Milan Vukov

Experimental validation of nonlinear MPC on an overhead crane using automatic code generation

Recent advances in improving the efficiency of nonlinear model predictive control (MPC) algorithms have made them suited for challenging mechatronic applications that require high sampling rates. We demonstrate this fact by applying a highly efficient nonlinear MPC algorithm to a laboratory-scale overhead crane setup, featuring a fast moving cart and a winch mechanism. The aim is to perform optimized point-to-point motions with varying line length while respecting actuator limits. In order to solve the resulting optimization problems in less than one millisecond, an automatically generated Gauss-Newton real-time iteration algorithm is employed. We show experimental results illustrating the control performance of the closed-loop system as well as the efficiency of the nonlinear MPC algorithm.

High-speed moving horizon estimation based on automatic code generation

Recent theoretical and algorithmic advances have led to efficient algorithms that allow for real-time optimisation of processes with fast nonlinear dynamics. This paper addresses the efficient implementation of algorithms for moving horizon estimation (MHE) for obtaining real-time estimates of process states or parameters that are not measured directly. To this end, we propose to combine the previously proposed concepts of real-time iteration schemes and automatic code generation to obtain highly efficient source code of MHE algorithms. This has led to major extensions of the ACADO Code Generation tool that automatically generates customised plain C code for both model predictive control (MPC) and MHE applications. As a proof of concept, we present numerical results of controlling a nonlinear ODE model by means of combined exported MHE and MPC algorithms in a closed-loop manner. These exported algorithms turn out to be significantly faster than their generically implemented counterparts.

Auto-generated algorithms for nonlinear model predictive control on long and on short horizons

We present a code generation strategy for handling long prediction horizons in the context of real-time nonlinear model predictive control (NMPC). Existing implementations of fast NMPC algorithms use the real-time iteration (RTI) scheme and a condensing technique to reduce the number of optimization variables. Condensing results in a much smaller, but dense quadratic program (QP) to be solved at every time step. While this approach is well suited for short horizons, it leads to unnecessarily long execution times for problem formulations with long horizon. This paper presents a new implementation of auto-generated NMPC code based on a structure exploiting auto-generated QP solver. Utilizing such a QP solver, the condensing step can be avoided and execution times scale linearly with the horizon length instead of cubically. Our simulation results show that this approach significantly decreases the execution time of NMPC with long horizons. For a nonlinear test problem that comprises 9 states and 3 controls on a horizon with 50 time steps, an improvement by a factor of 2 was observed, reducing the execution time for one RTI to below 4 milliseconds on a 3 GHz CPU.

Auto Generation of Implicit Integrators for Embedded NMPC with Microsecond Sampling Times

Abstract Algorithms for fast real-time Nonlinear Model Predictive Control (NMPC) for mechatronic systems face several challenges. They need to respect tight real-time constraints and need to run on embedded control hardware with limited computing power and memory. A combination of efficient online algorithms and code generation of explicit integrators was shown to be able to overcome these hurdles. This paper generalizes the idea of code generation to Implicit Runge-Kutta (IRK) methods with efficient sensitivity generation. It is shown that they often outperform existing auto-generated Explicit Runge-Kutta (ERK) methods. Moreover, the new methods allow to treat Differential Algebraic Equation (DAE) systems by NMPC with microsecond sampling times.

Nonlinear MPC and MHE for Mechanical Multi-Body Systems with Application to Fast Tethered Airplanes

Mechanical applications often require a high control frequency to cope with fast dynamics. The control frequency of a nonlinear model predictive controller depends strongly on the symbolic complexity of the equations modeling the system. The symbolic complexity of the model equations for multi-body mechanical systems can often be dramatically reduced by using representations based on non-minimal coordinates, which result in index-3 differential-algebraic equations (DAEs). This paper proposes a general procedure to efficiently treat multi-body mechanical systems in the context of MHE & NMPC using non-minimal coordinate representations, and provides the resulting computational times that can be achieved on a tethered airplane system using code generation.

Experimental Validation of Combined Nonlinear Optimal Control and Estimation of an Overhead Crane

Abstract This paper validates the combination of nonlinear model predictive control and moving horizon estimation to optimally control an overhead crane. Real-time implementation of this combined optimal control and estimation approach with execution times far below the sampling time was realized through the use of automatic code generation. Besides experiments that reflect good point-to-point performance, the approach showed to be good in disturbance rejection as well as in servo-tracking.

A new quadratic programming strategy for efficient sparsity exploitation in SQP-based nonlinear MPC and MHE

Abstract A large class of algorithms for nonlinear model predictive control (MPC) and moving horizon estimation (MHE) is based on sequential quadratic programming and thus requires the solution of a sparse structured quadratic program (QP) at each sampling time. We propose a novel algorithm based on a dual two-level approach involving a nonsmooth version of Newtons method that aims at combining sparsity exploitation features of an interior point method with warm-starting capabilities of an active-set method. We address algorithmic details and present the open-source implementation qpDUNES. The effectiveness of the solver in combination with the ACADO Code Generation tool for nonlinear MPC is demonstrated based on set of benchmark problems, showing significant performance increases compared to the established condensing-based approach, particularly for problems with long prediction horizons.

Convergence guarantees for moving horizon estimation based on the real-time iteration scheme

In this note, conditions are proven under which a real-time implementable moving horizon estimation (MHE) scheme is locally convergent. Specifically, the real-time iteration scheme of is studied in which a single Gauss-Newton iteration is applied to approximate the solution to the respective MHE optimization problem at each time-step. Convergence is illustrated by a challenging small scale example, the Lorenz attractor with an unknown parameter. It is shown that the performance of the proposed real-time MHE algorithm is nearly identical to a fully converged MHE solution, while its fixed execution time per sample would allow one to solve 30 000 MHE problems per second on current hardware.

A real-time MHE and NMPC scheme for wind turbine control

Model Predictive Control (MPC) is a strong candidate for the control of large Multi-Mega Watt Wind Turbine Generators (WTG). Several MPC and some Nonlinear MPC schemes have been proposed in the literature, formulating the problem of balancing the power generation against the structural and actuator fatigue through a reference-tracking scheme. While the resulting schemes offer very promising results in term of load reduction, especially when reliable LIDAR systems are available, no NMPC scheme fast enough to achieve a real-time implementation has yet been proposed. This paper presents such a real-time NMPC scheme. Moreover, the proposed scheme uses directly the power generation as a cost function, as opposed to tracking the optimal wind-dependent WTG steady-state.

An experimental test set-up for launch/recovery of an Airborne Wind Energy (AWE) system

This paper describes an experimental set-up for AWE systems. A novel approach of launching a rigid wing tethered airplane, using a rotational start-up, is presented. A test set-up performing this rotational start-up has been designed and built at KU Leuven. A scale analysis of this novel approach is conducted and provisions are made to accommodate future modifications to the experimental set-up. A sensor suite consisting of a stereo vision system and an inertial measurement unit are used for sensor fusion with an extended kalman filter (EKF). This EKF estimates the position, velocity and orientation of the airplane. Numerical and experimental validation of the EKF are presented in this paper as well.