Model Predictive Control (MPC)

Johannesson [51] compares the potential improvement in fuel economy depending on the amount of prior information that the controller has available. A baseline controller assumes perfect access to the complete future power demand and therefore DDP is used to calculate the optimal control. Three strategies are developed and tested for fuel efficiency over the same route. The first strategy is a SDP solution based on city driving usage patterns. Jo-hannesson also develops a single step MPC controller capable of using location and traffic data obtained from the Global Positioning System (GPS) on-board and in real-time. These controllers are compared to the DDP optimal solution. It is shown that the controller with the lowest amount of information can achieve a fuel economy 1-3% from the optimum, and the controller with traffic information can achieve within 0.3% of the optimal control

strat-egy. Johannesson concludes that the performance of the position dependent and optimal controllers is almost identical. The position independent controller is capable of very good performance as long it is well tuned to the drive cycles it is tested on. As the simulation is limited to repetitions of the same route, Johannesson suggests further work could be done to test the robustness of the algorithms on different routes and varying types of driving.

Johannesson also mentions that relying on previously measured data is often impracticable and investigation into a controller that uses information stored in a digital map would be worthwhile.

2.3.6 Summary

Machine learning techniques offer a significant benefit over heuristic controllers in that they are able to optimise the strategy in a holistic sense much more easily. The performance of heuristic controllers is generally very dependent on the specific vehicle configuration and usage pattern and as a result a strategy that performs well in one instance may be inadequate in another. There is a great variety of examples of many different machine learning techniques in the literature, although by far dynamic programming and SDP are the most common. DDP can provide the optimal solution to a specific duty cycle and is therefore very useful as a baseline for comparison or for tuning “rule-based” strategies for real-time implementation. Unfortunately, the solution provided by DDP is time dependent and requires perfect knowledge of the exact duty cycle a priori.

In order to overcome this issue, SDP instead finds the optimal solution to a statistical model of typical usage patterns. This produces a time-invariant policy which is based on the state of the vehicle. As a result, it can be directly implemented on board the vehicle.

There are a number of variants in the application of SDP to the EMS problem. Firstly, the inclusion of additional inputs to define the vehicle state allows the transitional probabili-ties to be more accurate and the cost function to be made more complex, however this can significantly increase the computational time required to solve the optimisation. Another area of refinement is the exact method used. Finite horizon solvers assume a fixed number of steps which can be chosen based on historical data [63]. Infinite horizon solvers, how-ever, continue to refine the strategy until it converges. In order to do this, they require a discount factor which exponentially reduces the weight on future steps. Finally, Shortest Path Stochastic Dynamic Programming (SP-SDP) solutions include an absorbing terminal state which does not accumulate cost. As a result, they are able to converge without the use of a discount factor. The choice of method is largely determined by the type of strategy required, with infinite horizon solutions tending to produce the most effective controllers for CS strategies and terminal state solutions proving most effective for CD strategies.

Alongside SDP, there are a number of other techniques which have been experimented with in the literature. Harmon [68] used a neural network to generate the EMS for an UAV, showing improvement when compared to “rule-based” algorithms, although no quantifiable comparison to SDP is given. Harmon did remark however, that the technique is much more computational efficient and as a result could be performed in real-time on board the vehicle. Dextreit [67] used GT in order to develop an EMS based on a non-cooperative game between the driver and the powertrain. It is noted that the EMS based on GT outperformed the SDP solution despite being much more computationally efficient, however the exact implementation of neither controller is given, which may have some bearing on the results.

Finally, Johannesson [51] investigated the potential benefit of providing real-time in-formation of the vehicles location to the EMS. MPC was used to provide an estimation of a single step using location data obtained using GPS. The results showed that performance within 0.3% of the optimal solution was achievable; however, this was only marginally bet-ter than the solution provided by SDP based on offline learning. As a result, the additional complexity of the technique may not be justified purely on a raw performance basis. One potential advantage of this technique however, is that it may be more robust than the SDP for real-world scenarios where the vehicles usage patterns may not be accurately repre-sented by the offline learning, or may change over time.

2.4 Conclusions

Due to the relatively immaturity of hybrid vehicles, there is a large variety of different ap-proaches to the problem of energy management and the optimisation of the powertrain.

