A tutorial on model predictive control for spacecraft rendezvous

This tutorial paper provides a review of recent advances in the field of spacecraft rendezvous using model predictive control (MPC), an advanced optimal control strategy based on on-line constrained optimisation of control inputs based on predictions of future trajectories. Firstly, the rendezvous objectives, and the generic constrained MPC problem formulation are summarised. This is followed by a discussion of how to select the three key ingredients used in an MPC design: the prediction model, the constraints and the cost function. Since MPC implementation relies on finding the solution to constrained optimisation problems in real-time, computational aspects are also briefly examined. The paper concludes with conjecture on ways the use of MPC in this application could be further advanced.This is the author accepted manuscript. The final version is available from IEEE via http://dx.doi.org/10.1109/ECC.2015.733072

Predictive Control with Parameter Adaptation to Achieve α-Protection in the RECONFIGURE Benchmark in the Presence of Icing

Undetected ice accretions on aerodynamic surfaces can deeply change the dynamic behaviour of aircraft, leading to poor performance of the automatic control systems. This is characterised by oscillatory behaviour, and overshoot of setpoints and ight envelope protection values. To mitigate this undesirable behaviour, this paper applies predictive control in combination with online estimation of the first and second order partial derivatives of the lift and pitching moment coeffcients with respect to the angle of attack using an Extended Kalman Filter, to achieve a constrained indirect adaptive ight control law. The design is evaluated on the RECONFIGURE benchmark, which is a nonlinear, high fidelity, industrially validated simulator of a large Airbus aircraft. In icing scenarios at high incidence, the resulting trajectories are shown to be better damped and more compliant with constraints when compared to a predictive control law employing only linear disturbance estimation.This is the final version of the article. It was first available from Elsevier via http://dx.doi.org/10.1016/j.ifacol.2015.11.27

Predictive control for spacecraft rendezvous in an elliptical orbit using an FPGA

A field programmable gate array (FPGA)-based predictive controller for a spacecraft rendezvous man{\oe}uvre is presented. A linear time varying prediction model is used to accommodate elliptical orbits, and a variable prediction horizon is used to facilitate finite time completion of man{\oe}uvres. The resulting constrained optimisation problems are solved using a primal dual interior point algorithm. The majority of the computational demand is in solving a set of linear equations at each iteration of this algorithm. To accelerate this operation, a custom circuit is implemented, using a combination of Mathworks HDL Coder and Xilinx System Generator for DSP, and used as a peripheral to a MicroBlaze soft core processor. The system is demonstrated in closed loop by linking the FPGA with a simulation of the plant dynamics running in Simulink on a PC, using Ethernet.This work was supported by the Engineering and Physical Sciences Research Council (Grant EP/G030308/1) as well as industrial support from Xilinx, Mathworks and the European Space Agency.European Control Conference 2013 (ECC13), July 17-19, Zurich, Switzerlan

A longitudinal flight control law based on robust MPC and H<inf>2</inf> methods to accommodate sensor loss in the RECONFIGURE benchmark

The feedback gains in state-of-the-art flight control laws for commercial aircraft are scheduled as a function of values such as airspeed, mass, and centre of gravity. If estimates of these are lost due to multiple simultaneous sensor failures, it is necessary for the pilot to either directly command control surface positions, or to revert to an alternative control law. This work develops a robust backup load-factor tracking control law, that does not depend on these parameters, based on application of theory from robust MPC and H2 control. First the methods are applied with loss only of airdata, and subsequently also with loss of mass and CoG estimates. Local linear analysis indicates satisfactory performance over a wide range of operating points. Finally, the resulting control laws are demonstrated on the nonlinear RECONFIGURE benchmark, which is derived from Airbus's high delity, industrially-validated simulator, OSMA.This is the author accepted manuscript. The final version is available from Elsevier via http://dx.doi.org/10.1016/j.ifacol.2015.09.65

Reconfigurable predictive control for redundantly actuated systems with parameterised input constraints

A method is proposed for on-line recon guration of the terminal constraint used to provide theoretical nominal stability guarantees in linear model predictive control (MPC). By parameterising the terminal constraint, its complete reconstruction is avoided when input constraints are modi ed to accommodate faults. To enlarge the region of feasibility of the terminal control law for a certain class of input faults with redundantly actuated plants, the linear terminal controller is de ned in terms of virtual commands. A suitable terminal cost weighting for the recon gurable MPC is obtained by means of an upper bound on the cost for all feasible realisations of the virtual commands from the terminal controller. Conditions are proposed that guarantee feasibility recovery for a de ned subset of faults. The proposed method is demonstrated by means of a numerical example.The research leading to these results has received function from the European Union Seventh Framework Programme FP7/2007{2013 under grant agreement no. 314 544.This is the accepted manuscript. The final version is available from Elsevier at http://www.sciencedirect.com/science/article/pii/S0167691114000127

