Charles Darwin and his son Francis studied plant growth, one of their interests was the bending of plants toward light caused by differential growth, is called

#Question id: 40563

#Unit 12. Biochemical Engineering

The transfer function of a Proportional-Integral (PI) controller 𝐺_𝐶(𝑠) is given by 

where 𝐾_𝐶 is the controller gain, 𝜏_𝐼 is the controller integral time constant and s is the Laplace variable. The role of the integral component of the controller is to ____________. 

#Question id: 31568

#Unit 12. Biochemical Engineering

Let 𝑦(𝑡) be a bacterial population whose growth is given by  where 𝜆 is the growth rate constant. If 𝑦(0) = 1 and 𝑦(1) = 4, then the value of 𝜆 is

#Question id: 31569

#Unit 12. Biochemical Engineering

The minimum value of the function for 𝑥 > 0 is 

#Question id: 31612

#Unit 12. Biochemical Engineering

The output 𝑦(𝑡) of a first-order process is governed by the following differential equation where 𝜏𝑝 is a non-zero time constant, 𝐾𝑝 is the gain and 𝑓(𝑡) is the input with 𝑓(0) = 0. Assume 𝑦(0) = 0. The transfer function for this process is (consider 𝑠 as the independent variable in the Laplace domain) 

#Question id: 31614

#Unit 12. Biochemical Engineering

Let 𝑚 and 𝑛 be fixed real numbers. If the function 𝑦(𝑡) = 𝐶₁𝑒 ^𝑡 + 𝐶₂𝑒 ^−𝑡 is a solution of for any constants 𝐶₁ and 𝐶₂, then 𝑚 + 𝑛 is equal to

#Question id: 31615

#Unit 12. Biochemical Engineering

If the function  where 𝑎 and 𝑏 are constants, is differentiable at 𝑥 = 0, then 𝑎 + 𝑏 is equal to