Chapter 7: Other Hybrid Vehicle Control Problems

7.1 Basics of internal combustion engine control

The primary function of engine control is to adjust the engine torque generated to meet the required torque from the driver and at same time to satisfy the requirements of emission, fuel economy, driving comfort, and safety. For a spark ignition (SI) engine, the torque is generated through a combustion process and determined by the air mass, fuel mass, and ignition time, as shown in Fig. 7.1. For a diesel engine, the torque is also generated by a combustion process, but it is a function of the injected fuel mass and injection time, as shown in Fig. 7.2. In order to achieve the objectives, all variables that influence the torque are controlled by the electronic/engine control unit (ECU). This section will briefly describe the general schematic diagrams of SI engine and diesel engine control. The detailed engine controls are very sophisticated, and they are beyond the scope of this book. The interested reader is refer to the literature for further studies (Guzzella and Onder, 2010).

SI Engine Control The SI engine control system is complex and consists of many subsystems. From a control point of view, it is a multi-input–multi-output (MIMO) interconnected control system where the fuel delivery and injection system, air fuel mixing system, and cooling and warming system are the main subsystems. The most important control functions include starting and poststarting enrichment control, warm-up enrichment control, acceleration enrichment control, full-throttle enrichment control, overrun fuel cutoff control, engine speed limits control, closed-loop engine idle-speed control, and lambda control. The overall SI engine control system is illustrated in Fig. 7.3. The measured variables of the SI engine include acceleration pedal position, brake pedal position, engine speed, coolant temperature, intake air flow, oxygen (lambda O₂ sensor), throttle position (idle and overrun, wide-open throttle), and cylinder pressure.

Diesel Engine Control The objective of diesel engine control is to adjust the injected fuel mass and time to make the generated torque and emissions meet the drivability and environmental requirements. The control system mainly includes minimum and maximum speed limit control, idle-speed governor, engine temperature control, and fuel mass injection control. The diesel engine control system is illustrated in Fig. 7.4. The measured variables of a diesel engine include engine speed, coolant temperature, intake air flow, oxygen level in emissions, and position of the acceleration pedal and brake pedal as well as cylinder pressure.

7.2 Engine torque fluctuation dumping control through electric motor

Due to the complexity of internal combustion, the generated torque presents a certain degree of fluctuation when it responds to throttle maneuvers reflecting power demand from the driver. As a result, the resonance vibration in drivelines is excited and transferred to passenger compartments through the suspension system and engine mount (Abe et al., 1989). A vibration mechanism model is shown in Fig. 7.5a which consists of the engine, transmission including clutch, torque converter and gear box, and vehicle body. When the acceleration pedal is depressed, the fuel mass and air flow are immediately increased to combustion, which produces transient torque to the powertrain, as shown in Fig. 7.5b; furthermore, resonance is generated due to the mass and stiffness of the powertrain and vehicle body, as shown in the Fig. 7.5c. In conventional powertrains, the torque fluctuations are attenuated by the damper system installed in the torque converter, which generally results in 5–15% efficiency loss; however, the hybrid powertrain provides an additional opportunity to attenuate the torque fluctuation by a well-controlled motor as the motor can generate either positive torque (power) or negative torque (regenerative). Engine transient fluctuation during dumping involves having the motor generate torque opposite in phase to engine torque (shown in Fig. 7.6); the control system diagram is shown in Fig. 7.7. In practice, there are many challenges to control engine torque fluctuation dumping, and several approaches have been investigated (Nakajima et al., 2000; Kim et al., 2009). It is necessary to apply an advanced control strategy for the designed vehicle to meet the requirements of drivability, silence, and comfort. In the following section, a sliding-mode control strategy is introduced to attenuate torque fluctuation at the drive shaft.

7.2.1 Sliding-Mode Control

Sliding-mode control is a nonlinear control method which alters the dynamic characteristics of a nonlinear system by a high-frequency switching control action. The designed switching control law is to drive the system state trajectory onto a predefined surface in the state space and to maintain the state trajectory on this surface for subsequent time. The surface is sometimes also called a sliding surface, switching hyperplane, or sliding manifold. Under the switch control action, the system state trajectory will go to one side of the surface from an initial state, and once the state trajectory reaches the other side of the surface, the switched control will enforce the state trajectory back to the surface (Utikin, 1992). Therefore, the surface actually determines how to regulate the control action in this method, and robustness is an advantage because the controlled system will naturally slide along the surface and rest on it in finite time. Sliding-mode control can be described mathematically as follows.

