State Estimation + MPC Co-Design — Making Predictive Control Work on Real Systems

Public reference use case (by others): This page summarizes publicly available reference implementations and papers. Not client results of Dr. Rafal Noga.

Why This Matters (Executive Summary)

• MPC that “works in simulation but not on the real system” almost always fails because of estimation problems — latency, drift, noise, or insufficient update rate in the state estimate.
• Co-designing the estimator and controller — with explicit latency budgets, fusion strategies, and fallback logic — is what makes MPC deployable on physical hardware.
• Reference implementations demonstrate: combined NMPC + MHE at 1 ms total compute on overhead cranes, servo bandwidth increased from 147 Hz to 208 Hz via explicit MPC + observer, and model-free incremental MPC using time-delay estimation that avoids explicit plant identification entirely.
• This pattern applies to any system where the controller needs states that are not directly measured: intralogistics, precision motion, robotics, and process control.

The Design Pattern Explained

State estimation and MPC are not independent modules. The estimator must produce state estimates at the rate, latency, and accuracy that the controller requires. When vision-based sensing introduces 50 ms of latency, the controller must either predict ahead or extrapolate — and this prediction must be co-designed with the MPC horizon.

Three main estimation approaches appear in the reference implementations:

1. Moving Horizon Estimation (MHE): an optimization-based estimator that, like MPC, solves a constrained problem at each step. MHE naturally handles constraints on states (e.g., “this temperature cannot be negative”) and provides consistency with the NMPC formulation.
2. Extended state observers: augment the plant model with disturbance states, enabling offset-free control without integral action in the MPC cost function. This is particularly effective for servo systems with persistent load disturbances.
3. Sensor fusion (EKF, complementary filters): combine complementary sensors — visual-inertial odometry with proprioceptive sensors, or position sensors with current measurements — to produce low-latency, high-rate estimates matched to the controller’s timing.

The key engineering principle is that latency is a design parameter, not an afterthought. Every millisecond of estimation delay either reduces control bandwidth or must be explicitly compensated.

Applications & Reference Implementations

Combined NMPC + MHE for Overhead Crane — Intralogistics

Nonlinear MPC was paired with Nonlinear Moving Horizon Estimation on an overhead crane system, using automatic code generation to achieve a combined average execution time of approximately 1.02 ms (peak 1.17 ms) against a 10 ms sampling time. The system validated point-to-point motion, disturbance rejection, and servo-tracking in hardware experiments. This demonstrates that optimization-based estimation and control can run together in real time on standard computing hardware, with a comfortable margin below the sampling period. The automatic code generation approach (ACADO toolkit) is directly transferable to industrial crane and gantry applications.¹

Explicit MPC + Extended State Observer for Linear Motor Servo — Precision Motion

A two-degree-of-freedom control architecture combining Explicit MPC with a Differential-Compensated Extended State Observer (DCESO) was applied to a linear motor positioning servo. The explicit MPC eliminates online optimization by pre-computing the control law as a piecewise-affine function of the state. Position loop bandwidth increased from 147 Hz to 208 Hz (a 41% improvement), and step-response settling time dropped from 5.38 ms to 3.13 ms (5% criterion). The extended state observer estimates disturbance forces in real time, enabling offset-free tracking without integral action in the MPC formulation.²

Incremental MPC with Time-Delay Estimation — Robotic Manipulator

An incremental MPC method was validated on a real 3-DoF robot manipulator, using time-delay estimation to construct an incremental model that avoids explicit plant identification entirely. This is significant because traditional MPC requires an accurate dynamic model, which can be costly to obtain and brittle when dynamics change (tool changes, wear, payload variation). The controller runs on a standard PC and was demonstrated with Maxon motors and incremental encoders. The approach treats unmodeled dynamics as disturbances estimated from delayed measurements, making it robust to model mismatch without requiring system re-identification.³

VIO + Leg Odometry Fusion for NMPC Locomotion — Quadruped Robotics (Solo12)

Visual-Inertial Odometry (VIO) was fused with leg odometry to support NMPC-based locomotion on the Solo12 quadruped robot, including outdoor experiments. The estimation pipeline runs an EKF at 200 Hz feeding an MPC at 20 Hz, with low-level control at 1 kHz. Neither VIO alone (which suffers from latency and dropout) nor leg odometry alone (which drifts) provides sufficient state quality for dynamic locomotion. The fusion approach addresses complementary failure modes: vision provides absolute drift correction while proprioception provides high-rate, low-latency velocity estimates.⁴

Perceptive Locomotion NMPC with Terrain Estimation — ANYmal (ETH Zurich)

A perception-planning-control pipeline centered on nonlinear MPC at 100 Hz was validated on the ANYmal quadruped robot. Terrain is encoded as convex foothold constraints plus a signed-distance field for collision avoidance, with perception running at 20 Hz and whole-body torque control at 400 Hz. The estimation layer must provide terrain geometry and robot state at rates and latencies that match the controller’s needs — a clear example of co-design where the perception system’s output format (convex constraint sets) is chosen specifically to be consumable by the MPC solver.⁵

