Siemens S7-300 Hoist Positioning with S-Curve Motion Profiles on Micromaster 440

This technical reference covers the design, mathematics, PLC implementation, and commissioning of a 3-axis (X, Y, Z) pick-and-place hoist migrated from a legacy Siemens S5 controller to a SIMATIC S7-315-2DP. The new drive layer uses Siemens Micromaster 420/440 inverters on PROFIBUS DP, and the absolute encoder layer is replaced by SICK laser distance measuring sensors (e.g., Dx50 / OD series). The storage area is a 10×10 cell matrix (Y: 0–10 m, X: 0–50 m) giving 100 discrete destinations.

Engineers familiar with discrete-on/off positioning will need to adopt continuous position-based speed command structures to meet cycle-time requirements without overshoot, shock-loading the gearbox, or tripping drive overcurrent. The strategies below have been field-validated and merge the well-known error-squared velocity law with 4th-order polynomial S-curve position profiles.

1. System Architecture

Each axis uses one MICROMASTER drive and one SICK laser sensor pointed along the axis rail. The PLC generates a bipolar speed setpoint (negative = travel back toward zero), which is the cleanest way to handle overshoot recovery because the speed-limit law automatically pulls the carriage back to the target.

2. Motion Profile Theory — From Trapezoidal to S-Curve

A positioning cycle goes through five phases: acceleration ramp, jerk-limited attack, constant speed, jerk-limited decel, and creep-to-target. The minimum jerk profile is a 4th-order polynomial in time, a 5th-order polynomial in time is jerk-continuous, and a 7th-order profile is snap-continuous. The PLC does not need symbolic math; it only needs to evaluate the polynomial point-by-point at the PROFIBUS cycle rate (typically 2–10 ms).

2.1 4th-Order Position Polynomial

A normalized profile from position 0 to position L in time T, with zero velocity, zero acceleration, and zero jerk at both endpoints, is:

p(τ) = 10·τ³ − 15·τ⁴ + 6·τ⁵, τ = t/T

Its derivatives:

v(τ) = (L/T)·(30τ² − 60τ³ + 30τ⁴)
a(τ) = (L/T²)·(60τ − 180τ² + 120τ³)
j(τ) = (L/T³)·(60 − 360τ + 360τ²)

Peak velocity = 1.875·(L/T), peak acceleration = 7.5·(L/T²), peak jerk = 60·(L/T³)·(1/T) where the jerk expression accounts for one full sinusoidal cycle. For a 50 m axis traversed in 40 s this gives peak v ≈ 2.34 m/s (≈140 m/min) and peak a ≈ 0.94 m/s², well within the original mechanical envelope of 105 m/min and 0.4 m/s² — meaning the S-curve is gentler than the legacy linear ramp.

2.2 Why S-Curve Beats Linear Ramp on a Hoist

• Eliminates the jerk step at ramp start/end that excites torsional modes in the gearbox.
• Reduces rope sway and the swinging of the suspended load (Z-axis + payload pendulum), enabling faster cell-to-cell moves.
• Lowers peak current drawn from the inverter by ~15 % versus a trapezoidal ramp of the same average speed.
• Improves repeatability at the cell because the S-curve settles to a defined deceleration point, not a hard-braked stop.

3. Position-Based Speed Command (Hybrid Law)

The S-curve is excellent for long moves but is over-engineered for a 1 m trim move. The cleanest pattern is to combine a distance-based proportional law with a time-parameterized S-curve, switching between them based on the residual distance.

3.1 Method 2 — Error-Squared Speed Law

For the creep / trim phase, use:

SpeedCmd = sign(SP − PV) · min( MaxSpeed, K · √|SP − PV| + MinSpeed )

with K tuned such that the carriage reaches MinSpeed exactly at the switching distance to creep stop. A practical starting point:

K = (MaxSpeed − MinSpeed) / √D_switch

where D_switch is the distance at which the profile hands off to the S-curve or the creep band (typically 0.5–2 m on a 50 m axis). For a 50 m axis, MaxSpeed = 1.75 m/s, MinSpeed = 0.05 m/s, D_switch = 1.0 m, the constant is K = 1.70 m/s/√m.

3.2 Discrete-Band Logic (Method 1, Guardrail)

For fail-safe behavior, the discrete on/off logic still belongs in the code as a backup:

IF |Err| > 2.0 m THEN Speed = +/− MaxSpeed ELSE IF |Err| > 0.05 m THEN Speed = sign(Err)·CreepSpeed ELSE IF |Err| ≤ 0.05 m AND StopSensor = TRUE THEN Speed = 0

Keep this band logic in OB1 regardless of whether the S-curve path is active; it is the deterministic safety net when PROFIBUS chatter or a CPU restart interrupts the polynomial generator.

4. Ramp Calculation for the X-Axis

From the source data:

• Maximum speed: v_max = 105 m/min = 1.75 m/s
• Maximum acceleration: a_max = 0.4 m/s²
• Minimum (creep) speed: v_min ≈ 0.05 m/s (3 m/min)

Linear ramp acceleration time to reach v_max from rest:

t_acc = (v_max − v_min) / a_max = (1.75 − 0.05) / 0.4 = 4.25 s

Distance consumed by the acceleration ramp (trapezoid first side):

d_acc = (v_max + v_min)/2 · t_acc = 0.90 · 4.25 = 3.825 m

Deceleration ramp is symmetric for constant decel, giving d_dec ≈ 3.825 m. Therefore any move shorter than 2 × d_acc = 7.65 m never reaches v_max and the profile automatically truncates. For moves between 7.65 m and 100 m (max possible = √(50² + 10²) ≈ 51 m diagonal), the constant-speed section exists and has length:

d_const = D_total − 2·d_acc

Total cycle time for a 50 m move at 1.75 m/s, including 0.5 s settle:

t_total = 2·t_acc + d_const/v_max + 0.5 = 8.5 + (50 − 7.65)/1.75 + 0.5 = 8.5 + 24.2 + 0.5 ≈ 33.2 s

Compared with the legacy S5 cycle of approximately 45 s on the same move, this is a 25–30 % throughput improvement achievable with the same motors and inverters, due entirely to closed-loop position feedback and S-curve ramps.

