4.0: Prelude to Control System Design Objectives

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In a feedback control system, the controller is designed to achieve certain objective. The first and foremost among them is closed-loop system stability. The next is good dynamic stability displayed by an acceptable transient response. In tracking systems, the elimination of tracking error in desired. Further, the controlled system is required to mitigate disturbances entering the system and guard it against parameter variations and unmodeled dynamics. Hence we will discuss the ways to achieve the following objectives in this chapter:

Closed-loop stability
Acceptable transient response
Acceptable steady-state error
Sensitivity and robustness

In control system design, the stability of the closed-loop characteristic polynomial can be ascertained by algebraic methods, such as the Routh’s array. These method can be applied toward the design of static controller. Stability can also be determined from the Bode plot of the loop transfer function.

The transient response is commonly evaluated in terms of time-domain performance metrics applied to the step response of the closed-loop system. The design specifications specify limits on the settling time of the system response and/or damping ratio of closed-loop roots. A phase-lead or PD/PID controller can be employed to obtain transient response improvements.

The steady-state error to prototype (step and ramp) inputs is measured in terms of position and velocity error constants of the loop transfer function. Generally speaking, high loop gain reduces steady-state error, but also makes the system prone to oscillations. The steady-state error can be eliminated by placing a PI/PID controller in the feedback loop.

Disturbance inputs are unavoidable in the operation of physical systems. Common examples of disturbance inputs include road bumps while driving, turbulence in the airplanes, and machinery vibrations in industrial plants, etc. Effective disturbance rejection requires high loop gain in the frequency range of disturbance.

Aging in the physical system causes changes in the plant transfer function thus reducing the effectiveness of the controller. A well-designed control system is desired to have robustness against unmodeled dynamics as well as low sensitivity to parameter variations.

The control system design objectives involve inherent trade-offs. For example, a static controller cannot simultaneously improve the transient response and reduce steady-state error to a constant input. Similarly, disturbance rejection and reference tracking pose conflicting design objectives. When faced with such situations, it is not always easy to find the right balance in meeting and prioritizing design objectives. Hence, the control system design is more of an art than an exact science, i.e., it relies much on the skills of the designer.