Design Procedure- Advanced Control System

1. By applying second-order approximation, the closed-loop bandwidth is determined i.e. required to meet the requirements of settling time, peak time, or rise time.
2. The gain, K, is set to the value that is required by the steady-state error specification.
3. Then, the Bode magnitude and phase diagrams for this gain value are plotted.
4. By applying second-order approximation, the phase margin is calculated to meet the damping ratio or the requirements of percent overshoot.
5. A new phase-margin frequency near ωBW is selected.
6. At the new phase-margin frequency, the additional amount of phase lead required to meet the phase-margin requirement is determined. Then, a small contribution is added that will be required after the lag compensator is added.
7. The lag compensator is designed by opting for higher break frequency one decade below the new phase-margin frequency. The lag compensator design is not critical, and any of the proper phase margin design will be demoted to the lead compensator. The lag compensator provides stability to the system with the gain needed for the steady-state error specification. The value of Ã‰Â£ from the lead compensator's requisites is found. By using the phase required from the lead compensator, the phase response curve of the Figure can be used to determine the value of É£ = 1/β. This value, and the previously found lag's upper break frequency, permits us to determine the lag's lower break frequency.
8. The lead compensator is designed. Using y value from the lag compensator design and that assumed for the new phase-margin frequency, the lower and upper break frequency for the lead compensator is found, after solving for T.
9. The bandwidth is to be checked to be ascertained that the speed requirement given in Step 1 is met.
10. Redesign it, if transient or phase-margin specifications are not met, as revealed by simulation or analysis.

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Improving Steady-State Error

There are multiple uses of the compensators, like it is used to improve the transient response of the system. The compensator can also be used to improve the steady state error characteristics. The steady-state error performance is deteriorated, when the system gain was adjusted to meet the transient response specification, since the transient response as well as the static error constant is related to the gain. With the high gain and the small steady state error, we will have the large percent overshoot. On the other hand, the steady state error increases with the reduced gain to reduced overshoot.

The compensating networks can be designed if we use the dynamic compensators that will allow us to meet transient and steady-state error specifications. Now, there is no need to compromise between the transient response and the steady state error as long as the system operates in its linear range.  Now, the next step is to the system type and driving the associated steady state error to zero. At the origin this additional pole requires integration for its realization. With the addition of the differentiation the transient response and the steady state error are improved with the addition of integration in the forward path.

Configurations

In this chapter, two configurations of compensation are covered; the cascade compensation and the feedback compensation. In the Figure 1 these methods are modeled. The compensating network, G1(s), with the cascade compensation, it is placed at the low power End of the forward path in cascade with the plant. The compensator, H1(s) is placed in the feedback path, if the feedback compensation is used. By using the both methods, the open loop poles and zeros are changed, thereby creating a new root locus that goes through the desired closed-loop pole location.

Compensators

The ideal compensators are those compensators that use the pure integration for improving steady-state error or pure differentiation for improving transient response. It is very necessary that the ideal compensators must be implanted with the active networks. In the case of electric networks, the additional power sources and the use of amplifiers can be used.   It is an advantage of it that steady state error is reduced to zero with the ideal compensators. For improving the transient response the electromechanical ideal compensators can be used since they can be conveniently interfaced with the plant.

Other design techniques that preclude the use of active devices for compensation can be adopted. These compensators do not use pure integration and differentiation and are not ideal compensators, which can be implemented with passive elements such as resistors and capacitors. The steady-state error is not driven to zero in cases where ideal compensators yield zero error; it is its greatest advantage. Therefore, the choice between an active or a passive compensator revolves around cost, weight, desired performance, transfer function, and the interface between the Compensator and other hardware.

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