Speed Control Design For A Vehicle System Using Fuzzy Logic

Introduction
Engine and other automobile systems are increasingly controlled electronically. This has led to improved fuel economy, reduced pollution, improved driving safety and reduced manufacturing costs. However the automobile is a hostile environment: especially in the engine compartment, where high temperature, humidity, vibration, electrical interference and a fine cocktail of potentially corrosive pollutants are present. These hostile factors may cause electrical contacts to deteriorate, surface resistances to fall and sensitive electronic systems to fail in a variety of modes. Some of these failure modes will be benign, whereas others may be dangerous and cause accidents and endanger to human life.
A cruise control system, or vehicle speed control system can keep a vehicle's speed constant on long runs and therefore may help prevent driver fatigue [2-5]. If the driver hands over speed control to a cruise control system, then the capability of the system to control speed to the set value is just as critical to safety as is the capability of the driver to control speed manually. So the cruise control system design is imperative and important to an automobile.

Design requirements
   a). Designing controller using fuzzy logic;
   b). Making the automobile’s speed keep constant.

Model description of the automobile

We can use fuzzy control method to design a cruise control system. Obviously, the fuzzy cruise control design objective is to develop a fuzzy controller that regulates a vehicle’s speed   to a driver-specified value .

Speed control design using fuzzy logic
Fuzzy control logic and neural networks are other examples of methodologies control engineers are examining to address the control of very complex systems. A good fuzzy control logic application is in cruise control area.

1) Design of PI fuzzy controller
Suppose that we wish to be able to track a step or ramp change in the driver-specified speed value   very accurately. A “PI fuzzy controller” can be used .The fuzzy controller is denoted by  ;  and are scaling gains; and   is the input of the integrator.                                      
   Find the differential equation that describes the closed-loop system. Let the state be   and find a system of three first-order ordinary differential equations that can be used by the Runge-Kutta method in the simulation of the closed-loop system.   is used to represent the controller in the differential equations.
For the reference input, three different test signals can be used as follows:
a: Test input 1 makes  =18m/sec (40.3 mph) for   and  ＝22 m/sec (49.2 mph) for  .
b: Test input 2 makes  =18m/sec (40.3 mph) for   and   increases linearly (a ramp) from 18 to 22  by  , and then   for  .
c: Test input 3 makes  =22 for   and we use  as the initial condition (this represents starting the vehicle at rest and suddenly commanding a large increase speed).
Use   for test input 1 and 2.
    Design the fuzzy controller   to get less than 2% overshoot, a rise-time between 5 and 7 sec, and a settling time of less than 8 sec (i.e., reach to within 2% of the final value within 8 sec) for the jump from 18 to 22   in “test input 1” that is defined above. Also, for the ramp input (“test input2” above) it must have less than 1 mph (0.447  ) steady-state error (i.e., at the end of the ramp part of the input have less than 1 mph error). Fully specify the controller (e.g., the membership functions, rule-base defuzzification, etc.) and simulate the closed-loop system to demonstrate that it performs properly. Provide plots of   and   on the same axis and   on a different plot. For test input 3 find the rise-time, overshoot, 2% settling time, and steady-state error for the closed-loop system for the controller that you designed to meet the specifications for test input 1 and 2.

2)  Design of PD fuzzy controller
Suppose that you are concerned with tracking a step change in   accurately and that you use the PD fuzzy controller shown in Fig. 5. To represent the derivative, simply use a backward difference
Where   is the integration step size in your simulation (or it could be your sampling period in an implementation).
   Design a PD fuzzy controller to get less than 2% overshoot, a rise-time between 7 and 10 sec. and a settling time of less than 10 sec for test input 1 defined in a). Also, for the ramp input ( test input 2 in 1)) it must have less than 1 mph steady-state error to the ramp (i.e., at the end of the ramp part of the input, have less than 1 mph error).
Fully specify your controller and simulate the closed-loop system to demonstrate that it performs properly. Provide plots of   and   on the same axis and   on a different plot. In the simulations, the Runge-Kutta method is used and an integration step size of 0.01.
Assume that   for test inputs 1 and 2 (hence we ignore the derivative input in coming up with the state equations for the closed-loop system and simply use the approximation for c(t) that is shown above so that we have a two-state system).

Summary
To keep an automobile’s speed constant, a speed control design method using fuzzy logic is
presented. PI fuzzy controller and PD fuzzy controller design schemes are given to regulate a vehicle’s speed to a driver-specified value. The simulation results show the validity and of the proposed technique.
The control design procedure can be summarized as follows:

Modeling and performance objectives
Basically, the role of modeling a fuzzy control design is quite similar to its role in
conventional control system design. In fuzzy control there is a more significant emphasis on the use of heuristics. Conventional feedback controller design entails constructing a controller to meet the closed-loop specifications (such as disturbance rejection properties, insensitivity to plant parameter variations, stability, overshoot, steady-state error et al), which is also applied to fuzzy control design.
Fuzzy controller design
Fuzzy control design essentially amounts to (1) choosing the fuzzy controller inputs and
outputs (2) choosing the preprocessing that is needed for the controller inputs and possibly postprocessing that is needed for the outputs, and (3) designing the four components of the fuzzy controller: (a) The fuzzification interface simply modifies the inputs so that they can be interpreted and compared to the rules in the rule-base. (b) The “rule-base” holds the knowledge, in the form of a set of rules, of how best to control the system. (c) The inference engine evaluates which control rules are relevant at the current time and then decides what the input to the plant should be. And (d) the defuzzification interface converts the conclusions reached by the inference engine into the inputs to the plant.
Computer simulation
To prove the effectivity of the controller design and check up whether the design requirements are realized or not.