# مساعدة عاجلة

#### بو مـلاك

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[FONT=&quot]SPECIFICATION[/FONT]
[FONT=&quot]The figure shows the schematic diagram of a simple vehicle containing two identical wheel modules with suspension of the nominal height h, which are interconnected by a link made of two horizontal bars coupled by a spring system.[/FONT]

شاهد الملف المرفق
[FONT=&quot]
[/FONT]
[FONT=&quot]We assume that the vehicle moves on a generally horizontal surface (which may have, nevertheless, many bumps, holes, etc.), the axes y1 and y2 are always kept vertical and the linking bars are always kept horizontal.[/FONT]
[FONT=&quot]Based on well-known laws of mechanics, the following model of the vehicle’s suspension can be proposed:[/FONT]
[FONT=&quot]where:[/FONT]
ü [FONT=&quot]m[/FONT][FONT=&quot] is the mass of a module (for convenience, you can assume that m = 1);[/FONT]
ü [FONT=&quot]b[/FONT][FONT=&quot] is the damping coefficient of both modules;[/FONT]
ü [FONT=&quot]k[/FONT][FONT=&quot] is the spring constant of both modules;[/FONT]
ü [FONT=&quot]K[/FONT][FONT=&quot] is the spring constant of the link;[/FONT]

[FONT=&quot]PROBLEM 1[/FONT]
[FONT=&quot]Draw the block diagram and derive the state-space model of the vehicle’s suspension.[/FONT]

[FONT=&quot]PROBLEM 2[/FONT]
[FONT=&quot]In practice, we are primarily interested in keeping the vehicle’s body as horizontal as possible, i.e. the actual output signal of interest is:[/FONT]
[FONT=&quot]y[/FONT][FONT=&quot]1[/FONT][FONT=&quot](t)[/FONT][FONT=&quot] - y2(t) + w1(t) - w2(t)[/FONT]​
[FONT=&quot]Moreover, the input signals are not independent, but they are identical (with the delay determined by the vehicle’s length L and its current speed V). In other words: [/FONT]
[FONT=&quot]w[/FONT][FONT=&quot]2[/FONT][FONT=&quot](t) = w1(t-L/V)[/FONT][FONT=&quot].[/FONT]​
[FONT=&quot]Using these assumptions, convert the previous model into a SISO (single input single output) system. Derive the transfer function of this SISO system and analyze its properties (stability, responses to various patterns of road bumps, etc.). How do the parameters b, k and K affect the system performances?[/FONT]

[FONT=&quot]PROBLEM 3[/FONT]
[FONT=&quot]Assume that the system is discretized, i.e. its inputs and outputs are sampled with a certain period Ts. (for convenience, you can assume that Ts = 1[ms]). Analyze how discretization modifies the solutions of PROBLEM 1 and PROBLEM 2.

اتمنى حد يساعدني في حل هالسوال الطويل جداا
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