For optimal performance, the controller must operate at an unstable equilibrium
point
Depending on the road conditions, the maximum braking torque may vary over a
wide range
The tyre slippage measurement signal, crucial for controller performance, is both
highly uncertain and noisy
On rough roads, the tyre slip rate varies widely and rapidly due to tyre bouncing
Brake pad coefficient of friction changes
The braking system contains transport delays which limit the control system’s
bandwidth
As stated in the previous section of this chapter, the ABS consists of a conventional hydraulic brake system plus anti-lock components which affect the control characteristics of the ABS. ABS control has a highly non-linear control problem due to the complicated relationship between direction and slip. Another impediment in this control problem is that the linear velocity of the wheel is not directly measurable and it must therefore be estimated. Friction between the road and tyre is also not readily measurable or potentially requires complicated sensors. Researchers have employed various control approaches to tackle this problem. One of the technologies which has been applied to the various aspects of ABS control is soft computing. A brief review of the ideas of soft computing and how they are employed in ABS control is given below.
2.4.1 Control Methods
The ABS system has its own characteristics. In addition to the requirements of the system anti-interference ability and the high reliability, an important requirement is the high-speed control of the process. The majority of ABS systems require a response within milliseconds from the control system. This is a limitation of the algorithm design. More complex algorithms based on the modern control theory are used in application of ABS [82] [85] [86][91].
1. Frequency Response
The transfer function of a control system is the core of the classical linear control theory. Normally, it uses a system with a single-input, single-output (SISO) as the object. The classic control research model is the differential equations.
2. Linear optimal control theory
The state-space method is another way to describe a linear system which uses first-order differential equations to describe the dynamic system characteristics. The state-space methods including Pole Control, Condition Monitoring and Optimal Control can deal with the problem of not only a linear system but also a non-linear or stochastic control system.
3. Adaptive Control System
The design of the controller is done offline. When the structure of the controller is determined, the parameters of dynamic model can be estimated through the online system identification of the adaptive control. From a practical point of view, the more identification parameters required, the more complex the procedures are going to be. These become more difficult for adaptive control.
4. Fuzzy Logic Control System
The model is not based on a mathematical model, but based on how the designers understand the system and summarize the rules of the ABS system. Fuzzy logic control is applicable to the control system in a similar way to the system controlled by human beings. Fuzzy logic control systems, however, lack a theoretical foundation, such as the stability of the control system.
2.4.2 Control Channel Layout on Vehicle Dynamics
With four wheels, many combinations are possible for grouping the wheels into channels. This may be done as a result of cost, performance, or complexity of the system. The number of channels in the system can vary from one to four. The layout refers to the pair of wheels that are grouped together [84] [87] [91].
1. One Channel: Select Rear Axle Control
One channel systems have been exclusively used to control only the rear wheels because the vehicle stability is more dependent on the forces on the rear wheels. Although such systems prevent the vehicle swerving in many situations, their basic shortcoming is the lack of steerability during an emergency stop due to the uncontrolled front wheels. Consequently, full braking during cornering and evasive manoeuvers may result in loss of control. This system configuration by no means meets the present traffic safety requirements.
2. Two Channel: Diagonal Split Control
In a diagonal split system there are two circuits: one is connecting the front-left wheel and the rear-right wheel and the other one is connecting the front-right wheel and the rear-left wheel. Diagonal split control independently modulates brake pressure in each of the diagonal circuits based on the information received from the four wheel speed
sensors. The front to rear braking ratio is controlled by a separate proportioning valve for each channel.
3. Three Channel: ABS with Individual Front wheel Control and Select Rear Axle Control
Four system configurations are possible with three channel systems. This system configuration assures full vehicle steerability and stability with braking in a turn, or evasive manoeuver. Due to the dynamic wheel load distribution during braking in a turn, the higher brake forces available on the front wheels are fully utilized. Only the lower brake force of the outer rear wheel is adjusted to the inner rear wheel. This method also minimizes the brake force differences on the rear axle on roads with different friction coefficients or during turning. Although the system does not offer all the advantages of an individual four wheel control system, its performance is considered satisfactory.
4. Four Channel: Individual Wheel Control
All the wheels are controlled independently of each other. This allows the brake forces on each wheel to be optimized. The stopping distance, steerability and stability is then dependent on the control philosophy used. This system is more expensive because of the extra controls that are required. This system is the only one to pass the current stringent test requirement.