Real‐time model predictive control based on dual gradient projection: Theory and fixed‐point FPGA implementation

This paper proposes a method to design robust model predictive control (MPC) laws for discrete‐time linear systems with hard mixed constraints on states and inputs, in case of only an inexact solution of the associated quadratic program is available, because of real‐time requirements. By using a recently proposed dual gradient‐projection algorithm, it is proved that the discrepancy of the optimal control law as compared with the obtained one is bounded even if the solver is implemented in fixed‐point arithmetic. By defining an alternative MPC problem with tightened constraints, a feasible solution is obtained for the original MPC problem, which guarantees recursive feasibility and asymptotic stability of the closed‐loop system with respect to a set including the origin, also considering the presence of external disturbances. The proposed MPC law is implemented on a field‐programmable gate array in order to show the practical applicability of the method. Copyright © 2016 John Wiley & Sons, Ltd.     

Multiobjective model predictive control

This paper proposes a novel model predictive control (MPC) scheme based on multiobjective optimization. At each sampling time, the MPC control action is chosen among the set of Pareto optimal solutions based on a time-varying, state-dependent decision criterion. Compared to standard single-objective MPC formulations, such a criterion allows one to take into account several, often irreconcilable, control specifications, such as high bandwidth (closed-loop promptness) when the state vector is far away from the equilibrium and low bandwidth (good noise rejection properties) near the equilibrium. After recasting the optimization problem associated with the multiobjective MPC controller as a multiparametric multiobjective linear or quadratic program, we show that it is possible to compute each Pareto optimal solution as an explicit piecewise affine function of the state vector and of the vector of weights to be assigned to the different objectives in order to get that particular Pareto optimal solution. Furthermore, we provide conditions for selecting Pareto optimal solutions so that the MPC control loop is asymptotically stable, and show the effectiveness of the approach in simulation examples.     

Analysis of data from various indentation techniques for thin films intrinsic hardness modelling

Due to the influence of the substrate, direct measurement of the hardness of thin films by standard micro-indentation tests is not always possible. In such situation, determination of the intrinsic film hardness requires the analysis of a set of experimental apparent hardness values obtained for different indentation loads. A number of mathematical equations based on various assumptions were proposed in literature for that purpose.Most of the models were established on the basis of standard Vickers indentation. Using these models to process the data obtained by Knoop indentation does not provide the same intrinsic hardness value, even after Knoop/Vickers standard conversion, than the one obtained from Vickers indentation. The same problem arises when processing the data coming from depth-sensing indentation. A method to obtain comparable hardness values is proposed in the present work by considering an “equivalent” Vickers hardness in the case of Knoop indentations and the corresponding Martens hardness for depth-sensing indentation. This method has been used to determine the intrinsic hardness of titanium nitride film.     

Liquid xenon scintillation calorimetry and Xe optical properties

The optical properties of liquid xenon (LXe) in the vacuum ultra violet (VUV), determining the performance of a scintillation calorimeter, are discussed in detail. The available data, measured in a wider spectral region from visible to UV light, and in a large range of Xe densities, from gas to liquid, are examined. It is shown that this information can be used for deriving the LXe optical properties in the VUV. A comparison is made with the few direct measurements in LXe for VUV light resulting from the LXe excitation by ionizing particles. A useful relation is obtained which connects the Rayleigh scattering length to the refractive index in LXe.     

Event‐driven model predictive control of timed hybrid Petri nets

Hybrid Petri nets represent a powerful modeling formalism that offers the possibility of integrating, in a natural way, continuous and discrete dynamics in a single net model. Usual control approaches for hybrid nets can be divided into discrete‐time and continuous‐time approaches. Continuous‐time approaches are usually more precise, but can be computationally prohibitive. Discrete‐time approaches are less complex, but can entail mode‐mismatch errors due to fixed time discretization. This work proposes an optimization‐based event‐driven control approach that applies on continuous time models and where the control actions change when discrete events occur. Such an approach is computationally feasible for systems of interest in practice and avoids mode‐mismatch errors. In order to handle modelling errors and exogenous disturbances, the proposed approach is implemented in a closed‐loop strategy based on event‐driven model predictive control. Copyright © 2013 John Wiley & Sons, Ltd.     

Output-feedback predictive control of constrained linear systems via set-membership state estimation

This paper combines model predictive control (MPC) and set-membership (SM) state estimation techniques for controlling systems subject to hard input and state constraints. Linear systems with unknown but bounded disturbances and partial state information are considered. The adopted approach guarantees that the constraints are satisfied for all the states which are compatible with the available information and for all the disturbances within given bounds. Properties of the proposed MPC-SM algorithm and simulation studies are reported.     

Low-complexity piecewise-affine virtual sensors: theory and design

This paper is focused on the theoretical development and the hardware implementation of low-complexity piecewise-affine direct virtual sensors for the estimation of unmeasured variables of interest of nonlinear systems. The direct virtual sensor is designed directly from measured inputs and outputs of the system and does not require a dynamical model. The proposed approach allows one to design estimators which mitigate the effect of the so-called ‘curse of dimensionality’ of simplicial piecewise-affine functions, and can be therefore applied to relatively high-order systems, enjoying convergence and optimality properties. An automatic toolchain is also presented to generate the VHDL code describing the digital circuit implementing the virtual sensor, starting from the set of measured input and output data. The proposed methodology is applied to generate an FPGA implementation of the virtual sensor for the estimation of vehicle lateral velocity, using a hardware-in-the-loop setting.     

Robust explicit model predictive control via regular piecewise-affine approximation

This paper proposes an explicit model predictive control design approach for regulation of linear time-invariant systems subject to both state and control constraints, in the presence of additive disturbances. The proposed control law is implemented as a piecewise-affine function defined on a regular simplicial partition, and has two main positive features. First, the regularity of the simplicial partition allows one to efficiently implement the control law on digital circuits, thus achieving extremely fast computation times. Moreover, the asymptotic stability (or the convergence to a set including the origin) of the closed-loop system can be enforced a priori, rather than checked a posteriori via Lyapunov analysis.