Consider the rover system from Homework 8. Recall that naively discretizing an analog controller did not...

Transcribed Image Text:

Consider the rover system from Homework 8. Recall that naively discretizing an analog controller did not produce the desired system response. Instead designing a digital controller directly proved to be a better method for controlling the system. With this wisdom in hand, Zac now sets out to design an optimal digital controller to drive up a hill. To make his job easier, he constrains his controller to the following form where K R is a tunable gain. 0.4 D(z) = K+ z-1 (1) Unfortunately, he does not know how to find an optimal gain or even what optimality means quan- titatively. However, armed with an engineer's greatest tool, brute force, he plans to partition the interval a < K Consider the rover system from Homework 8. Recall that naively discretizing an analog controller did not produce the desired system response. Instead designing a digital controller directly proved to be a better method for controlling the system. With this wisdom in hand, Zac now sets out to design an optimal digital controller to drive up a hill. To make his job easier, he constrains his controller to the following form where K R is a tunable gain. 0.4 D(z) = K+ z-1 (1) Unfortunately, he does not know how to find an optimal gain or even what optimality means quan- titatively. However, armed with an engineer's greatest tool, brute force, he plans to partition the interval a < K