is fixed at 200 ms; Full mode uses the global [tuning].poll_interval_ms setting.

Dead time is represented by a queue of delayed MV samples. The queue length is approximately:

ceil(theta / delta_t)

The simulator's logical clock advances by delta_t on each PV read without sleeping for that amount of wall-clock time. This allows a complete synthetic tune to run quickly while keeping the model's timing deterministic.

Noise and initial conditions

Measurement noise is added after the process update. It is sampled uniformly from:

[-noise_amplitude, +noise_amplitude]

A zero noise amplitude disables noise. A fixed RNG seed produces the same noise sequence for the same simulator configuration and MV-write sequence within the same supported platform and build; the RNG algorithm is not a cross-version portability guarantee.

The initial PV is assumed to be the steady-state value for the initial MV. The configured PV and MV ranges constrain the tuning setup and initial values; they do not turn the simulator into a separate process model for each process category.

Relationship to MRFT and PID

During a tune, MRFT drives the simulated MV directly by writing the relay output. The simulator does not run a PID controller in the background. BHTune also contains a separate VirtualPid helper for closed-loop validation, but that helper is not part of SimulatorDriver and does not affect simulator tune results.

The selected DCS/PLC template remains meaningful in Simulator mode because it formats the calculated constants using that system's native conventions, such as gain versus proportional band and the applicable integral or derivative units. It changes result interpretation, not the FOPDT physics.

In Demo mode, Reverse controller action is the default convention for every process, and the process gain is constrained to positive values from 0.1 through 5.0.