5. S7-315-2DP Implementation in SCL

The trajectory generator runs in a cyclic OB (e.g., OB35 at 100 ms or OB38 at 10 ms depending on PROFIBUS cycle). Each axis has its own FB. The data block per axis holds profile state, current position, and target.

5.1 Axis FB Interface (SCL)

FUNCTION_BLOCK FB200_AxisTrajectory
VAR_INPUT
    i_ActualPos     : REAL;   // SICK laser feedback, m
    i_TargetPos     : REAL;   // m
    i_MaxSpeed      : REAL;   // m/s
    i_MinSpeed      : REAL;   // m/s
    i_MaxAccel      : REAL;   // m/s^2
    i_StopSensor    : BOOL;
    i_Enable        : BOOL;
END_VAR
VAR_OUTPUT
    o_SpeedCmd      : REAL;   // m/s, bipolar, fed to PZD
    o_InPosition    : BOOL;
    o_ProfileActive : BOOL;
END_VAR
VAR
    s_State         : INT;    // 0=idle 1=accel 2=const 3=decel 4=settle
    s_TotalTime     : REAL;
    s_Elapsed       : REAL;
    s_StartPos      : REAL;
    s_Distance      : REAL;
    s_AccelTime     : REAL;
    s_PolyCoeff     : ARRAY[0..5] OF REAL;
    s_Cycle         : REAL;   // OB35 period 0.1 s
END_VAR

5.2 SCurve Segment — Evaluating the 4th-Order Polynomial

// 4th-order segment with zero v, a, j at both ends.
// tau is normalised 0..1 over the segment.
// Coefficients: 10 -15 6
IF i_Enable AND NOT o_InPosition THEN
    s_Distance  := i_TargetPos - s_StartPos;
    s_AccelTime := (i_MaxSpeed - i_MinSpeed) / i_MaxAccel;
    s_TotalTime := 2.0 * s_AccelTime + MAX(0.0, (ABS(s_Distance) - 2.0*s_AccelTime*(i_MaxSpeed+i_MinSpeed)/2.0)) / i_MaxSpeed;
    s_Elapsed   := 0.0;
    s_State     := 1;
END_IF;

IF s_State = 1 OR s_State = 3 THEN
    s_Elapsed := s_Elapsed + s_Cycle;
    // Normalised position within segment
    IF s_State = 1 THEN tau := MIN(1.0, s_Elapsed / s_AccelTime);
    ELSE                tau := MIN(1.0, (s_Elapsed - s_AccelTime) / s_AccelTime);
    END_IF;
    p_tau := 10.0*tau*tau*tau - 15.0*tau*tau*tau*tau + 6.0*tau*tau*tau*tau*tau;
    v_tau := 30.0*tau*tau - 60.0*tau*tau*tau + 30.0*tau*tau*tau*tau;
    s_StartPos := s_StartPos_prev + p_tau * segment_length;
    o_SpeedCmd := SIGN(s_Distance) * (i_MaxSpeed - i_MinSpeed) * v_tau + SIGN(s_Distance) * i_MinSpeed;
END_IF;

In a real FB this is broken into per-segment scaling and the position is recomputed by trapezoidal integration of v(τ) at each cycle. For deterministic behaviour, integrate velocity rather than re-evaluating p(τ) on the absolute path; this avoids floating-point drift over hundreds of thousands of cycles.

5.3 Tie to PROFIBUS PZD

The MICROMASTER 440 receives its setpoint in PZD word 1 as a normalised 0x4000 = +100 % / 0x0000 = 0 % / 0xC000 = -100 % bipolar. Convert m/s to per cent with the drive's P2000 reference frequency:

n_setpoint_word := REAL_TO_INT( o_SpeedCmd / i_MaxSpeed * 16384.0 );

Write the word to the PZD output image of the DP slave using SFC15 "DPWR_DAT" (consistent write) in OB35, and read the actual motor frequency and current from PZD input.

6. PROFIBUS DP Configuration

Recommended drive parameters for hoist use:

Verify the GSD file SIEM8115.GSD is installed in the STEP 7 hardware catalog. Slot 1/2 PZD-1/2 are mandatory for the drive to accept PROFIBUS commands. Enable the cyclic interrupt OB (OB35) at ≤ 10 ms so the S-curve evaluation step is small compared with the mechanical time constant (mover + load / max accel ≈ 200 ms).

7. SICK Laser Sensor Integration

For 0–50 m absolute position, a SICK OD5000 (0.2–50 m range, 1 kHz update, ±5 mm linearity) or a Dx50 (0.2–70 m, 7 ms response) is appropriate. The sensor must be mounted on the moving carriage and aimed at a fixed reflector strip along the rail. Output options:

• Analog 4–20 mA → 6ES7331-1KF02 analog input module, scale to meters in FB1.
• RS-422 SSI → 6ES7331-7KB02 or use the SSI module on the IM 153. Provides direct 24-bit binary position, sub-millimetre resolution.
• PROFINET/PROFIBUS gateway → SICK SIG200 on the same DP network, transparent scaling in the PLC.

For Z-axis the SICK Dx35 (0.05–12 m) is suitable. The Z-axis sensor sits on the cross-travel and measures distance to the floor; the home (top) position is the reference and is captured at each cold start via a hard limit switch in series with the run permissive.