Consider the nonlinear system

7.1

where x = (x₁ x₂ x_n)^T is a state vector, A(x) and B(x) are the appreciate nonlinear vector functions, and u is a scalar control variable.

Sliding-mode control is discontinuous and of the form

7.2

where u⁺ ≠ u⁻ are control laws corresponding with the state trajectory being on different sides of the hyperplane S, which is a linear switching hyperplane in equation (7.2), and C^T = (c₁ c₂ c_n) is a constant vector.

Take the two-phase variable for instance shown in Fig. 7.8. In this example, if S ≥ 0, when t = 0, the system state vector x will reach the plane S = 0 in a finite time t under control action u⁺, the control u⁺ forces the system state x to pass through the switching plane and enter the domain of S < 0, and the control suddenly changes from u⁺ to u⁻, which enforces that the state passes through the switching plane again in the opposite direction and enters into the domain of S > 0 once more, and then a sliding mode is formed.

Therefore, the state x will be restricted on the switching plane S = 0 by the sliding control u, and the condition to form a sliding mode is

7.3

that is, , which forces the system motion toward the hyperplane S = 0.

It is apparent that the sliding mode will be formed if the following equation is held by a control action:

7.4

where sgn(S) is the sign function of S, the term − ε sgn(S) generates a variable structure control to form a sliding mode at the desired hyperplane S, and the item kS makes the trajectory coverage exponential.

As an example, sliding-mode control can be designed as follows:

where ε and k are the given positive constants, which are not sensitive to the system operation setpoint.

7.2.2 Engine Torque Fluctuation Dumping Control Based on Sliding-Mode Control Method

Since the sliding-mode control is very robust to the disturbances and plant parameter variations, it has been widely applied to control DC motors, permanent magnet synchronous motors, and induction motors. In addition, it is also used in DC/DC converters, DC/AC inverters, and other power electronic devices (Utkin et al., 1999). Based on the nature of the engine transient torque dumping control system, the sliding-control strategy is also a good control candidate and can be implemented as follows.

Assume that the dynamics of the engine drive shaft is described by the state space equation

7.8

where x₁ is the torque on the engine drive shaft produced by combustion, x₂ is the speed of the engine drive shaft, and u is the antitorque generated by either the electric motor or vehicle or both.

Based on the torque–speed characteristics of an engine, the sliding surface can be set as a simple surface expressed by equation (7.9) or (7.10) and shown in Fig. 7.9a,b, respectively:

7.9

7.10

As an example, if equation (7.9) is selected as the sliding surface, the control law can be designed to make the sliding mode occur according to the equation

7.11

where ε is a positive constant that defines the boundary of the sliding-mode zone and k is also a positive constant and determines the sliding frequency to the plane S = 0. Figure 7.10 shows the performance of the example sliding mode. At t = 0, the states move to the sliding surface under the control action and will remain on the plane, as shown by the bold red line; however, due to system inertia, limited control action, action delay, or other imperfections, system states will pass through the sliding plane leaving chatter in the sliding zone within a range [ − ρ ρ] depending on the actual system characteristics and control ability.

If we assume that the drive shaft dynamics are described by equation (7.8) and the sliding surface and sliding-mode behavior are defined by equations (7.9) and (7.11), the following sliding-mode control law can be obtained to dump engine torque fluctuation on the drive shaft by the motor in an HEV.

From equations (7.8) and (7.9), we have

7.12

Substituting (7.11) into (7.12) yields

7.13

Equating the right side of equations (7.12) and (7.13), the sliding-mode control law can be derived as

7.14

7.3 High-voltage bus spike control

Both hybrid electric vehicles and pure electric vehicles have a high-voltage bus connected to the battery system, DC/DC converter, and DC/AC inverter for low-voltage components and the propulsion motor, as shown in Fig. 7.11. When the vehicle accelerates or the regenerative brake pedal pressed, the DC/DC converter or DC/AC inverter will generate spikes which frequently hit battery limits, especially during low-temperature operation, as shown in Fig. 7.12.