NMPC for Magnetic Levitation with State Estimation — Laboratory Demonstration

Real-time NMPC was experimentally demonstrated on a fast nonlinear magnetic levitation plant, compared against a PID baseline. The system is open-loop unstable, meaning the controller cannot function without continuous state estimation. NMPC reported better control performance than PID, illustrating that for inherently unstable systems, the estimation-control co-design determines whether the system can operate at all, not merely how well it performs.⁶

What This Means for Your Operations

• If your MPC project stalled during commissioning, the root cause is likely estimation. Audit the latency, update rate, and noise characteristics of your state estimates before re-tuning the controller.
• Latency budgets are non-negotiable: for a 100 Hz MPC, the estimator must deliver states in under 5 ms. Document and verify these budgets during design.
• Sensor fusion is not optional for mobile or multi-axis systems: no single sensor modality provides the rate, accuracy, and robustness needed for dynamic control.
• MHE is underused in industry: if your NMPC already solves an optimization at each step, adding MHE uses the same solver infrastructure and provides constraint-consistent state estimates.

How We Deliver This (Engagement Model)

• Phase 0: NDA + data request — characterize available sensors, measurement rates, latencies, and current estimation approach.
• Phase 1: Fixed-scope discovery — estimation architecture design, latency budget analysis, and feasibility of MPC co-design.
• Phase 2: Implementation + validation + commissioning — estimator development, MPC integration, Hardware-In-the-Loop testing, and field validation.
• Phase 3: Monitoring + training + scaling — estimation health dashboards, degraded-mode fallback logic, and expansion to additional axes or units.

Typical KPIs to Track

• Estimation quality: state estimation error (RMS), estimator update rate, end-to-end latency (sensor to controller input)
• Control performance: tracking error, settling time, bandwidth, constraint violation rate
• Robustness: performance under sensor dropout, degraded-mode behavior, time to recover from estimation reset
• Compute margin: solver time vs. sampling period ratio (target: peak solve time below 50% of sampling period)

Risks & Prerequisites

• Sensor characterization: every sensor’s noise, bias, latency, and failure modes must be documented. This is non-negotiable for co-design.
• Compute budget: running both MHE and NMPC doubles the optimization workload. Code generation tools (ACADO, acados, CasADi) are essential for meeting real-time constraints.
• Fallback logic: what happens when the estimator diverges or a sensor fails? Degraded-mode operation (e.g., fallback to reduced-order observer) must be designed, not improvised.
• Calibration and initialization: estimators need initial conditions. Start-up procedures and sensor calibration routines are part of the deliverable.

FAQ

Q: When should I use MHE instead of an EKF? Use MHE when you have state constraints (e.g., physical bounds on temperatures, positions, or concentrations) that the estimator must respect, or when the system is highly nonlinear and the EKF linearization introduces unacceptable errors. MHE is more computationally expensive but provides constraint-consistent estimates.

Q: Can I use machine-learning-based estimation with MPC? Yes, but with care. Neural-network-based estimators can provide fast inference, but they do not naturally handle constraints and their failure modes are less predictable. A common pattern is to use ML for perception (terrain maps, object detection) and optimization-based estimation for the control-relevant states.

Q: How much does estimation latency actually matter? Every millisecond of latency effectively shortens your MPC prediction horizon by one step. For a 100 Hz controller, 10 ms of latency means the controller is always “one step behind” reality. For unstable systems (magnetic levitation, balancing), this can be the difference between stable operation and failure.

Q: What if we cannot add more sensors? State observers and soft sensors can often reconstruct unmeasured states from available measurements. The key question is observability: can the states you need be inferred from what you measure? A fixed-scope discovery engagement includes an observability analysis for your specific system.

Book a 30-Minute Discovery Call

Ready to explore whether this pattern fits your system?

Dr. Rafal Noga — Independent APC/MPC Consultant

Email me | noga.es

Fixed-scope discovery — NDA-first — DACH on-site available

Public References

Footnotes

1. Debrouwere et al., “Combined NMPC + NMHE for overhead crane control” (KU Leuven / University of Freiburg, 2014). PDF ↩

2. “Explicit MPC + ESO servo algorithm for linear motor positioning” (MDPI Actuators, 2025). Link ↩

3. “Incremental MPC exploiting time-delay estimation for robot manipulator control” (TUM / DLR). PDF ↩

4. Dhedin et al., “Visual-Inertial and Leg Odometry Fusion for Dynamic Locomotion” (arXiv, 2022). PDF ↩

5. “Perceptive Locomotion through Nonlinear Model Predictive Control” (arXiv, 2022). PDF ↩

6. Novotny, “Magnetic levitation: real-time NMPC demonstrated experimentally vs PID baseline” (Springer, 2025). Link ↩