Jan Åslund

An Efficient Algorithm for Finding Minimal Overconstrained Subsystems for Model-Based Diagnosis

In model-based diagnosis, diagnostic system construction is based on a model of the technical system to be diagnosed. To handle large differential algebraic imemodels and to achieve fault isolation, a common strategy is to pick out small overconstrained parts of the model and to test these separately against measured signals. In this paper, a new algorithm for computing all minimal overconstrained subsystems in a model is proposed. For complexity comparison, previous algorithms are recalled. It is shown that the time complexity under certain conditions is much better for the new algorithm. This is illustrated using a truck engine model.

Look-ahead control - consequences of a non-linear fuel map on truck fuel consumption

Abstract Consequences of non-linearities in specific fuel consumption (SFC) of a heavy truck combustion engine are studied with focus on such small road gradients that a constant speed is optimal if the engine torque has an affine relation to fuelling. A quasi-static analysis gives valuable insights into the intrinsic properties of minimization of fuel consumption. Two objective functions are shown to give different optimal velocity trajectories on a constant road gradient, when the non-linearity in SFC is significant, a notation which is quantified. For a significant non-linearity, when a constraint is set to keep a final time, switching between two characteristic speeds is optimal. Alternatively, if consumed time, in addition to fuel consumption, is part of the objective function, then keeping to one constant speed is optimal also for significant non-linearities. However, the different optimal solutions still show similarities, since for a certain significant non-linearity a specific speed range determined by the characteristic velocities is shown to be unobtainable for both optimality criteria. Similar results are obtained for a full dynamic model including a realistic fuel map and other realistic constraints.

Optimal Operation of a Turbocharged Diesel Engine during Transients

Recent development has renewed the interest in drivetrain concepts which give a higher degree of freedom by disconnecting the engine and vehicle speeds. This freedom raises the demand for active control, which especially during transients is not trivial but of which the quality is crucial for the success of the drivetrain concept. In this work the fuel optimal solution for a turbocharged diesel engine connected to a load which does not restrict the engine speed is derived, analysed and utilized for finding a suboptimal operating point trajectory. We use a Willan s efficiency model for the engine, expanded with a first order delay dependent torque reduction representing the turbocharger pressure, and study different output power transients. The analysis is made with dynamic programming, Pontryagin’s maximum principle and a suboptimal strategy based on the static optimal operating points. We present a method for using Pontryagin’s maximum principle for deriving the optimal operating point trajectory. The time needed for computation was reduced a factor >100 compared to dynamic programming, but this method is only applicable to load cases with steps between different high output powers. We also present a suboptimal method which shows a 1000 compared to dynamic programming.

Horizon Length and Fuel Equivalents for Fuel-Optimal Look-Ahead Control

Abstract Recent studies from several authors show that it is possible to lower the fuel consumption for heavy trucks by utilizing information about the road topography ahead of the vehicle. The approach in these studies is receding horizon control where horizon length and residual cost are main topics. To approach these topics, fuel equivalents previously introduced based on physical intuition are given a mathematical interpretation in terms of Lagrange multipliers. Measures for the suboptimality, caused by the truncated horizon and the residual cost approximation, are defined and evaluated for different routes and parameters.

Diagnosability Analysis Considering Causal Interpretations for Differential Constraints

This paper is focused on structural approaches to study diagnosability properties given a system model taking into account, both simultaneously or separately, integral and differential causal interpretations for differential constraints. We develop a model characterization and corresponding algorithms, for studying system diagnosability using a structural decomposition that avoids generating the full set of system analytical redundancy relations. Simultaneous application of integral and differential causal interpretations for differential constraints results in a mixed causality interpretation for the system. The added power of mixed causality is demonstrated using a Reverse Osmosis Subsystem from the Advanced Water Recovery System developed at the NASA Johnson Space Center. Finally, we summarize our work and provide a discussion of the advantages of mixed causality over just derivative or just integral causality.

Fault Diagnosis Based on Causal Computations

This paper focuses on residual generation for model-based fault diagnosis. Specifically, a methodology to derive residual generators when nonlinear equations are present in the model is developed. A main result is the characterization of computation sequences that are particularly easy to implement as residual generators and that take causal information into account. An efficient algorithm, based on the model structure only, which finds all such computation sequences, is derived. Furthermore, fault detectability and isolability performances depend on the sensor configuration. Therefore, another contribution is an algorithm, also based on the model structure, that places sensors with respect to the class of residual generators that take causal information into account. The algorithms are evaluated on a complex highly nonlinear model of a fuel cell stack system. A number of residual generators that are, by construction, easy to implement are computed and provide full diagnosability performance predicted by the model.

