ENEM14015 Dynamic System Modelling And Control

The method of motorbike model controlling process have many criteria. This project explains the performance of dynamic system modelling and control of the motorbike. In any kind of automobile system the suspension performance is widely used. Because the suspension is mainly used to maintain the grip on the road.

The main goal of this projects to implement the techniques of two degree of freedom and to construct the three degree of freedom system. This process will be analyzed by using mat lab Simulink. The Laplace transform modelling equations and transfer functions will be determined in two degree of freedom (Homer, 2014).The transmissibility factor and magnification factor will be calculated for two degree of freedom in Simulink. The simulation process of multiple degree of freedom will be analyzed. 

1. Mathematical model of dynamic system  

           The Schematic diagram of given system is given below. The performance of the dynamic system shows in this diagram. The input signal is a throttle and it is performed by ECU signal. Sometimes the traffic conditions will occurs, during this condition the dynamic system only controlled by a user. In the dynamic system the signal is processed in two methods. The transmission actuator and clutch actuator is a two process to drive a vehicle. The vehicle speed is determined by ECU signal.

2. Suspension performance Analysis

Suspension performance classified into two types. The two types are

• Spring mass
• Unspring mass

A spring mass is main condition to support the suspension system. It is one of the part of the vehicle (Hopkins, J. and Culpepper, 2010). The wheel bear, axles and wheel hub is directly connected to the unspring mass. The imperfections of road is obtained by the unnecessary and uneven force on the unspring mass. Dynamic system is divided into three types. These are Active Suspension system, Passive Suspension system and semi active suspension system.

Active suspension system

        It is important system in the suspension system. The rate of the suspension of spring can be varied in the active suspension system. These variations make good ability to the system. It is also known as modern suspension system.

Passive suspension system

Passive suspension is extensively used system and it is very important. The passive suspension system also called as conventional suspension system. Compared to other suspension system it is very popular system and low cost.

Semi-active suspension system

The semi-active suspension system is otherwise called as adaptive control system. Usage of this system is less and this system have less power. The system provide good handling when the motorbike running in the normal surface.

3. Two degree of freedom model

The motion of 2 DOF dynamic system will be expressed with the help of two different co-ordinates and more than one masses are required to model this system. In other hand 1 DOF system one mass is used to develop the model. One equation is enough to describe about 1 DOF dynamic system. In case of 2 DOF, two equations are need to develop the dynamic system model. To represent the motion of the system two independent co-ordinates are used. The required equations are created with the help of mass and stiffness matrices (Berbyuk, 2007). This model shows the free body diagram of the two degree freedom.

In this model, force F1 and F2 are applied to the system to the masses m1, m2.

4. Simulation of Two degree of freedom 

This diagram shows the 2 DOF output. In this model the two masses are used. And it is used to calculate the gain of the model. The Stiffness and motion are used to get the output. Two integrators are used in the two degree of freedom. Totally two sum operations is used to implement the process. The one step input signal is given into the sum operation. The integrator output port is connected to scope operator. Then the final output of 2 DOF is displayed (Dukkipati, 2008).

5. 2DOF Simulink 

The above waveform describes the output of the two degree freedom of dynamic system. This result shows linear wave method. Compared to single degree of freedom this output have some changes (Bagdasaryan, 2011).

6. Vibration analysis

Forced vibration and free vibration are generated in dynamic model which is the main response created by the system. The free vibration is the initial condition generated by the system. Some vibrations are generated by external force called forced vibration. Resonance in the system will be occurred by some external forces. In every model external frequency and natural frequencies are generated naturally (Bu?kiewicz, 2008). 

7. Transmissibility factor of 2DOF output

The two degree of freedom transmissibility factor of is executed using Matlab code. 

8. Modelling Equation of 2DOF Laplace transform

Laplace transform would be obtained for the system with damped and undamped conditions.For damped system the motion of the system is given by the equation which is the result of applied force.Laplace transforms of the system when force is applied to the system. 

Transfer Function

The Transfer function can be obtained the using the Laplace transform of the equation. The transfer function is defined as the ratio between Laplace transform output and the Laplace of a system input. 

9. Comparison between 1DOF and 2DOF
10. 2 DOF uses two different equation to develop the model but in case of 1 DOF only one equation is enough to create the dynamic system model.
11. Compared with 2 DOF, modelling of 1 DOF system is simple.
12. Frequency response in 1DOF is ?=. In case of 2 DOF, the frequency response of first mode is ?=. In 2 DOF second mode, the frequency response is ? =.

 Conclusion

The model of two degree of freedom has been analyzed by using Matlab Simulink. In two degree of freedom, The Laplace transform modelling equations and transfer functions has been determined the transmissibility factor was calculated for the two degree of freedom in Simulink. The suspension performance and difference between 1 DOF and 2 DOF were discussed. The simulation process of two degree of freedom has been done. 

References

Bagdasaryan, A. (2011). Discrete dynamic simulation models and technique for complex control systems. Simulation Modelling Practice and Theory, 19(4), pp.1061-1087.

Berbyuk, V. (2007). Towards dynamics of controlled multibody systems with magnetostrictive transducers. Multibody System Dynamics, 18(2), pp.203-216.

Bu?kiewicz, J. (2008). A dynamic analysis of a coupled beam/slider system. Applied Mathematical Modelling, 32(10), pp.1941-1955.

Dukkipati, R. (2008). Control systems. Harrow, U.K.: Alpha Science International Ltd.

Homer, J. (2014). Levels of evidence in system dynamics modeling. System Dynamics Review, 30(1-2), pp.75-80.

Hopkins, J. and Culpepper, M. (2010). Synthesis of multi-degree of freedom, parallel flexure system concepts via Freedom and Constraint Topology (FACT) – Part I: Principles. Precision Engineering, 34(2), pp.259-270.