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Martin Mönnigmann

Publications and source records attributed to Martin Mönnigmann.

36 records · Page 2Linked to original sources
arXiv2020

Estimating load points of a motor-pump system using pressure and inverter drive data

We propose a novel method for the estimation of rotor position, speed, and torque of a motor-pump system consisting of a progressive cavity pump (PCP) driven by an induction motor which operates under V/f open-loop control. We compute the speed and rotor position of the PCP by applying a phase locked loop to the pressure signal at the pressure side of the pump. An extended Kalman filter is used to estimate the torque of the PCP based on the speed, effective value of the stator current of the induction motor and a nonlinear motor model. Furthermore, we derive a tractable condition under which the convergence of the observer is guaranteed. We use a laboratory experiment to verify our results.

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arXiv2020

Regional predictive control with suboptimally extended regions of validity

Model predictive control (MPC) is based on perpetually solving optimization problems. The solution of the optimization is usually interpreted as the optimal input for the current state. However, the solution of the optimization does not just provide an optimal input, but an entire optimal affine feedback law and a polytope on which this law is optimal. We recently proposed to use this feedback law as long as the system remains in its polytope. This can be interpreted as an event-based approach, where leaving the current polytope is the event that triggers the next optimization. This approach is especially appropriate for a networked control setting since the feedback laws and their polytopes can be evaluated with a low computational effort on lean local nodes. In this article the region of validity for a feedback law is extended. More precisely, the optimal polytopes are extended to nonlinearly bounded regions of validity resulting from the intersection of a feasibility and stability region. As a result, fewer quadratic programs need to be solved compared to the optimal approach. The new validity regions are still suitable for the evaluation on a lean local node. Moreover, the regions can be adjusted for a desired closed-loop performance.

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arXiv2020

Accelerating MPC by online detection of state space sets with common optimal feedback laws

Model predictive control (MPC) samples a generally unknown and complicated feedback law point by point. The solution for the current state $x$ contains, however, more information than only the optimal signal $u$ for this particular state. In fact, it provides an optimal affine feedback law $x\rightarrow u(x)$ on a polytope $Π\subset \mathbb{R}^n$, i.e., on a full-dimensional state space set. It is an obvious idea to reuse this affine feedback law as long as possible. Reusing it on its polytope $Π$ is too conservative, however, because any $Π$ is a state space set with a common affine law $x\rightarrow (u_0^\prime (x), \dots, u_{N-1}^\prime (x))^\prime\in\mathbb{R}^{Nm}$ for the entire horizon $N$. We show a simple criterion exists for identifying the polytopes that have a common $x\rightarrow u_0(x)$, but may differ with respect to $u_1(x), \dots, u_{N-1}(x)$. Because this criterion is too computationally expensive for an online use, we introduce a simple heuristics for the fast construction of a subset of the polytopes of interest. Computational examples show (i) a considerable fraction of QPs can be avoided (10% to 40%) and (ii) the heuristics results in a reduction very close to the maximum one that could be achieved if the explicit solution was available. We stress the proposed approach is intended for use in online MPC and it does not require the explicit solution.

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arXiv2020

Accelerated Nonlinear Model Predictive Control by Exploiting Saturation

We present an approach for accelerating nonlinear model predictive control. If the current optimal input signal is saturated, also the optimal signals in subsequent time steps often are. We propose to use the open-loop optimal input signals whenever the first and some subsequent input signals are saturated. We only solve the next optimal control problem, when a non-saturated signal is encountered, or the end of the horizon is reached. In this way, we can save a significant number of NLPs to be solved while on the other hand keep the performance loss small. Furthermore, the NMPC is reactivated in time when it comes to controlling the system safely to its reference.

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arXiv2020

State space sets with common optimal feedback laws for nonlinear MPC

In model predictive control (MPC), an optimal control problem (OCP) is solved for the current state and the first input of the solution, the optimal feedback law, is applied to the system. This procedure requires to solve the OCP in every time step. Recently, a new approach was suggested for linear MPC. The parametric solution of a linear quadratic OCP is a piecewise-affine feedback law. The solution at a point in state space provides an optimal feedback law and a domain on which this law is the optimal solution. As long as the system remains in the domain, the law can be reused and the calculation of an OCP is avoided. In some domains the optimal feedback laws are identical. By uniting the corresponding domains, bigger domains are achieved and the optimal feedback law can be reused more often. In the present paper, we investigate in how far this approach can be extended from linear to nonlinear MPC, we propose an algorithm and we illustrate the achieved savings with an example.