Since these spikes are very harmful to battery life, some hybrid vehicles are equipped with an overvoltage protection device, shown as the box on the right side of Fig. 7.11. If this is the case, the vehicle controller needs to send a control signal to turn the device on or off to attenuate the spikes, protecting the battery and other components on the high-voltage bus. The control diagram is illustrated in Fig. 7.13. This section introduces three strategies to control the overvoltage protection unit (OVPU).

Bang-Bang Control Strategy of Overvoltage Protection Bang-bang control to prevent the voltage on the DC bus from going over the limit is a strategy that determines the duration that the OVPU should be on and off based on the actual bus voltage. When the charging (regenerative) voltage is greater than the upper setpoint, the OVPU turns on, and when the charging voltage is below the lower setpoint, the OVPU turns off, as shown in Fig. 7.14.

The control strategy and OVPU turn-on/off setpoint can be described as

7.15

7.16

where u is the signal to control OVPU on or off and δ₁ and δ₂ are calibratable variables. Obviously, bang-bang control is not optimal, but it is effective and has a low implementation cost.

PID-Based On/Off Control Strategy of Overvoltage Protection The OVPU can be controlled based on the following PID control strategy:

7.17

where e(t) = V_setpoint(t) − V_actual(t) is the control error, u(t) is the signal to control OVPU on or off, V_setpoint is the maximum bus voltage, V_actual is actual bus voltage, and K, T_i, T_d are the parameters of PID controller.

Fuzzy Logic–Based On/Off Control Strategy of Overvoltage Protection A fuzzy logic–based on/off control strategy can also be developed to control OVPU. The control inputs are the error between maximum bus voltage setpoint and actual bus voltage and the derivative of the error. The output is the signal controlling OVPU on or off. A diagram of the fuzzy logic–based OVPU on/off control strategy is shown in Fig. 7.15, and the control design procedure is as follows:

7.4 Thermal control of HEV battery system

Since the performance of a thermal system has a significant impact on the vehicle's fuel economy, vehicle manufacturers have been making great strides in improving the performance of the HEV thermal system. The HEV cooling system is very complex and consists of several independent cooling loops, such as the engine cooling loop, transmission cooling loop, motor and DC/AC inverter cooling loop, battery pack cooling loop, and accessory power cooling loop. Some of them are liquid cooled, others are air cooled, and each cooling loop has a temperature setpoint. The engine cooling loop normally has the highest temperature setpoint, but the cooling loop of the battery system is the most sophisticated and lowest temperature loop in an HEV, normally set between 25 and 35°C. A diagram of an HEV/EV battery system cooling loop is illustrated in Fig. 7.16.

From Fig. 7.16, the battery system can be cooled by a chiller and/or radiator/cooling fan set or heated by an electric heater. The coolant pump and four-position electrical coolant valve provide additional measures to control battery temperature more efficiently. If the battery temperature is slightly lower than the setpoint, the coolant goes through a short cycling path by closing the channels to the radiator and chiller from the four-poistion valve. If the battery temperature is much lower than the setpoint in the deep winter, the heater is on and the channels to the radiator and chiller are closed by the four-position valve. If the battery temperature is slightly higher than the setpoint, the coolant goes only through the radiator channel, and the cooling fan can be turned on or off depending on the battery temperature. If the battery is very hot in the summer, the chiller will be turned on in addition to the radiator channel. From a control point of view, the battery cooling subsystem is a multiple variable system, and the electrical load (battery current) can be considered as a process disturbance. The simplified thermal loop diagram is shown in Fig. 7.17, and the battery system thermal behaviors can be described by the equations

7.18

that is,

7.19

or

7.20

where I is the battery terminal current (A), R_ess is the internal resistance (Ω) of the battery system, T_ess is the battery cell temperature (K), T_c is the coolant temperature (K), C_ess is the specific heat (J/kg·K) of the battery system, C_c is the specific heat (J/kg·K) of coolant, h is heat transfer coefficient (W/m² · K), A_H/C is the heating/cooling surface area (m²) between the battery pack and the heating/cooling channel, M_ess is the mass (kg) of the battery system, M_c is the mass of total coolant (kg), is the energy transfer rate (W) of the heater or chiller, η_H/C is the efficiency of the heater or chiller, is the mass flow rate (kg/s) of coolant, P_pump is the power (W) of the heating/cooling system pump, and k is the transfer coefficient of pump power to mass flow rate.