Management of Kinetic and Electric Energy in Heavy Trucks

Trucks are responsible for the major part of inland freight and so, they are a backbone of the modern economy but they are also a large consumer of energy. In this context, a dominating vehicle is a truck with heavy load on a long trip. The aim with look-ahead control is to reduce the energy consumption of heavy vehicles by utilizing information about future conditions focusing on the road topography ahead of the vehicle. The possible gains with look-ahead control are evaluated by performing experiments with a truck on highway. A real-time control system based on receding horizon control (RHC) is set up where the optimization problem is solved repeatedly on-line for a certain horizon ahead of the vehicle. The experimental results show that significant reductions of the fuel consumption are achieved, and that the controller structure, where the algorithm calculates set points fed to lower level controllers, has satisfactory robustness to perform well on-board in a real environment. Moreover, the controller behavior has the preferred property of being intuitive, and the behavior is perceived as comfortable and natural by participating drivers and passengers. A well-behaved and efficient algorithm is developed, based on dynamic programing, for the mixed-integer nonlinear minimum-fuel problem. A modeling framework is formulated where special attention is given to properly include gear shifting with physical models. Fuel equivalents are used to reformulate the problem into a tractable form and to construct a residual cost enabling the use of a shorter horizon ahead of the vehicle. Analysis of errors due to discretization of the continuous dynamics and due to interpolation shows that an energy formulation is beneficial for reducing both error sources. The result is an algorithm giving accurate solutions with low computational effort for use in an on-board controller for a fuel-optimal velocity profile and gear selection. The prevailing approach for the look-ahead problem is RHC where main topics are the approximation of the residual cost and the choice of the horizon length. These two topics are given a thorough investigation independent of the method of solving the optimal control problem in each time step. The basis for the fuel equivalents and the residual cost is formed from physical intuition as well as mathematical interpretations in terms of the Lagrange multipliers used in optimization theory. Measures for suboptimality are introduced that enables choosing horizon length with the appropriate compromise between fuel consumption and trip time. Control of a hybrid electric powertrain is put in the framework together with control of velocity and gear. For an efficient solution of the minimum-fuel problem in this case, more fuel equivalence factors and an energy formulation are employed. An application is demonstrated in a design study where it is shown how the optimal trade-off between size and capacity of the electrical system depends on road characteristics, and also that a modestly sized electrical system achieves most of the gain. The contributions develop algorithms, create associated design tools, and carry out experiments. Altogether, a feasible framework is achieved that pave the way for on-board fuel-optimal look-ahead control.

Optimized engine transients

Recent development has renewed the interest in drivetrain concepts which give a higher degree of freedom by disconnecting the engine and vehicle speeds. This freedom raises the demand for active control, which especially during transients is not trivial but of which the quality is crucial for the success of the drivetrain concept. This work attempts to analyze and explain the fuel optimal solution for the simplest drivetrain setup, which is an engine connected to a load which does not restrict the engine speed. This is made by using a Willans model for the engine and deriving the fuel optimal solution during output power transients. The analysis is made with dynamic programming, Pontryagins maximum principle and backward simulation under a static optimal line restriction. The analysis show that the optimal transients can be explained, visualized and, in simple cases, derived from phase planes of the engine speed and the Lagrange multiplier. In these cases the time needed for computation was reduced a factor > 1000 compared to dynamic programming. Restricting the engine to the static optimal line turns out to be very close to optimal, even during highly transient operation, while reducing the time needed for computation a factor ≫ 1000.

Design of a Well-behaved Algorithm for On-board Look-ahead Control

A look-ahead controller is developed for a heavy diesel truck that utilizes information about the road topography ahead of the vehicle when the route is known. A dedicated prediction model is formulated where special attention is given to properly include gear shifting. The nature of the problem is analyzed for the purpose of optimization, and a well performing dynamic programming algorithm is tailored. A key step for satisfactory solutions with a sufficiently low computational effort is to avoid numerical problems. The focus here is the choice of discretization method, and it turns out that a basic analysis give decisive insight into the interplay between the criterion and the discretization errors. The resulting algorithm is demonstrated to perform well in real on-line tests on a highway.

Look-ahead control for heavy trucks to minimize trip time and fuel consumption

Abstract The scenario studied is a drive mission for a heavy diesel truck. With aid of an on board road slope database in combination with a GPS unit, information about the road geometry ahead is extracted. This look-ahead information is used in an optimization of the velocity trajectory with respect to a criterion formulation that weighs trip time and fuel consumption. A dynamic programming algorithm is devised and used in a predictive control scheme by constantly feeding the conventional cruise controller with new set points. The algorithm is evaluated with a real truck on a highway, and the experimental results show that the fuel consumption can be significantly reduced.