(35 points) The Martian adventures: Mark is running a botanical experiment where he is trying to...

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(35 points) The Martian adventures: Mark is running a botanical experiment where he is trying to replicate recent scientific research that tiny electrical 'shocks' given to plants can improve chemical synthesis (hypothetically resulting in better yields on Mars). You can read more about it here. This experiment calls for very precise control of the electrical current provided to the plant. If the rate of change of voltage across the resistive component of the plant (i.e. dRp/dt) goes beyond 0.15 V/s, the plant dies. The E R Plant Rp RH Cp electrical resistance of the plant is R = 3k, and its capacitance is C = 2.5 10-F. The apparatus draws power from a 24 V DC electrical bus (E) which has a resistance of R = 1 kN. Mark has a pretty lonely life so he also spends a lot of time listening to music. His headphones also draw power from the same electrical bus and have a resistance of R = 2.5 kn. Initially the switch S is closed and the system is in steady state. At time t = 0, Mark unplugs the headphones causing a change in the steady state and causing a dynamic response in the system. Did the mere act of unplugging his headphones kill the first plants on Mars? Determine the current flowing through the circuit at time t = 0, i.e. just before the headphones were unplugged. (Think about how the capacitor behaves in steady state). Write the element equations. Derive the governing equations using KVL, KCL and the element equations. Obtain the state-space model. (35 points) The Martian adventures: Mark is running a botanical experiment where he is trying to replicate recent scientific research that tiny electrical 'shocks' given to plants can improve chemical synthesis (hypothetically resulting in better yields on Mars). You can read more about it here. This experiment calls for very precise control of the electrical current provided to the plant. If the rate of change of voltage across the resistive component of the plant (i.e. dRp/dt) goes beyond 0.15 V/s, the plant dies. The E R Plant Rp RH Cp electrical resistance of the plant is R = 3k, and its capacitance is C = 2.5 10-F. The apparatus draws power from a 24 V DC electrical bus (E) which has a resistance of R = 1 kN. Mark has a pretty lonely life so he also spends a lot of time listening to music. His headphones also draw power from the same electrical bus and have a resistance of R = 2.5 kn. Initially the switch S is closed and the system is in steady state. At time t = 0, Mark unplugs the headphones causing a change in the steady state and causing a dynamic response in the system. Did the mere act of unplugging his headphones kill the first plants on Mars? Determine the current flowing through the circuit at time t = 0, i.e. just before the headphones were unplugged. (Think about how the capacitor behaves in steady state). Write the element equations. Derive the governing equations using KVL, KCL and the element equations. Obtain the state-space model.