example digital control

8/16/2019 Example Digital Control

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1 | P a g e Dr.Laith Abdullah Mohammed

Example 1: Transfer function of an interacting system

A two-path signal-flow graph is shown in Figure (a) and the corresponding block diagram is shown

in Figure (b). An example of a control system with multiple signal paths is a multi-legged robot. The paths connecting the input R(s) and output Y(s) are

P 1 = G X G2G2G A(path 1) and P 2 = G5G6 G7 G8(path 2).

There are four self-loops: L1= G2 H 2 , L2 = H 3G3 , L3 = G6H6, and L4 = G7 H 7 .Loops L1, and L2 do not touch L3 and L4. Therefore, the determinant is

∆ = 1 - (L1 + L2 + L3 + L4) + (L1 L3 + L1L4 + L2L3 + L2L4).The cofactor of the determinant along path 1 is evaluated by removing the loops that touch path 1 from A.Hence, we have

L1 = L2 = 0 and ∆1 = 1 - (L3 + L4).Similarly, the cofactor for path 2 is

∆2 = 1 - (L1 + L2)


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A similar analysis can be accomplished using block diagram reduction techniques.The block diagram shown in Figure (b) has four inner feedback loops within the overall block diagram.The block diagram reduction is simplified by first reducing the four inner feedback loops and then placingthe resulting systems in series. Along the top path, the transfer function is


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Example 2: Transfer function of a multiple-loop systemA multiple-loop feedback system is shown in Figure in block diagram form.

There is no need to redraw the diagram in signal-flow graph form, and so we shall proceed as usual by using

Mason's signal-flow gain formula. There is one forward path P x = G1G2G3G4. The feedback loops are

EXAMPLE 3: Transfer function of a complex system Consider a reasonably complex system that would be difficult to reduce by block diagram techniques. Asystem with several feedback loops and feed forward paths is shown in Figure below. The forward pathsare


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Signal-flow graphs and Mason's signal-flow gain formula may be used profitably for the analysis offeedback control systems, electronic amplifier circuits, statistical systems, and mechanical systems,among many other examples.


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Question 1: A four-wheel antilock automobile braking system uses electronic feedback to control

automatically the brake force on each wheel. A block diagram model of a brake control system isshown in Figure below, where Ff(s) and FR(s) are the braking force of the front and rear wheels,

respectively, and R(s) is the desired automobile response on an icy road. Find Ff(s)/ R(s).

Question 2: Off-road vehicles experience many disturbance inputs as they traverse over rough roads. An

active suspension system can be controlled by a sensor that looks "ahead" at the road conditions.An example of a simple suspension system that can accommodate the bumps is shown in Figure

below. Find the appropriate gain K 1 so that the vehicle does not bounce when the desired

deflection is R(s) = 0 and the disturbance is Td(s).

example digital control

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