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Based on analyzing principle about the smart car’s speed control system, the system mathematical model is built. Considering the control optimization, a novel control scheme is proposed based on internal model control, and the internal model controller of speed control system is established. Regarding this subject, the internal control theory is introduced to verify the control performance; the traditional PID control method is employed in the experiment. The experiment indicates that the proposed method based on internal model control is easier to determine parameter and has a well robust and good control result of smart car’s speed.

Cars have been the most important transportation for the progress of science and technology. While we have to face the more serious traffic problems meanwhile enjoying the convenience of the cars, the intelligent transportation system (ITS), which was put forward in recent years, has made people believe that the problems would be solved. However, due to the restriction of experimental environment and cost, research about ITS is very hard to open up in real life. Scaling down the model of ITS in proportional could get a high accuracy simulation and analysis of the real one [

The research about smart car includes the technology, methods of navigation, positioning, motion planning, and speed control. The technology and methods of the speed control are important to the achievement of smart car. There are some algorithms of control, such as an approach based on fault-tolerant control [

Smart car control system is a closed loop control system, which consisted of speed detection module, DC motor driver module, and power supply module. The error between set speed and measurement speed is the input of speed controller, by which the DC motor driver attains the corresponding driving signal; thus the smart car can be driven by a certain speed.

It is hard to build an accurate mathematical model through the analysis of the car’s physical characteristics with the reason that not only the motor type, tire size, and the weight of the car are uncertain but also the power voltage, the wind resistance, and the road friction keep changing. With the analysis of the large amount of experimental data and the reference of the related paper [

It is well known that the measured data of the encoder of the smart car has a linear relationship to the real speed of the smart car through some practical testing; therefore the real speed of the smart car can be easily gained and expressed by the encoder. The smart car model with four wheels is shown in Figure

Model of smart car.

The relationship between the data of encoder and the time is shown in Figure

Relationship between the car’s speed and time.

A specific mathematical model can be achieved by the processing and the analysis to the measured data, and the parameters of model are as follows:

In order to have a good control result and easy operation to the speed control system, we proposed a control scheme based on IMC after the analysis of the mathematic model.

The IMC is a kind of control strategy whose controller is designed on the basis of the process mathematical model. The IMC strategy was firstly proposed by Garcia and Morari in 1982, which caught the researchers and the engineers’ attention simultaneously for its merits of simplicity, good tracking performance, robustness, and ability of eliminating the unmeasured disturbance. It does not need accurate object model and can probably acquire the better robustness after introducing the filter. In addition, the inner model controller not only is able to adjust parameters easily but also has a dual stability and ideal controller features of zero steady-state error.

The inner control model structure is shown in Figure

The IMC structure diagram.

The equivalent IMC structure.

The input of the model is equal to the process output if the above model is accurate (that is to say that expression

Due to the control scheme we proposed IMC which has simple operation and good tracking performance; we began to design an inner model controller for the speed control system to validate it.

For one-order inertial lag model, the design of the inner model controller is divided into two parts including the design of ideal controller and the introduction of the filter.

The IMC structure in Figures

Relationship between the IMC structure and the feedback control structure.

The defined IMC controller is as follows:

It is known that the speed control model in the smart car is one-order inertial lag model from the expression (

This paper mainly discusses the design of the speed controller of the smart car. However, due to the difficulty of building the speed control model of the smart car and the influence of the battery voltage, the environment friction coefficient, and so on, the author constructs an approximate one-order inertia pure lag mathematical model aiming at the speed control system with four wheels and one single DC motor, and the parameter of the motor model is gained by a large number of experiments. The mathematical model of the motor is displayed in expression (

As is said above, the mathematical model of the inner model controller is displayed in expression (

As is discussed above, it is easy to find that the IMC controller has only one parameter about the filter coefficients in the case of the known system. The only one parameter makes it easier to reach the expected result. When looking for the best parameter value, the strategy based on IMC could not be affected by other parameters more directly and conveniently.

The different results are shown in Figure

Different output results of the IMC controller.

Figure

In this paper, aiming at the smart car’s speed control system with characteristics of first-order inertia, the author has simulated the effect of the IMC controller and the PID controller. According to the actual debugging, one group of good parameters of the PID controller is as follows:

The simulation result is in Figure

Comparison to the effect of the IMC and the PID controller with step input.

According to the analysis of Figure

The simulation result is in Figure

Effects of the IMC and the PID controller with disturbance input.

According to the analysis of Figure

In this paper, we propose a strategy of smart car’s speed control system which is based on the IMC and do the research and analysis of its simulation. We can conclude that the system based on IMC has a more superior stability, rapidity, and capacity of resisting disturbance than the one based on the traditional PID control from the simulation results of the two strategies. Meanwhile, the simulation of IMC controller in different parameters within a certain range proves that the IMC has a good ability to adapt. In conclusion, the speed control based on IMC could attain the result of PID control. Moreover, the strategy of IMC could greatly reduce the difficulty of adjusting the parameter of controller. In application, the scheme based on the IMC makes it easier to reach the same control effect compared with other strategies and has strong operability and less demand on the environment. Therefore, our scheme which was proposed based on the IMC can be good for the smart car’s speed control system. With the rapid development of ITS, how to create a precise speed control model in order to achieve a more precise speed control is the next step to in-depth study of the subject.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This present work was supported partially by the Polish-Norwegian Research Programme (Project no. Pol-Nor/200957/47/2013). The authors highly appreciate the above financial support.