3.- ORIENTACIÓN EDUCATIVA: PRINCIPIOS BÁSICOS Será uno de los elementos claves del proyecto educativo

The control strategy of a hybrid vehicle is defined as an algorithm which regulates the operation of the vehicle powertrain [93]. It is usually implemented in the hybrid vehicle controller which has a supervisory role in regard to the operation of the vehicle. The main objectives of the hybrid vehicle control strategy are to continuously monitor the driver’s demand, vehicle status, current traffic information, and even the information provided by the Global Positioning System (GPS) to determine the proper vehicle operating state for optimal fuel economy, minimum overall energy use, and vehicle performance [69, 93,

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94]. Hybrid vehicle control strategies can be divided into three categories: ruled-based, numerical optimisation-based and real-time optimisation [95]. All the main solutions are classified according to Figure 7-1.

Figure 7-1 Classification of hybrid vehicle control strategies

7.2.1.1 Rule-based Control Strategies

The rule-based control strategies are designed without a priori knowledge of the driving cycle. Therefore, they are effective in the real-time supervisory control of the power flow in the hybrid powertrain. The rules can be obtained by using heuristics, intuition, human expertise, and even mathematical models [93]. The objective of rule-based control strategies is often “load-levelling” which tends to shift the actual IC engine operating point as close as possible to the optimal point of the efficiency, fuel consumption, or emissions at a particular engine speed. Although the control approaches can offer an improvement in energy efficiency, it is clear that they do not guarantee an optimal result in all conditions [95]. Two typical rule-based control strategies are introduced here: respectively (i) a logic threshold control strategy and (ii) a fuzzy logic control strategy. The logic threshold control strategy is widely used because of its speed and simplicity [12]. It based on analysis of power flow in a hybrid powertrain, efficiency/fuel or emission maps of an IC engine, and human experience is utilized to design deterministic rules, generally implemented via lookup tables, to split the requested power between power converters [93]. In other words, the logic threshold control strategy selects the operating mode of the powertrain according to the prevailing and predicted conditions of

Hybrid vehicle control strategies Rule-Based control strategies Global optimization Real-time optimization Logic threshold control strategy Fuzzy logic Dynamic programming Linear programming Model predictive control Equivalent consumption minimization strategy (ECMS)

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the vehicle. The transition between operating modes is decided based on a change in driver demand, or a change in vehicle operating condition.

Looking into the hybrid powertrain as a multi-domain, nonlinear, and time-varying plant, a fuzzy logic control strategy offers a number of advantages including an accessible format and the potential for non-linear behaviour [93]. The fuzzy logic control strategy is an extension of the conventional rule-based control strategy typified by a logic threshold control strategy [93]. The fuzzy logic control strategy uses the decision-making property instead of using deterministic rules. As a result, it can be adopted to realize a real-time though possibly suboptimal power split. The main advantages of the fuzzy logic control strategy are robustness and the potential for adaptive behaviour [93].

7.2.1.2 Global Optimisation

The global optimisation approach can find the global optimum solution by performing the optimisation over a prescribed driving cycle. It is non-causal in nature and requires a priori knowledge of the driving cycle information and could be used directly for real-time hybrid vehicle control strategy. However, the result of the global optimisation can be considered as the benchmark for designing rules for online implementation or comparison for evaluating the quality of other control strategies. The most common global optimisation approach, Dynamic Programming (DP), is introduced later.

DP seems to be a reasonable approach for optimal power split in hybrid vehicles, since it is a powerful tool to save general dynamic optimisation problems, easily handling the constraints and nonlinearity of the problem while obtaining a globally optimal solution [93]. DP calculates every possible combination energy output of the IC engine and another power source in the hybrid powertrain such as motor power at each step, ensuring that the global optimum can be reached. When utilizing DP in the hybrid powertrain optimisation, the model of hybrid vehicle can be expressed in the form of Equation (7-1) where XK is the state vector that includes vehicle speed, State of Charge

(SOC) of the energy store, engine speed, motor speed, etc. While uK is the control vector

that covers gear number, generator torque, engine torque, motor torque, etc. The optimisation goal is to find the control uK at each step to minimize a cost function shown

at Equation (7-2). Also, the constraints in Equation (7-3) are necessary for the optimisation process.

156 𝑋𝐾+1= 𝑓(𝑋𝐾, 𝑢𝐾) (7-1) [96] {_𝐽 𝐽0(𝑋0) = 𝐽0 𝑘(𝑥𝑘) = min𝑢_𝑘∈𝑈_𝑘[𝑓𝑢𝑒𝑙(𝑥𝑘, 𝑢𝑘) + 𝐽𝑘−1(𝑥𝑘−1)] 𝑘 = 1, … , 𝑁 (7-2) [96] { 𝜔𝐼𝐶𝐸 𝑚𝑖𝑛≤ 𝜔𝐼𝐶𝐸 ≤ 𝜔𝐼𝐶𝐸 𝑚𝑎𝑥 𝑇𝐼𝐶𝐸 𝑚𝑖𝑛(𝜔𝐼𝐶𝐸(𝑘)) ≤ 𝑇𝐼𝐶𝐸(𝑘) ≤ 𝑇𝐼𝐶𝐸 𝑚𝑎𝑥(𝜔𝐼𝐶𝐸(𝑘)) 𝑇𝑚 𝑚𝑖𝑛(𝜔𝑚(𝑘), 𝑆𝑂𝐶(𝑘)) ≤ 𝑇𝑚(𝑘) ≤ 𝑇𝑚 𝑚𝑎𝑥(𝜔𝑚(𝑘), 𝑆𝑂𝐶(𝑘)) 𝑆𝑂𝐶𝑚𝑖𝑛≤ 𝑆𝑂𝐶(𝑘) ≤ 𝑆𝑂𝐶𝑚𝑎𝑥 (7-3) [96]

Where ωICE min – minimum speed of the engine,

ωICE max – maximum speed of the engine,

Tmax – torque limitation of the engine,

Tm min and Tm max – motor torque limitation,

The variable SOC(k) is constrained within the permitted minimum value SOCmin and the

maximum value SOCmax of the battery.

