Generic Structures First-Order Negative Feedback

10D-4475-22.2 Example 2: Population-Death systemFigure 3 models the dynamics of a population of mules. The mule population isthe stock and the death rate is the outflow. The death fraction is the fraction of mulesthat die each year. The implicit goal of the mule system is zero. With no births in thesystem, the mules will eventually die out.The death rate = mule population * death fraction.mule populationdeath ratedeath fractionFigure 3. Population-Death systemExamples 1 and 2 both share the same underlying structure of a stock with anoutflow proportional to the stock. Both have an implicit goal of zero, which drives theexponential decay.2.3 Example 3: Company Downsizing SystemThe third example in Figure 4 shows a negative feedback structure with thenumber of employees in a company as the stock and the firing rate as the outflow.Instead of having an implicit goal of zero as in examples 1 and 2, the company’s goal isthe desired number of employees. The distance to goal is the difference between thelevel and the goal, and is simply the number of employees that the firm must reduce by toreach the goal. Thedistance to goal = number of employees – desired number of employees.