Matlab SimMechanics: Double Mass Spring Damper - Essay Example

Their relationship is inverse that is when one is increasing the other is decreasing. Matlab SimMechanic’s has been to assess frequency response and to simulate the system transient response. System performance specification was based upon open-loop time-domain criteria of rising time and damping ratio. The compensators were designed using analog frequency response design methods, based upon open-loop frequency response criteria of phase margin (PM) and gain crossover frequency (ωcg). The design method assumed second-order relationships between open-loop frequency and closed-loop time response measures. These assumptions were invested to determine their reasonableness in the system. Having obtained the required compensators in analog form, a digital equivalent was evaluated. The performance of the continuous-time and discrete-time controllers was compared. It emphasizes the building of systems in the right way as well as focusing on selecting the appropriate systems and their interactions with an aim of satisfying design requirements. In addition, it addresses operations and development of monumental products, as well as the development and functionality of evolving programs. Whereas systems modeling has been an ongoing trend, efforts are likely to continue in the definition and development of systems modeling and accomplishments. The process of modeling remains fundamentally a design process and so differs from system analysis. This makes it relevant in the future for the invention of new configurations. Moreover, a strong fascination remains with the creative process of modeling.
Matlab SimMechanics- Double Mass Spring Damper
The system to be modeled is the Double Mass Spring Damper system which works by changes.
Damping constant of mass =400 N.m/s(c2)
Damping constant of suspension system =12000 N.m/s(c1)
Spring stiffness constant =70000 N/m(K1)
Tire stiffness constant (k) =70000 N/m(K2)
Mass (sprung mass) (m1) =1500 Kg
Mass (m2) =500 Kg
Simulink Model Of The System
The figure shows the Simulink model for Double Mass Spring Damper built for this case

This is an Open-Loop Response and it can be seen that to improve the response of the Double Mass Spring Damper is changing the Damping constant of the suspension system. A typical complex notation in a control system computation is also made up of the time and frequency domains that contain a single signal in each of these domains that are constituted by complex numbers. It is thus important to note that since each complex variable consists of two numbers, the multiplication of these variables must involve the combination of the four individual components in order to form a single product that is also made up of two components just like the initial variables.
The process of synthesizing the frequency domain from the separate single signals undergoes three main essential loops which are also concentric in nature. The outermost loop is the one that runs through a number of stages while the middle loop is the one that moves through each of the individual frequency spectra that are in the stage currently being worked on. The final loop which is also the innermost is what now uses the butterfly diagram mentioned earlier in the calculation of the points that are in each frequency spectra. This shows the impact of one mass on the suspension system. It should be noted that the final 1 point signals are no longer time-domain signals but rather, a frequency spectrum. Lastly, the frequency spectra are then supposed to be recombined in the reverse order that is exactly similar to the order followed during the decomposition of the time domain. Since the bit reversal formula is not applicable for this recombination, the reverse process is performed one stage at a time. The reverse process is known as synthesis and this is done stage-wise from the single point spectra and finally forming the 16 point frequency spectrum. The different flow diagrams used to represent this synthesis are referred to as a butterfly and it is also what forms the basic computational element of the system as it transforms two complex points into two different but still complex points.
In frequency response, controllers are designed by pole-zero that is matched through limited frequencies that are 50 times lower than the second mass. The coefficients are determined using indirect or direct design. The frequency response depends on the quickness of waveforms applied.