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Digital Control System. Digital Controller DAC ADC Plant Sensor + -. 

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Digital Controller DAC ADC Plant Sensor + -

The  analog signals  are converted to  digital signals  by an analog-to-digital converter ( ADC ), while the digital signal from the computer is converted into an  analog signal  by a digital-to-analog converter ( DAC ).

Continuous and Discrete. T he inputs and outputs of electrical, mechanical, chemical and biological processes are measured as functions of time with amplitudes expressed in terms of voltage, current, torque, pressure, etc. These functions are called continuous-time signals , and to process them with a computer they must be converted into binary sequences—or a string of ones and zeros that is understood by the computer . In a digital computer, differentiation and integration can be done only approximately, and the solution of ordinary differential equations requires a discretization process.. 

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T he  inputs and outputs of electrical, mechanical,  chemical and  biological processes are  measured as functions of time  with amplitudes expressed in  terms of  voltage, current, torque, pressure, etc. These functions are called  continuous-time signals , and  to process  them with a computer they must be converted into binary sequences—or a string of ones  and zeros  that is understood by the computer . In a digital computer, differentiation and integration can be done only approximately, and the  solution of  ordinary differential equations requires a discretization  process.

Infinitesimal Calculus , or just plain  Calculus , deals with functions of one or more continuously  changing variables. Finite Calculus , on the other hand, deals with sequences.

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6. Simulink Model. Ts=O.1s t sin 10 ZOH Ts = 0.05s ZOHI. 

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Ts=O.1s
t
sin
10
ZOH
Ts = 0.05s
ZOHI

Derivative and Forward Finite Difference. Derivative operator:  Forward finite difference operator:. 

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Derivative operator:  Forward finite difference operator:

Check-1. The forward finite difference is Coinciding with the derivative.. 

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The  forward  finite difference  is Coinciding  with the derivative.

Check-2. The forward finite difference is The derivative is. 

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The  forward finite difference  is The derivative  is

Check-3. The forward finite difference is The derivative is. 

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0 0.01 0 1 0.03 0.02 2 0.05 0.04 3 0.07 0.06

Conclusion. 11. Number of samples, n. Number of samples, n. 

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12. Simulink Model. Is Sample Time 0.01 Au Ts = 0.01s 0.02 Scope 0.01. 

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Is
Sample Time
0.01
Au
Ts = 0.01s
0.02
Scope
0.01

Derivative and Backward Finite Difference. 13. 

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Derivative and Backward Finite Difference

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15. Matlab Program. Matlab Program. Ts = 0.1 ; %% forward finite difference for n=0:N-1, x1 = 4*cos(2*pi*(n+1)* Ts ); x2 = 4*cos(2*pi*n* Ts ); del_x1(n+1) = x1-x2; end yf = del_x1/ Ts ; %% backward finite difference for n=0:N-1, x1 = 4*cos(2*pi*n* Ts ); x2 = 4*cos(2*pi*(n-1)* Ts ); del_x2(n+1) = x1-x2; end yb = del_x2/ Ts ;. 

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Ts  =  0.1 ; %%  forward finite difference for n=0:N-1,     x1 = 4*cos(2*pi*(n+1)* Ts );     x2 = 4*cos(2*pi*n* Ts );     del_x1(n+1) = x1-x2; end yf  = del_x1/ Ts ;   %% backward finite difference for n=0:N-1,     x1 = 4*cos(2*pi*n* Ts );     x2 = 4*cos(2*pi*(n-1)* Ts );     del_x2(n+1) = x1-x2; end yb  = del_x2/ Ts ;

Signals and Systems