At one end of the scale there are a number of papers describing heuristic controllers which have been developed and implemented on board test vehicles. These range in complex-ity from simple “thermostatic” battery SoC management, to complex state machines which vary their behaviour depending on the operating conditions of the vehicle and the actions of the driver. At the other end of the scale, there are theoretical results for advanced opti-misation techniques such as dynamic programming and even predictive control based on real-time location data.

In consideration of the techniques presented in the literature there are a number of areas with scope for further research. Firstly, limited work has been found to apply GT, although Dextreit [67] suggests that it can outperform SDP, which is by far the most popu-lar technique in recent years. Because SDP calculates the statistically optimal solution, this is a surprising result, and warrants further investigation. One plausible reason for this is that SDP requires discretization of the vehicles state space. Due to the computational bur-den of the optimisation process, and despite modern processing speeds, this discretization is usually quite coarse in order to produce results in a reasonable amount of time. Dex-treit mentions that the GT controller is optimised approximately 200 times quicker than the SDP strategy and therefore it is possible that finer control is achievable using GT. Con-versely, other authors have mentioned that diminishing returns are seen when increasing the fidelity of the SDP optimisation and therefore it is equally possible that given a finer discretization, the SDP may still be more effective.

Another possible area with scope for further research is MPC, and the potential for improving the performance of the EMS using real-time information about location, route and road conditions. Many modern vehicles are factory fitted with GPS navigation and internet connectivity. As a result, the assumption that the duty cycle of the vehicle cannot be known in advance is no longer necessarily valid. It may soon be possible to implement DDP on board the vehicle, calculating the optimal EMS for any journey. There are two major challenges with this however. Even with advanced technology, such as real-time road condition information provided for by systems such as Intelligent Transport Systems (ITSs), it is impossible to have perfect knowledge of the future loading conditions on the EMS.

Therefore, it would be interesting to investigate the robustness of such controllers given imperfect information. Secondly, DDP is computationally expensive and it may be difficult to perform the optimisation in real-time. However, one way to get around this problem would be to perform the optimisation off-board and transmit the solution to the vehicle using wireless networking.

In addition to the method used for the optimisation, the variables to be optimised must also be taken into consideration. A significant proportion of the work in the literature focuses solely on the optimisation of the fuel consumption. Although this makes a good baseline for the comparison of different techniques, it has been found when performing vehicle testing that other concerns such as component reliability and the driver’s percep-tion are equally important. Strategies optimised purely on the fuel consumppercep-tion tend to require subsequent modification to ensure that they are suitable for real-world use, which inevitably results in a loss of performance. Optimisation of a cost function which takes

into account these additional considerations often results in a strategy which is suitable for real-world testing with only a minor increase in fuel consumption.

A relatively broad literature review has been undertaken which has considered not only FCHEVs, but also other types of hybrid vehicle including gasoline hybrid passenger vehi-cles, commercial vehicles and even UAVs. At this point, it is therefore important to bring the focus back to FCHEVs in particular and how these innovations identified from surrounding research areas can be applied in the context of this project.

In contrast to their ICE hybrid counterparts, the vast majority of research into the design of the EMS specifically for FCHEVs is relatively sparse. There are a number of papers in which the ICE emissions are optimised alongside the fuel consumption, or the number of gear shifts is minimised to improve the drive-ability of a parallel hybrid fitted with an automatic gearbox. The main area of focus specific to fuel cells is generally focussed on the reduction of transient loading using heuristic techniques, however, and very little work has been found to minimise this using computational optimisation techniques. No work has been found that is intended to specifically reduce the effect of other degradation methods such as those caused by open-circuit conditions or excessive temperature.

As was mentioned in Chapter 1, the reliability of the fuel cell stack is one of the prin-cipal areas which requires further development for transport applications. The EMS can have a significant effect on the degradation due to the fact that it is directly responsible for controlling the operating point of the fuel cell at any time. Therefore, the management of fuel cell lifetime using the EMS will form the main focus of this work. This will differ from previous work in the literature in that a quantitative model of the fuel cell degrada-tion suitable for SDP optimisadegrada-tion will be developed. This model will include a number of degradation causes, not just transient loading, and will allow estimation of the fuel cell lifetime to be predicted. The resulting controller can be compared to other controllers in the literature in order to assess its benefit and also be used for component sizing exercises for investigation and optimisation of the hybrid powertrain design.