Towards Online Model Predictive Control on a Programmable Logic Controller: Practical Considerations

Given the growing computational power of embedded controllers, the use of model predictive control (MPC) strategies on this type of devices becomes more and more attractive. This paper investigates the use of online MPC, in which at each step, an optimization problem is solved, on both a programmable automation controller (PAC) and a programmable logic controller (PLC). Three different optimization routines to solve the quadratic program were investigated with respect to their applicability on these devices. To this end, an air heating setup was built and selected as a small-scale multi-input single-output system. It turns out that the code generator (CVXGEN) is not suited for the PLC as the required programming language is not available and the programming concept with preallocated memory consumes too much memory. The Hildreth and qpOASES algorithms successfully controlled the setup running on the PLC hardware. Both algorithms perform similarly, although it takes more time to calculate a solution for qpOASES. However, if the problem size increases, it is expected that the high number of required iterations when the constraints are hit will cause the Hildreth algorithm to exceed the necessary time to present a solution. For this small heating problem under test, the Hildreth algorithm is selected as most useful on a PLC

Model Predictive Control Algorithms for Applications with Millisecond Timescales (Modelgebaseerde predictieve controle algoritmes voor toepassingen met milliseconde tijdschalen)

The last three decades have seen a rapidly increasing number of applications where model predictive control (MPC) led to better control performance than more traditional approaches. This thesis aims at lowering the practical burden of applying fast MPC algorithms in the real-world. To this aim, it contributes two software packages, which are released as open-source code in order to stimulate their widespread use. Both packages implement previously published methods but enrich them with a number of new theoretical and algorithmic ideas. The first part of this thesis focusses on efficiently solving quadratic programs (QPs) as arising in linear MPC problems. To this end, it reviews the author's previous work on developing an online active set strategy to exploit the parametric nature of these QPs. This strategy is extended with ideas for initialising the solution procedure and treating QPs with semi-definite Hessian matrices. The software package qpOASES implements the online active set strategy and its extensions together with a number of tailored solution variants for special QP formulations. It offers interfaces to third-party software like Matlab/Simulink and has been successfully used in a number of academic real-world MPC applications. Moreover, two industrial applications of qpOASES--dealing with emission control of integral gas engines and feasibility management for MPC in the process industry--are described. These industrial case studies also led to further theoretical ideas, namely the use of MPC with an asymmetric cost function and a novel method for handling infeasible QPs based on the online active set strategy. The second part addresses nonlinear MPC problems and presents the ACADO Toolkit, a new software environment and algorithm collection for automatic control and dynamic optimisation. It has been designed for setting-up nonlinear optimal control and MPC problems in a user-friendly way and solving them efficiently. In particular, the ACADO Toolkit implements two algorithmic variants of the real-time iteration scheme: a Gauss-Newton approach for nonlinear MPC formulations involving a tracking objective function as well as an exact Hessian approach for tackling time-optimal formulations. The underlying QP subproblems are solved by means of the online active set strategy. The ACADO Toolkit features an intuitive symbolic syntax for formulating MPC problems, which offers a couple of advantageous possibilities. Most importantly, it allows the user to automatically generate optimised, highly efficient C code that is tailored to each respective MPC problem formulation. Numerical results show that the exported code exhibits a promising computational performance allowing application of nonlinear MPC to non-trivial processes at kilohertz sampling rates.nrpages: 186status: publishe

On the implementation of model predictive control for on-line walking pattern generation

Abstract — This article addresses the real-time implementation issues of a model predictive control based walking pattern generation for a humanoid robot. We approximate the multibody dynamic model with a linear discrete time system, and at each step solve a quadratic program in order to keep the output within a predefined set of constraints. The focus is on creating an efficient framework for forming and solving the underlying optimization problem. For that purpose we develop: a) a reliable guess for the active constraints at optimality; b) a fast way of generating an initial feasible point with respect to the set of constraints for each preview interval; c) a variable discretization sampling time. A simple implementation of a standard primal active set algorithm which exploits a “hot start ” is used to demonstrate the advantages of the first point, while the latter one is verified using an existing dual solver. I

On the Implementation of Model Predictive Control for On-line Walking Pattern Generation

This article addresses the real-time implementation issues of a model predictive control based walking pattern generation for a humanoid robot. We approximate the multibody dynamic model with a linear discrete time system, and at each step solve a quadratic program in order to keep the output within a predefined set of constraints. The focus is on creating an efficient framework for forming and solving the underlying optimization problem. For that purpose we develop: a) a reliable guess for the active constraints at optimality; b) a fast way of generating an initial feasible point with respect to the set of constraints for each preview interval; c) a variable discretization sampling time. A simple implementation of a standard primal active set algorithm which exploits a “hot start” is used to demonstrate the advantages of the first point, while the latter one is verified using an existing dual solver

Moving Horizon Estimation and Nonlinear Model Predictive Control for Autonomous Navigation of Agricultural Vehicles

Controllers working in uncertain environments are often required to adapt themselves continuously to changing conditions to avoid steady-state errors, oscillations at the output or even instability of the closed loop system. The moving horizon estimation (MHE)–nonlinear model predictive control (NMPC)framework being proposed combines these two optimization-based methods to control field vehicles utilizing an adaptive nonlinear kinematic model. The full system state, including two unknown slip parameters and the unmeasurable vehicle orientation, is estimated by the MHE after each new measurement and fed afterwards to the NMPC routine which provides a wheel velocity and a steering rate to follow arbitrary time-based reference trajectories in difficult environmental conditions. This control problem occurs in modern agriculture e.g. in planting or mechanical weeding while slippery conditions make these operation difficult and off-track navigation results in plant damage. The experimental results show accurate reference tracking performance of the MHE–NMPC framework on a wet and bumpy grass field. The feedback times lie in the range of 0.6–1.6 ms when the ACADO Code Generation tool is used, which is part of the open-source software toolkit ACADO.publisher: Elsevier articletitle: Moving horizon estimation and nonlinear model predictive control for autonomous agricultural vehicles journaltitle: Computers and Electronics in Agriculture articlelink: http://dx.doi.org/10.1016/j.compag.2013.06.009 content_type: article copyright: Copyright © 2013 Elsevier B.V. All rights reserved.status: publishe

Towards online model predictive control on a programmable logic controller : practical considerations

Given the growing computational power of embedded controllers, the use of model predictive control (MPC) strategies on this type of devices becomes more and more attractive. This paper investigates the use of online MPC, in which at each step, an optimization problem is solved, on both a programmable automation controller (PAC) and a programmable logic controller (PLC). Three different optimization routines to solve the quadratic program were investigated with respect to their applicability on these devices. To this end, an air heating setup was built and selected as a small-scale multi-input single-output system. It turns out that the code generator (CVXGEN) is not suited for the PLC as the required programming language is not available and the programming concept with preallocated memory consumes too much memory. The Hildreth and qpOASES algorithms successfully controlled the setup running on the PLC hardware. Both algorithms perform similarly, although it takes more time to calculate a solution for qpOASES. However, if the problem size increases, it is expected that the high number of required iterations when the constraints are hit will cause the Hildreth algorithm to exceed the necessary time to present a solution. For this small heating problem under test, the Hildreth algorithm is selected as most useful on a PLC. © 2012 Bart Huyck et al.status: publishe