Final answer:
The pole-zero cancelation design of the plant 1/(S-1) followed by a compensator of the form (S-1)/(s+1) is unsatisfactory because it leads to an unstable system.
Step-by-step explanation:
The pole-zero cancelation design of the plant 1/(S-1) followed by a compensator of the form (S-1)/(s+1) is unsatisfactory because it leads to an unstable system. When the pole and zero cancel out in the system, it introduces a high-frequency gain in the closed-loop transfer function, which can result in oscillations and instability.
For example, if we consider the compensator (S-1)/(s+1) with the plant 1/(S-1), the closed-loop transfer function becomes ((S-1)/(s+1)) * (1/(S-1)), which simplifies to (1/(s+1)). This means that the closed-loop system has a pole at -1, which makes it unstable.
In order to design a stable system, pole-zero cancelation should be avoided or compensated for through proper control design techniques.