Initial tuning of predictive controllers by reverse engineering

This paper demonstrates a method for finding the cost function and state observer to be used in model predictive control (MPC) so that when constraints are inactive a pre- existing low order controller is reproduced. The MPC controller thereby inherits its desirable properties. This can be used as a baseline for further tuning. The available degrees of design freedom are explored, in order to facilitate, as appropriate, exploitation of constraint-handling, offset-free and redundancy management capabilities of MPC.This work is supported by the EPSRC, the European Space Agency, and EADS Astrium

Field programmable gate array based predictive control system for spacecraft rendezvous in elliptical orbits

A field programmable gate array (FPGA)-based model predictive controller (MPC) for two phases of spacecraft rendezvous is presented. Linear time varying prediction models are used to accommodate elliptical orbits, and a variable prediction horizon is used to facilitate finite time completion of the longer-range man{\oe}uvres, whilst a fixed and receding prediction horizon is used for fine-grained tracking at close range. The resulting constrained optimisation problems are solved using a primal dual interior point algorithm. The majority of the computational demand is in solving a system of simultaneous linear equations at each iteration of this algorithm. To accelerate these operations, a custom circuit is implemented, using a combination of Mathworks HDL Coder and Xilinx System Generator for DSP, and used as a peripheral to a MicroBlaze soft core processor on the FPGA, on which the remainder of the system is implemented. Certain logic that can be hard-coded for fixed sized problems is implemented to be configurable online, in order to accommodate the varying problem sizes associated with the variable prediction horizon. The system is demonstrated in closed loop by linking the FPGA with a simulation of the spacecraft dynamics running in Simulink on a PC, using Ethernet. Timing comparisons indicate that the custom implementation is substantially faster than pure embedded software-based interior point methods running on the same MicroBlaze, and could be competitive with a pure custom hardware implementation.This work was supported by the Engineering and Physical Sciences Research Council Grant Number [EP/G030308/1] as well as industrial support from Xilinx, Mathworks, and the European Space Agency

Designing output-feedback predictive controllers by reverse-engineering existing LTI controllers

An approach to designing a constrained output-feedback predictive controller that has the same small-signal properties as a pre-existing output-feedback linear time invariant controller is proposed. Systematic guidelines are proposed to select an appropriate (non-unique) realization of the resulting state observer. A method is proposed to transform a class of offset-free reference tracking controllers into the combination of an observer, steady-state target calculator and predictive controller. The procedure is demonstrated with a numerical example.This work was supported by Engineering and Physical Sciences Research Council grant EP/G030308/1, the European Space Agency and EADS Astrium.This is the author's version of an article that has been published in IEEE Transactions on Automatic Control. Changes were made to this version by the publisher prior to publication. The final version of record is available at: http://dx.doi.org/10.1109/TAC.2013.2258781 (c) 2013 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works

Graphical FPGA design for a predictive controller with application to spacecraft rendezvous

A reconfigurable field-programmable gate array (FPGA)-based predictive controller based on Nesterov’s fast gradient method is designed using Simulink and converted to VHDL using Mathworks’ HDL Coder. The implementation is verified by application to a spacecraft rendezvous and capture scenario, with communication between the FPGA and a simulation of the relative dynamics occuring over Ethernet. For a problem with 120 decision variables and 240 constraints, computation times of 0.95 ms are achieved with a clock rate of 50 MHz, corresponding to a speed up of more than 2000 over running the algorithm directly on a MicroBlaze microprocessor implemented on the same FPGA.This work was supported by the Engineering and Physical Sciences Research Council (Grant EP/G030308/1) as well as industrial support from Xilinx, Mathworks and the European Space Agency.52nd IEEE Conference on Decision and Control, December 10-13, 2013, Palazzo dei Congressi, Florence, Italy

Predictive control using an FPGA with application to aircraft control

Alternative and more efficient computational methods can extend the applicability of MPC to systems with tight real-time requirements. This paper presents a “system-on-a-chip” MPC system, implemented on a field programmable gate array (FPGA), consisting of a sparse structure-exploiting primal dual interior point (PDIP) QP solver for MPC reference tracking and a fast gradient QP solver for steady-state target calculation. A parallel reduced precision iterative solver is used to accelerate the solution of the set of linear equations forming the computational bottleneck of the PDIP algorithm. A numerical study of the effect of reducing the number of iterations highlights the effectiveness of the approach. The system is demonstrated with an FPGA-inthe-loop testbench controlling a nonlinear simulation of a large airliner. This study considers many more manipulated inputs than any previous FPGA-based MPC implementation to date, yet the implementation comfortably fits into a mid-range FPGA, and the controller compares well in terms of solution quality and latency to state-of-the-art QP solvers running on a standard PC