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arXiv2020

Controllability analysis and optimal control of biomass drying with reduced order models

Complex industrial processes such as the drying of combustible biomass can be modeled with computational fluid dynamics simulations. Due to their complexity, it is not straightforward to use these models for the analysis of system properties or for solving optimal control problems. We show reduced order models can be derived and used for these purposes for industrial drying processes.

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arXiv2020

An observer for partially obstructed wood particles in industrial drying processes

In order for biomass drying processes to be efficient, it is crucial to achieve the target residual water content within a close margin, since more conservative drying would result in a waste of energy. A method for a reliable estimation of the water content is therefore of obvious importance. Ideally, such a method does not require any expensive sensors. We show reduced order models and extended Kalman filters can be combined to reliably determine the water content and temperature of wood particles based on only surface temperature measurements. The proposed observer works reliably if measurements are only available for parts of a particle face. It can therefore still be applied if particle surfaces are partially obstructed, which is a prerequisite for use in industrial processes and units, such as rotary dryers. The extended Kalman filter uses a reduced order model that is obtained by applying proper orthogonal decomposition and Galerkin projection to coupled PDEs that model heat conduction and water diffusion in anisotropic particles. In contrast to the original PDE simulation model, the reduced model and the filter based on it are suitable for real time computations and monitoring.

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arXiv2020

Supervisory model predictive control for PV battery and heat pump system with phase change slurry thermal storage

We present the design, implementation and experimental validation of a supervisory predictive control approach for an electrical heating system featuring a phase change slurry as heat storage and transfer medium. The controller optimizes the energy flows that are used as set points for the heat generation and energy distribution components. The optimization handles the thermal and electrical subsystems simultaneously and is able to switch between different objectives. We show the control can be implemented on low-cost embedded hardware and validate it with an experimental test bed comprising an installation of the complete heating system, including all hydraulic and all electrical components. Experimental results demonstrate the feasibility of both, a heat pump heating system with a phase change slurry, and the optimal control approach. The main control objectives, i.e., thermal comfort and maximum self-consumption of solar energy, can be met. In addition, the system and its controller provide a load shifting potential.

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arXiv2019

A dynamic programming approach to solving constrained linear-quadratic optimal control problems

The solution of a constrained linear-quadratic regulator problem is determined by the set of its optimal active sets. We propose an algorithm that constructs this set of active sets for a desired horizon N from that for horizon N-1. While it is not obvious how to extend the optimal feedback law itself for horizon N-1 to horizon N, a simple relation between the optimal active sets for two successive horizon lengths exists. Specifically, every optimal active set for horizon N is a superset of an optimal active set for horizon N-1 if the constraints are ordered stage by stage. The stagewise treatment results in a favorable computational effort. In addition, it is easy to detect the solution of the current horizon is equal to the infinite-horizon solution, if such a finite horizon exists, with the proposed algorithm.

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arXiv2019

A Complexity Analysis of Event-Triggered Model Predictive Control on Industrial Hardware

We implement a recently proposed event-triggered networked MPC approach on industrial hardware to analyze its practical relevance. There exist several alternatives for such an implementation that differ with respect to the distribution of computational load between local and central nodes, and with respect to network bandwidth requirements. These alternatives have been analyzed theoretically before, but when implemented it becomes evident that their usefulness cannot be predicted based on theoretical considerations alone. It is the purpose of the present paper to account for both practical and theoretical aspects in determining which alternative is most appropriate for an implementation on industrial hardware. The smallest possible bandwidth is known to result for a variant in which only the active set of constraints is transmitted from the central to the local nodes. Since local nodes must determine the control law from the active set in this case, which requires matrix inversions, an unattractive computational cost results at first sight. Somewhat surprisingly, the computational cost scales practically linearly in the problem size when implemented. We confirm this result with a more detailed theoretical complexity analysis than given in previous papers. All results are illustrated with data obtained with an implementation on industrial hardware components.

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arXiv2019

On the structure of the set of active sets in constrained linear quadratic regulation

The constrained linear quadratic regulation problem is solved by a continuous piecewise affine function on a set of state space polytopes. It is an obvious question whether this solution can be built up iteratively by increasing the horizon, i.e., by extending the classical backward dynamic programming solution for the unconstrained case to the constrained case. Unfortunately, however, the piecewise affine solution for horizon N is in general not contained in the piecewise affine law for horizon N + 1. We show that a backward dynamic programming does, in contrast, result in a useful structure for the set of the active sets that defines the solution. Essentially, every active set for the problem with horizon N + 1 results from extending an active set for horizon N , if the constraints are ordered stage by stage. Consequently, the set for horizon N + 1 can be found by only considering the constraints of the additional stage. Furthermore, it is easy to detect which polytopes and affine pieces are invariant to increasing the horizon, and therefore persist in the limit N to infinity. Several other aspects of the structure of the set of active sets become evident if the active sets are represented by bit tuples. There exists, for example, a subset of special active sets that generates a positive invariant and persistent (i.e., horizon invariant) set around the origin. It is very simple to identify these special active sets, and the positive invariant and persistent region can be found without solving optimal control or auxiliary optimization problems. The paper briefly discusses the use of these results in model predictive control. Some opportunities for uses in computational methods are also briefly summarized.

