0195136047.pdf

784 BASIC CONTROL SYSTEMS

as the Laplace transform of the impulse response. The impulse response of a linear system

is defined as the output response of the system when the input is a unit impulse function.

• All initial conditions of the system are assumed to be zero.


• The transfer function is independent of the input.
  Theblock diagramis a pictorial representation of the equations of the system. Each block
  represents a mathematical operation, and the blocks are interconnected to satisfy the governing
  equations of the system. The block diagram thus provides a chart of the procedure to be followed
  in combining the simultaneous equations, from which useful information can often be obtained
  without finding a complete analytical solution. The block-diagram technique has been highly
  developed in connection with studies of feedback control systems, often leading to programming
  a problem for solution on an analog computer.
  The simple configuration shown in Figure 16.2.2 is actually the basic building block of a
  complex block diagram. The arrows on the diagram imply that the block diagram has a unilateral
  property; in other words, a signal can pass only in the direction of the arrows. A box is the
  symbol for multiplication; the input quantity is multiplied by the function in the box to obtain the
  output. With circles indicating summing points (in an algebraic sense), and with boxes or blocks
  denoting multiplication, any linear mathematical expression can be represented by block-diagram
  notation, as in Figure 16.2.3 for anelementary feedback control system. The expression for the
  output quantity with negative feedback is given by
  C=GE=G(R−B)=G(R−HC) (16.2.1)
  or

C=

G

1 +HG

R (16.2.2)

InputR(s) G(s) C(s) = OutputG(s)R(s)

Figure 16.2.2Basic building block of a block diagram.

R(s) reference variable (input signal)

C(s) output signal (controlled variable)

B(s) feedback signal, = H(s)C(s)

E(s) actuating signal (error variable), = R(s) − B(s)

G(s) forward path transfer function or open-loop transfer function, = C(s)/E(s)

M(s) closed-loop transfer function, = C(s)/R(s) = G(s)/1 + G(s)H(s)

H(s) feedback path transfer function

G(s)H(s) loop gain

Feedback elements (loop)

Controlled variable

(output signal)

Feedforward

Reference variable(input signal) Actuatingsignal elements (loop)

Error detector

(comparator)

Feedback

signal

H(s)

G(s) C(s)

c(t)

+ E(s)

− e(t)

R(s)

r(t)

B(s)

b(t)

Figure 16.2.3Block diagram of an elementary feedback control system.