Question 12.7: Analog Computer Simulation of Automotive Suspension Implemen...
Analog Computer Simulation of Automotive Suspension
Implement the analog computer simulation of the automotive suspension system of Figure 12.37.
Known Quantities: Mass, spring rate, and damping parameters of automotive suspension.
Find: Component values of analog computer circuit of Figure 12.39.
Schematics, Diagrams, Circuits, and Given Data: M=400 \mathrm{~kg} ; K=1.6 \times 10^{5} \mathrm{~N} / \mathrm{m}; B=20 \times 10^{3} \mathrm{~N} / \mathrm{m}-\mathrm{s}.
Assumptions: Assume ideal op-amps. Express all resistors in \mathrm{M} \Omega and all capacitors in \mu \mathrm{F}.
Analysis: With reference to Figure 12.39, we observe that the analog computer simulation of the automotive suspension requires: a four-input summer, two integrators, two coefficient multipliers, and one sign inverter.
Expressing all resistors in \mathrm{M} \Omega and all capacitors in \mu \mathrm{F} is useful because each integrator has a multiplier of -1 / R C. Using R=1 \mathrm{M} \Omega and C=1 \mu \mathrm{F} results in -1 / R C=-1. Figure 12.40 depicts the integrator configuration. The four-input summing amplifier uses 1-\mathrm{M} \Omega resistors throughout, so that the gain for each input is also equal to -1. On the other hand, the two coefficient multipliers are required to have gains -K / M=-4,000 and -B / M=50, respectively. Thus we select 10-\mathrm{M} \Omega and 2.5-\mathrm{k} \Omega resistors for the first coefficient multiplier, and 1-M \Omega and 20-k \Omega resistors for the second. Finally, the inverter can be realized with two 1-M \Omega resistors. The various elements are depicted in Figure 12.40.
Comments: Note that it is not necessary to employ five op-amps in this analog simulator. The summing amplifier function and the first integrator could, for example, be combined into a single op-amp, and one of the two coefficient multipliers could be eliminated. This idea is explored further in the homework problems.
