Chapter 4 Feedback Control System Characteristics Open- and Closed-Loop Control Systems Sensitivity of Control Systems to Parameter Variations Control of the Transient Response of Control Systems Disturbance Signals in Closed-loop Systems Steady-State Error

Open- and Closed-Loop Control Systems An open-loop (direct) system operates without feedback and directly generates the output in response to an input signal. R(s) R(s) Y(s) G(s) Y(s) G(s) R(s) Ea(s) Y(s) R(s) + 1 Ea(s) Y(s) G(s) - -H(s) H(s)

Feedback control systems are widely used in manufacturing, mining, automobile and other hardware applications. In response to increased demands for increased efficiency and reliability, these control systems are being required to deliver more accurate and better overall performance in the face of difficult and changing operating conditions.

Why Feedback Control Systems? Decrease in the sensitivity of the system to variation in the parameters of the process G(s). Ease of control and adjustment of the transient response of the system. Improvement in the rejection of the disturbance and noise signals within the system. Improvement in the reduction of the steady-state error of the system

Sensitivity of Control Systems to Parameter Variations A process, represented by G(s), whatever its nature, is subject to a changing environment, aging, ignorance of the exact values of the process parameters, and the natural factors that affect a control process. The sensitivity of a control system to parameter variations is very important. A main advantage of a closed-loop feedback system is its ability to reduce the system’s sensitivity. The system sensitivity is defined as the ratio of the percentage change in the system transfer function to the percentage change of the process transfer function.

The sensitivity of the feedback system to changes in the feedback element H(s) is

Control of the Transient Response of a System One of the most important characteristics of control systems is their transient response. The transient response is the response of a system as a function of time. The transient response often must be adjusted until it is satisfactory. If an open-loop system does not provide satisfactory response, then the process, G(s), must be replaced with a suitable process. Sometimes, the response may be altered by inserting a suitable cascade controller preceding the process G(s). A closed-loop system may often be adjusted to yield the desired response by adjusting the feedback loop parameters.

Disturbance Signals in a Feedback Control System A disturbance signal is an unwanted input signal that affects the system’s output signal. Sources of unwanted signal include: noise from amplifiers, wind gusts affecting antennas and radar systems, and nonlinearity of systems. Feedback systems have the advantage that the effect of distortion, noise, and unwanted disturbances may be effectively reduced.

Armature-Controlled DC Motor 1/Ra Km 1/Js+b Kb Va(s) Ia(s) + - Tm(s) Td(s)  (s) Motor back emf TL(s)

For the Open-loop System The Final Value Theorem Often, it is useful to know the value of a signal as time approaches infinity, that is, the signals final value. From the transfer function, which is in the `s' domain, we can determine the final value, by using the final value theorem. The theorem basically states:

For the Closed-loop System Td(s) R(s) Ea(s) Ka Ia(s) Tm(s) - TL(s) + 1/Ra Km 1/Js+b  (s) + + - - Motor back emf Kb Kt Vf(s) Td(s) R(s) Ea(s) G1(s) G2(s) (s) -H(s)

Steady-State Error The steady-state error is the error after the transient response has decayed, leaving only the continuous response.

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