7.4.1 Combined PID Feedback with Feedforward Battery Thermal System Control Strategy

In addition to feedback control, feedforward control can significantly improve system performance if major disturbances can be measured before they affect the process output. Figure 7.18 shows PID feedback with a feedforward control strategy for battery thermal system control. The power of the heater/chiller is the input variable and battery temperature is the output, while battery load, the cooling fan, and coolant flow path and flow rate (power of the coolant pump) are considered as major disturbances. In this control system, the speed of the cooling fan, the system operating mode (heating or cooling), the flow path (positions of electrical valve), and flow rate (power of coolant pump) are logically set based on the battery temperature, ambient temperature, and target temperature (setpoint) of the battery system. The feedforward variables include cooling fan speed, coolant flow rate, and generated heat (I²R_ess) by the battery system itself. The relationships among these variables are established by look-up tables which are set separately in heating mode and cooling mode. Since the generated heat I²R_ess by the battery system has significant impact on battery temperature, it is directly and independently fed forward to the process control.

In this control strategy, the feedback control action is calculated by the PID equation

7.21

where e(t) = T_sp(t) − T_ess(t) is the error between the set temperature and actual temperature, u_PID(t) is the calculated PID control action and is a sum of three terms: the P term Ke(t), which is proportional to the error; the I term , which is proportional to the integral of the error; and the D term K · T_d[de(t)/dt] which is proportional to the derivative of the error.

The discrete form can be obtained by approximating the integral and the derivative terms using

7.22

7.23

where T_s is the sampling period of time and k is the discrete step at time t, k_p = K, k_i = K/T_i, k_d = K · T_d.

The feedforward control action is calculated as

7.24

where u_cfan is the feedforward control action of the cooling fan, which is calculated using a look-up table at the given operating mode; u_cf is the feedforward control action related to coolant flow rate, which is calculated using a look-up table at the given operating mode; is the feedforward control action related to the generated heat by the battery system; and is online estimated ESS internal resistance through a recursive least-squares algorithm based on the measured ESS terminal voltage and current.

The actual control action is given as

7.25

The parameters of the feedback PID controller are turned offline but changed in realtime based on the outputs of logic control reflecting battery thermal system operating mode and conditions. For PID control and detailed turning parameter methods and recursive least-squares estimation algorithm, the interested reader is referred elsewhere (Åstrom and Hägglund, 1995; Goodwin and Payne, 1977; Ljung, 1987).

7.4.2 Optimal Battery Thermal Control Strategy

Since battery thermal control has an impact on the overall fuel economy of an HEV, it is necessary to trade off control accuracy and cooling system power consumption with an optimal control strategy, which means that the control u^*(t) denotes the control function u(t) giving the minimum objective function J in the required time t_f once J is set. If we assume that the optimal control u^*(t) does exist and has the form shown in Fig. 7.19, this u^*(t) minimizes the objective function J, and the controll path between two end points T_ess(0) and T_ess(t_f) is labeled . In practice, optimal control is normally appended to PID control, and once the battery temperature reaches the setpoint, the control strategy will be switched to the feedback PID with feedforward control described above to maintain the battery system at the target temperature.

If we assume that the thermal process is described by the following state space equation, the optimal control can be determined as follows

7.26

where I is the battery system terminal current (A), R_ess is the internal resistance (Ω) of the battery system, T_ess is the cell temperature (K), T_c is the temperature (K) of coolant, a_ij is the component of the state matrix which is a function of the operating power of the coolant pump and implemented by look-up tables, b₂ is the component of the control vector which is a constant for a given cooling system, and u is the control variable which is the power of the heater/chiller.

A. Define Objective Function The objective function of optimal thermal system control can be defined as

7.27

where T_sp is the setpoint of the battery system thermal control, T_ess(t) is the measured battery temperature, t_f is the required time to complete the control, P_pump is the operating power of the coolant pump which results in a coolant flow rate, u is the operating power of the heater/chiller, w₁ and w₂ are the weight factors for the control action P_pump and u.

The discrete form is

7.28

where ΔT is the control time interval and N represents the required steps to reach the control target.