When the energy management strategy is designed, the constraints have to be respected [97]. For example, in order to mitigate battery degradation, the SOC should be maintained within a certain range. The torque capacity of the engine and electric motor vary with their rotational speed or environmental temperature, and the speed of the engine and electric motor must be limited to the specific range to ensure safety and reliability [97].

DP will supply a benchmark which can be compared with the rule-based control strategy’s result. Although the DP can find the global optimum, it is an off-line algorithm.

7.2.1.3 Real-time Optimisation

In order to develop a cost function to be used in a real-time optimisation process, the rate of fuel consumption must be available as a measurement. Variations of the stored electrical energy should also be taken into account to guarantee electrical self- sustainability [93]. Although the solution to such a problem is not globally optimal, it is particularly suited to real-time implementation and is reported to be close to optimal in practice [98]. The most well-known approach of the real-time optimisation is the Equivalent Consumption Minimization Strategy (ECMS).

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The “equivalent fuel consumption” of the ECMS is the electrical energy flow costed according how much it will cost in fuel terms to restore that energy to the store. Application of the ECMS method includes an assessment of the relative value derived from a drive cycle of electricity and fuel. The process includes the notion of the “free” energy that is derived from regenerative braking [95]. In [93], one approach, that of calculating the equivalent fuel consumption using mean efficiencies is used when not all components set points are known is introduced as follows:

𝐶𝐸𝑞(𝑘(𝑡), 𝑇𝑒(𝑡)) = {

𝑇𝑒< 0 𝑆𝐹𝐶𝑟𝑒𝑐ℎ_𝑐∙𝜂 ∙𝑃𝑐(𝜔𝑐,𝑇𝑐)

𝑒∙𝜂𝑏𝑎𝑡𝑡

𝑇𝑒≥ 0 𝑆𝐹𝐶𝑑𝑖𝑠∙𝑃𝑒(𝜔𝑒_𝑐,𝑇𝑒)∙𝜂𝑒∙𝜂𝑏𝑎𝑡𝑡

(7-4) [93]

where SFCrech – mean specific fuel consumption for the recharge cases,

SFCdis – mean specific fuel consumption for the discharge cases,

𝜂_𝑒 – mean efficiencies of the motor during recharge, 𝜂_{𝑏𝑎𝑡𝑡} – mean efficiencies of the battery during recharge, c – constant.

The Electric Motor (EM) power to produce Te at ωe is denoted by Pe. And, the total

equivalent fuel consumption CTOT(k(t),Te) is the sum of the real fuel consumption of the

IC engine CICE(k(t),Te) and the equivalent fuel consumption of the EM CEq(k(t),Te). This

allows a unified representation of both the energy used from the battery and the IC engine respectively. As a result, the instantaneous control problem is

min𝑇_𝑒(𝑡),𝑘(𝑡)𝐽 = 𝐶𝑇𝑂𝑇(𝑘(𝑡), 𝑇𝑒(𝑡)) ∙ Δ (7-5) [93]

Zhao et al. [95] used the idea of the ECMS to realize a real-time optimisation of the fuel economy of an HEV. The optimisation problem can be explicitly formulated as minimizing the following cost function in terms of energy:

𝐽𝑓(𝑡𝑓, 𝜇, 𝑆𝑂𝐶) = ∫ 𝑚̇_𝑡𝑡₀𝑓 𝑓(𝜏, 𝜇, 𝑥) 𝑑𝜏 + 𝜑(𝑆𝑂𝐶(𝑡0), 𝑆𝑂𝐶(𝑡𝑓)) (7-6) [95]

where μ – control variables,

x – engine, motor, and battery states, SOC(t0) – initial SOC values,

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SOC(tf) – final SOC values,

𝜑(∙) – penalty function regarding any SOC deviation from its initial value to the final value. The penalty function is also called the equivalent fuel consumption. For the sake of optimality, the boundary condition of the terminal state

𝑆𝑂𝐶(𝑡0) = 𝑆𝑂𝐶(𝑡𝑓) (7-7) [95]

is to be satisfied.

Although the ECMS is designed for the HEV, it still can be transferred to control the pneumatic hybrid vehicles. As mentioned in Chapter 2, some of the pneumatic hybrid vehicles use the pneumatic energy to drive the vehicle in the AM mode or APA mode. It means it can save the fuel by using the pneumatic instead of. As a result, the “equivalent fuel consumption” of the ECMS in the pneumatic hybrid vehicle is the pneumatic energy flow costed according how much it will cost in fuel terms to restore that energy to the store. Application of the ECMS method includes an assessment of the relative value derived from a drive cycle of air and fuel. Furthermore, in the commercial vehicle like buses and trucks, some auxiliaries are driven by the electricity now. It could be driven by the air in the future. Therefore, in the pneumatic hybrid vehicles, the fuel used to drive the auxiliaries can be saved by using the air. As a result, the air usage can be calculated how much it cost in fuel terms. Here, in this research, the pneumatic hybrid powertrain is to realize three special functions. It does not drive the vehicle alone by realizing the AM mode or APA mode. So there is no fuel saved by using the pneumatic energy. Consequently, there is no energy to be calculated in fuel term. Therefore, the ECMS will not be chosen for controlling the pneumatic hybrid city bus in this research and not be discussed in detail.

7.2.2 Logic Threshold Based Energy Control Strategy for Pneumatic