ABSTRACT
The problem of optimal loop shaping encompasses two fairly independent parts that can be solved sequentially. The first part is feedback bandwidth maximization, which is solved by appropriately shaping the feedback loop response at higher frequencies. The second part is the distribution of the available feedback over the functional feedback band. The feedback bandwidth is limited by the sensor noise effect at the system output, the sensor noise effect at the actuator input, plant tolerances, and non-minimum phase lag in the feedback loop. The integral of the phase lag in this system is larger than in the absolutely stable system, and as a result, the feedback over the functional bandwidth is larger. This response can be generated by pasting together several elementary responses. Webster’s Collegiate Dictionary defines the word optimal as “most favorable or desirable,” and in practical engineering the optimal design is that which maximizes customer satisfaction.