B. Set Control Constraints The constraints of battery system thermal optimal control include:

• Coolant flow rate range, that is, the operating power range of the coolant pump:

  7.29

  where P_min is the minimum operating power of the coolant pump to maintain the required minimum flow rate and P_max is the maximum allowable operating power of the coolant pump to generate the maximum flow rate.

• The operating power range of the heater/chiller is given as

  7.30

where is the maximum heating or cooling power of the heater/chiller.

C. Set Initial Condition and End Point Value

7.31

where is the initial coolant temperature, is the initial battery temperature, is the target coolant temperature (setpoint), and is the target battery temperature (setpoint).

The battery system of an HEV generally has the following setpoints and constraints to ensure its best efficiency and health state:

• Target operation temperature: 25–35°C
• Maximum coolant pressure: 40 kPa (5.8 psi)
• Thermal gradient within the battery system: ≤ 3°C

D. Determine Control Law There are two methods that can be used to solve the problem: One is Bellman's dynamic programming and the other is Pontryagin's minimum principle (Pontryagin, 1962). Pontryagin's minimum principle provides a necessary condition for optimal control rather than a direct computation of the control itself, but the detailed application depends on the type of problem posed. The fundamental theory of the dynamic programming method is the principle of optimality, that is, “an optimal policy has the property that whatever the initial state and the initial decision are, the remaining decisions must constitute an optimal policy with regard to the state resulting from the first decision” (Bellman, 1957, page 83). The dynamic programming technique is a favorable method to find the optimal control law for battery system thermal control, and the interested reader is referred to Lewis and Syrmos (1995) for a detailed solution for an actual battery system.

7.5 HEV/EV traction motor control

Since the electric motor is the sole power source of a series HEV and EV, the quality of the traction motor control significantly affects the vehicle's drivability and safety. In addition, compared with the conventional powertrain, the electrical powertrain of an HEV/EV has superior dynamic behavior, such as higher stalling torque and faster transient response. In this section, two key control problems are briefly addressed.

7.5.1 Traction Torque Control

During standing start, acceleration, or braking, how much force can be transferred to the road from the wheels depends on the traction availability between the tires and the road surface. The adhesion and slip curves for acceleration and braking are shown in Fig. 7.20. The electric motor output torque during acceleration and regenerative (braking) should be limited by the amount of slip, allowing the response to remain within the stable range. From the curves, it is can be seen that any increase in slip up to a certain point is accompanied by a corresponding increase in available adhesion, but beyond that point, further increases in slip take the curves through the maximum adhesion into the unstable range, resulting in a reduction of adhesion. The regenerative braking will result in the wheel locking within a short period of time. Under acceleration, the driving wheels will start to spin more and more if traction torque exceeds the maximum adhesion point.

The PID feedback with feedforward control, shown in Fig. 7.21, can be used to control the traction force, which provides closed-loop control of the torque at the drive wheels. In this control diagram, vehicle speed compares with wheel speed, and the difference is fed to the PID controller, and then its output is added to the direct demand torque from driver so the motor's output torque is adjusted. To further improve traction motor control performance, a more sophisticated control strategy may be needed, and the interested reader is referred to Appendix B for advanced control methods.

7.5.2 Anti-Rollback Control

Rollback occurs during the transition between release of the brake pedal and application of the accelerator on an incline. If it is not done at the same time, the vehicle will roll down the incline. For a conventional vehicle with an automatic transmission, the anti-rollback feature can be easily implemented by transmission control (Tamimi et al., 2005). Since there is no such transmission in a series HEV or EV, anti-rollback control is necessary when the vehicle is parked on an incline. This function is also necessary to support the stop–start feature in the hybrid powertrain by holding the vehicle on an incline and preventing the undesired motion. Although the rollback can be prevented by sending an appropriate control signal to the electrical or hydraulic brake control module, it is the most efficient and economic way to apply traction/regenerative torque to prevent rollback in an HEV/EV.

A control diagram to implement anti-rollback is given in Fig. 7.22 for an HEV/EV. Based on the request throttle torque from the driver, the grade of the incline, and other vehicle states such as the key state and vehicle position (down or uphill), the vehicle controller sets the desired speed on the wheels. The desired wheel speed and the grade of the incline are fed to a calibratable look-up table to set a traction/brake torque, and simultaneously a PID controller outputs a torque based on the difference between desired wheel speed and actual wheel speed. The sum of the set traction/brake torque and PID output traction/brake torque is the amount of anti-rollback torque the traction motor needs to generate.

