Posted: June 25th, 2022

ENEM14015 Dynamic System Modelling And Control

Question:

Discuss the differences expected between real system performance and analysis results.

Compare your Bode diagram showing the plots of magnification and transmissibility factors.

– Consider the advantages and disadvantages that frequency domain analysis has over time domain analysis (Laplace frequency response, etc.)

Consider your final suspension design.

Is the spring damper selection suitable? What steps could you take to improve it? Would you change anything if you had to redo the design/analysis?

Answer:

There are many factors that go into the motorbike model control process.

This project will explain the performance of dynamic model modelling and control of the motorcycle.

The suspension performance can be used in any type of vehicle.

The suspension’s main purpose is to keep the road in place.

This project aims to implement techniques of two degree freedom and construct the three-degree of freedom system.

The mat lab Simulink will analyze this process.

Two degree of freedom will be used to determine the Laplace transform modeling equations and transfer function (Homer, 2014.). Simulink will calculate the transmissibility factor as well as magnification factor for Simulink.

Simulink will analyze the simulation process for multiple degrees of freedom.

Mathematical Model For Dynamic System

Below is the Schematic Diagram of Given System.

This diagram shows the performance of the dynamic systems.

The input signal is the throttle, and it is controlled by an ECU signal.

Traffic conditions can sometimes occur, and the dynamic system is only controlled by the user.

The signal in the dynamic system is processed using two methods.

Two processes are required to drive a vehicle: the transmission actuator and the clutch actuator.

ECU signals determine the vehicle’s speed.

There are two types of suspension performance.

These are the two types.

Spring mass

Unspring mass

The suspension system is supported by a spring mass.

It is a key component of the vehicle (Hopkins J. and Culpepper 2010, 2010).

The unspring mass is directly connected to the wheel bear, wheels and axles.

Road imperfections are caused by uneven and unnecessary force exerted on the unspring mass.

There are three types of dynamic system.

These are Active Suspension System, Passive Suspension System and Semi-Active Suspension System.

Active Suspension System

This is an important part of the suspension system.

In the active suspension system, the rate of suspension can be adjusted.

These variations give the system a lot of flexibility.

It is also called modern suspension system.

Passive Suspension Systems

It is a very popular system, and passive suspension is extremely important.

Passive suspension is also known as conventional suspension system.

It is very affordable and popular, compared to other suspension systems.

Semi-Active Suspension Systems

The semi-active suspension system can also be called adaptive control system.

This system has a lower usage and less power.

It provides good handling for motorbikes that are running on normal surfaces.

Model of Two Degrees Of Freedom

Two different co-ordinates will be used to express the motion of a 2 DOF dynamic system. Additionally, more than one mass is required to model this system.

For 1 DOF systems, one mass is required to create the model.

A dynamic system with a DOF of 1 DOF can be described using one equation.

Two equations are required to create a dynamic system model for 2 DOF.

Two independent co-ordinates can be used to represent the system’s motion.

With the aid of stiffness and mass matrices, equations can be created (Berbyuk 2007).

This diagram shows the two-degree freedom free body diagram.

This model uses force F1 (force F2) to apply the system to the masses of m1, and m2.

Simulation of Two Degrees Of Freedom

This diagram illustrates the output of 2 DOF.

These two masses are used in this model.

It is used to calculate model gain.

To calculate the output, you need to use motion and stiffness.

In the two degrees of freedom, there are two integrators.

The process is implemented using two sum operations.

The sum operation receives the one-step input signal.

The scope operator is connected to the integrator output port.

The final output of 2 DOF will then be displayed (Dukkipati 2008).

2DOF Simulink

This waveform represents the output of a dynamic system with two degrees of freedom.

This is a linear wave method.

This output has some differences from single degrees of freedom (Bagdasaryan 2011,).

Vibration Analysis

The main response of the system is dynamic model, which generates both free vibration and forced vibration.

The initial condition of the system is called free vibration.

Forceed vibration is an external force that generates vibrations.

Some external forces can cause resonance in the system.

Every model has an external frequency and natural frequency that are naturally generated (Bu?kiewicz 2008).

Transmissibility factor of 2DOF Output

Matlab code is used to calculate the two degree of freedom transmissibility factor.

The system will have a Laplace transform if it is subject to applied force.

Transfer Function

You can obtain the Transfer function by using the Laplace transformation of the equation.

The Laplace transform output is the Laplace input. This is the transfer function.

Comparison of 1DOF and 2DOF

2 DOF requires two equations to build the model, but 1 DOF requires only one equation to create the dynamic model.

Modeling a 1 DOF system is much easier than modeling 2 DOF.

Frequency response for 1DOF is:?=.

For 2 DOF, frequency response in first mode is??.

The frequency response of 2 DOF second mode is?=.

Conclusion

Matlab Simulink was used to analyze the model of two degrees of freedom.

Two degree of freedom was achieved by using Matlab Simulink. The Laplace transform modeling equations and transfer function were used to calculate the transmissibility factor for Simulink.

Discussions were held on the suspension performance and the difference between 1 DOF (and 2 DOF)

Simulation of two degrees of freedom was done.

Refer to

Technique for complex control systems using discrete dynamic simulation models.

Simulation Modelling Theory and Practice, 19(4), 1061-1087.

The dynamics of controlled multibody systems using magnetostrictive transmitters.

Multibody System Dynamics 18(2), pp.203–216.

Dynamic analysis of a coupled beam/slider-system.

Control systems.

Harrow, U.K. : Alpha Science International Ltd.

Evidence levels in system dynamics modeling.

System Dynamics Review, 30(1), pp.75-80.

Hopkins, J., and Culpepper M. (2010).

Synthesis of parallel multi-degree-of-freedom flexure system concepts using Freedom and Constraint Topology. Part I: Principles.

Precision Engineering, 34(2). pp.259–270.