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arXiv2019

A method for the optimization of nonlinear systems with delays that guarantees stability and robustness

We present a method for the steady state optimization of nonlinear delay differential equations. The method ensures stability and robustness, where a system is called robust if it remains stable despite uncertain parameters. Essentially, we ensure stability of all steady states of the nonlinear system on the steady state manifold that results from the variation of the uncertain parameters. The uncertain parameters are characterized by finite intervals, which may be interpreted as error bars and therefore are of immediate practical relevance. Stability despite uncertain parameters can be guaranteed by enforcing a lower bound on the distance of the optimal steady state to submanifolds of saddle-node and Hopf bifurcations on the steady state manifold. We derive constraints that ensure this distance. The proposed method differs from previous ones in that stability and robustness are guaranteed with constraints instead of with the cost function. Because the cost function is not required to enforce stability and robustness, it can be used to state economic or similar goals, which is natural in applications. We illustrate the proposed method by optimizing a laser diode. The optimization finds a steady state of maximum intensity while guaranteeing asymptotic or exponential stability despite uncertain model parameters.

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arXiv2019

Normal Vectors on Modified Hopf Manifolds of Delay Differential Equations

This document states the normal vector system for modified Hopf boundaries of delay differential systems with state and parameter dependent delays. Specifically, it states the proof for Proposition 1 in the paper entitled "Robust optimization of delay differential equations with state and parameter dependent delays" by the same authors [1].

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arXiv2015

Improved automatic computation of Hessian matrix spectral bounds

This paper presents a fast and powerful method for the computation of eigenvalue bounds for Hessian matrices $\nabla^2 φ(x) $ of nonlinear functions $φ: U \subseteq R^n\rightarrow R$ on hyperrectangles $B \subset U$. The method is based on a recently proposed procedure for an efficient computation of spectral bounds using extended codelists. Both the previous approach and the one presented here substantially differ from established methods in that they do deliberately not use any interval matrices and thus result in a favorable numerical complexity of order $O(n)\,N(φ)$, where $N(φ)$ denotes the number of operations needed to evaluate $φ$ at a point in its domain. We improve the previous method by exploiting sparsity, which naturally arises in the underlying codelists.

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arXiv2015

Simulation studies on online constraint removal with a Lyapunov function

We apply a recently proposed method for the acceleration of model predictive control (MPC) to 36 MPC implementations, which result from combining six sample receding horizon control problems with six quadratic programming solvers. We implement each of the 36 system-solver-combinations both with and without constraint removal and compare computational times for statistically relevant numbers of runs.

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arXiv2013

Robust optimization of periodically operated nonlinear uncertain processes

We present a method for determining optimal modes of operation for autonomously oscillating systems with uncertain parameters. In a typical application of the method, a nonlinear dynamical system is optimized with respect to an economic objective function with nonlinear programming methods, and stability is guaranteed for all points in a robustness region around the optimal point. The stability constraints are implemented by imposing a lower bound on the distance between the optimal point and all stability boundaries in its vicinity, where stability boundaries are described with notions from bifurcation theory. We derive the required constraints for a general class of periodically operated processes and show how these bounds can be integrated into standard nonlinear programming methods. We present results of the optimization of two chemical reaction systems for illustration.

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arXiv2012

Efficient Computation of Spectral Bounds for Hessian Matrices on Hyperrectangles for Global Optimization

We compare two established and a new method for the calculation of spectral bounds for Hessian matrices on hyperrectangles by applying them to a large collection of 1522 objective and constraint functions extracted from benchmark global optimization problems. Both the tightness of the spectral bounds and the computational effort are assessed. Specifically, we compare eigenvalue bounds obtained with the interval variant of Gershgorin's circle criterion [2,6], Hertz and Rohn's [7,16] method for tight bounds of interval matrices, and a recently proposed Hessian matrix eigenvalue arithmetic [12], which deliberately avoids the computation of interval Hessians.

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