7.6 Active suspension control of HEV/EV systems

The purpose of the vehicle suspension system is to provide driving comfort and operating safety through damping vertical oscillations of the vehicle and improving vehicle body and wheel/tire transient dynamics. A traditional suspension system consists of steel springs and shock absorbers to transmit and smooth all forces between the body and the road. The primary function of the spring is to carry the vehicle mass and isolate the vehicle body from road irregularities, while the absorber damps out the up–down motions of a vehicle on its springs. Such a suspension system is also called a passive suspension system. Generally speaking, the softer dampers provide a more pleasurable drive, while the vehicle is more stable if a stiffer damper is used. Therefore, the design must choose between driving comfort and operating safety.

On the other hand, the suspension systems, in which the damping properties can be adjusted to some extent, are active suspension systems and can be further classified as semiactive and active. Compared with passive suspension systems, in semiactive suspension systems the damping characteristics of the spring and/or shock absorber can adapt to actual demands, while the active suspension systems are equipped with separate actuators that can exert an extra force on the suspension system. Figure 7.23 illustrates the passive, semiactive, and active suspension systems. Conventional active suspension systems are implemented through high-speed hydraulic, hydropneumatic, or pneumatic systems, and the vehicle body oscillations are compensated for by adjusting the hydraulic fluid or compressed air supply. However, due to the complexity of the control, cost of implementation, and high and quick peak power demand, currently only a few high-end conventional vehicles are equipped with such active suspension systems.

Advances in electronics led to the development of new sensors and actuators and advanced control strategies result in suspension systems that can be controlled by adjusting the properties of the springs and dampers. So far, the active suspension system in an HEV/EV has emerged as an active research and development area to improve driving comfort, operating safety, and fuel economy. Unlike the active suspension systems in conventional vehicles, active suspension systems in an HEV/EV are controlled by electric actuators, and they are further divided into two major categories: rotary motorbased and linear motorbased, as shown in Fig. 7.24. The advantages of the electric active suspension system over the conventional hydraulic/pneumatic active suspension system are superior dynamic performances and regenerative capability. Using the electric active suspension system, the kinetic energy of vehicle body vibration can be converted into electric energy to charge the battery system, rather than wasting it as heat energy as in a conventional suspension system, which results in extended mileage of the electric vehicle or improved fuel economy of the hybrid electric vehicle. Since the linear motor–based active suspension system is still in the developing stage, this section only introduces the controls of the rotary motor–based active suspension system.

7.6.1 Suspension System Model of a Quarter Car

The free-body diagram of the suspension system of a quarter car is shown in Fig. 7.25, with the following notation:

According to Fig. 7.25 and based on Newton's second law, the dynamics of a suspension system can be described by the differential equation

7.32

Reorganizing equation (7.32), we get

7.33

If we define that the disturbance input is the road level disturbance v = z₀, control input is actuator force u = F_u, state variables are x₁ = z₁, x₂ = ₁, x₃ = z₂, x₄ = ₂, and outputs are wheel/tire displacement and vehicle body displacement, that is, y₁ = z₁ and y₂ = z₂, then we have the following state space equation of the active suspension system:

7.34

The transfer function between the control input voltage and the output force of the actuator can be assumed as

7.35

7.6.2 Active Suspension System Control

The output force of the electric actuator can be controlled against the road disturbance, and the control objective is to minimize the vehicle body displacement, that is, the output variable y₂. This section presents PID and model predictive control strategies of the active suspension system based on the following parameters of the suspension system and vehicle body:

From the above system parameters, the system model (7.34) is detailed as

7.36

Furthermore, the following transfer functions can be obtained:

PID Control Strategy The PID-based active suspension control system is shown in Fig. 7.26, where the output of PID control is the manipulated variable of the actuator, and in turn the actuator outputs the associated force to the suspension system. The road level displacement is considered as the measured disturbance input. Output limits of the PID controller are − 5 V V and the corresponding actuator output limits are − 2800 N N. Since the control objective is to minimize the displacement of the vehicle body, the tuned PID controller is actually set as a PI controller. The gain Kand integral time constant T_i are set as 50 and 0.4, respectively.

