Closed loop control system feedback systems, transfer function

Fig. 4.1 Block diagram of a closed-loop control system. R s) = Laplace transform of reference input r(t) C(s) = Laplace transform of controlled output c(t) B s) = Primary feedback signal, of value H(s)C(s) E s) = Actuating or error signal, of value R s) - B s), G s) = Product of all transfer functions along the forward path H s) = Product of all transfer functions along the feedback path G s)H s) = Open-loop transfer function = summing point symbol, used to denote algebraic summation = Signal take-off point Direction of information flow.

Hence the closed-loop control system for steady state conditions may be described by the forward transfer function of (2.52), using the positive root, and the feedback transfer function of... 

A control system may have several feedback control loops. For example, with a ship autopilot, the rudder-angle control loop is termed the minor loop, whereas the heading control loop is referred to as the major loop. When analysing multiple loop systems, the minor loops are considered first, until the system is reduced to a single overall closed-loop transfer function. 

The closed-loop transfer function for any feedback control system may be written in the factored form given in equation (5.41)... 

Suppose that we use simple feedback control. For this system it was found in Example 19.1 that the open-loop transfer function has crossover frequency (Oco = 2.3 rad/min and ultimate gain Kc = 1.52. The fact that the ultimate gain is 1.52 forced us to use Kc < 1.52. Nevertheless, the system is very close to the brink of instability and has a rather unacceptable offset (see Section 14.2) ... 

Find the closed-loop transfer function YlYgp for the complex control system in Fig. 11.12. Notice that this block diagram has two feedback loops and two disturbance variables. This configuration arises when the cascade control scheme of Chapter 16 is employed. 

In the previous examples, the denominator of the closed-loop transfer function was either a first- or second-order polynomial in s. Consequently, the transient responses to specified inputs were easily determined. In many control problems, the order of the denominator polynomial is three or higher, and the roots of the polynomial have to be determined numerically. Furthermore, for higher-order (n > 2) systems, feedback control can result in unstable responses if inappropriate values of the controller settings are employed. 

The block diagram of a special feedback control system is shown in Fig. El 1.9. Derive an expression for the closed-loop transfer function, Y(s)/D(s). 

A feedback control system has the open-loop transfer function, Gql s) =. SKf l V s + 1). Determine the values of Kc for which the closed-loop system is stable using two approaches ... 

As a starting point for the analysis, consider the block diagram of a feedback control system in Fig. 12.2. The closed-loop transfer function for set-point changes was derived in Section 11.2 ... 

Next we show that the transfer function between a controlled variable and a manipulated variable depends on whether the other feedback control loops are open or closed. Consider the control system in Fig. 18.3fl. If the controller for the second loop Gq2 is out of... 

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