The following simulation example shows that when exerting a road disturbance signal, shown in Fig. 7.27, oscillations of the vehicle body are significantly attenuated by the active suspension control. Figures 7.28 and 7.29 present the vehicle body and tire/wheel responses of the suspension system with/without active control action. Figures 7.30 and 7.31 show the output force and consumed/regenerated electric power of the actuator based on the PID control strategy, respectively.

Model Predictive Control Strategy The model predictive active suspension control system is shown in Fig. 7.32. The inputs of the model predictive controller are the reference setpoint and measured road disturbance. The vehicle body displacement is one of the measured system outputs, and it is fed back to the input. The output of the model predictive controller is the input of the actuator, and the actuator generates the corresponding manipulated force to the active suspension system.

The set control objective is to minimize the displacement of the vehicle body, and detailed parameters of the model predictive controller are as follows:

• Sampling time: 100 μs
• Prediction horizon: 10
• Control horizon: 2
• Weight factor of manipulated variable rate: 0.1
• Weight factor of manipulated variable: 1
• Weight factor of output variable: 1000
• Actuator input constraints: − 5 V V
• Actuator output constraints: − 2800 N N

The achieved simulation results are as follows: When exerting the same road disturbance signal as for the PID controller, shown Fig. 7.27, the dynamics of the vehicle body are significantly improved by the active control action, shown as Fig. 7.33; the tire/wheel responses of the suspension system with/without active control action are shown in Fig. 7.34; the output force and consumed/regenerated electric power of the actuator based on the MPC control strategy are shown in Fig. 7.35 and Fig. 7.36.

The active suspension system shows that it is a challenge to control the dynamic behavior to meet driving comfort and operating safety requirements. From the presented active suspension control strategies, it can be found that the control strategy plays a very important role in an active suspension system and an advanced control strategy can effectively improve the performance and efficiency of the active suspension system. Since the 1990s, advanced active suspension control systems have been extensively researched, and most recent work has focused on control strategy development and application, such as optimal feedback control and adaptive control strategies, to achieve the desired system performance to overcome the degradation of component performance over time (Fischer and Isermann, 2004).

References

Abe, T., et al. “Nissan's New High-Drivability Vibration Control System.” Technical Paper No. 891157, Society of Automotive Engineers, Warrendale, PA, 1989.

Åstrom, K., and Hägglund, T. PID Controllers: Theory, Design, and Tuning, 2nd ed. Instrument Society of America, Research Triangle Park, NC, 1995.

Bellman, R. Dynamic Programming. Princeton University Press, Princeton, NJ, 1957.

Fischer, D., and Isermann, R. “Mechatronic Semi-Active and Active Vehicle Suspensions.” Control Engineering Practice, 12, 1353–1367, 2004.

Goodwin, G., and Payne, R. Dynamic System Identification: Experiment Design and Data Analysis, Mathematics in Science and Engineering, Vol. 136. Academic, New York, 1977.

Guzzella, L., and Onder, H. C. Introduction to Modeling and Control of Internal Combustion Engine Systems. Springer-Verlag, Berlin, 2010.

Kim, S., et al. “Transient Control Strategy of Hybrid Electric Vehicle during Mode Change.” SAE Paper No. SAE-2009-01-0228, Society of Automotive Engineers, Warrendale, PA, 2009.

Lewis, F., and Syrmos, V. Optimal Control, 2nd ed. Wiley, New York, 1995.

Ljung, L. System Identification Theory for the User. Prentice-Hall, Englewood Cliffs, NJ, 1987.

Nakajima, Y., et al. “A Study on the Reduction of Crankshaft Rotational Vibration Velocity by Using a Motor-Generator.” JSAE Review, 21, 335–341, 2000.

Pontryagin, L. The Mathematical Theory of Optimal Processes. Vol. 4, Wiley-Interscience, New York, 1962.

Tamimi, M., et al. “Hill Hold Moding.” SAE Technical Paper Series 2005-01-0786. Society of Automotive Engineers (SAE) (http://www.sae.org), 2005.

Utikin, V. I. Sliding Modes in Control and Optimization. Springer-Verlag, Berlin, 1992.

Utkin, V. I., Guldner, J., and Shi, J. Sliding Mode Control in Electromechanical Systems. Taylor & Francis, London, 1999.