CONTROL SYSTEM DESIGN by using MATLAB Creation of Transfer Functions sys = tf(num,den) creates a continuous-time transfer function with numerator(s) and denominator(s) specified by num and den.  OPEN LOOP T.F  G(s) in OUT tf = 𝑜𝑢𝑡 𝑖𝑛

CONTROL SYSTEM DESIGN by using Creation of Transfer Functions sys = tf(num,den) creates a continuous-time transfer function with numerator(s) and denominator(s) specified by num and den.  CLOSED LOOP T.F  in out G(s) H(s) tf = 𝑮(𝒔) 𝟏+𝑮 𝒔 𝑯(𝒔)

CONTROL SYSTEM DESIGN by using MATLAB Creation of Transfer Functions sys = tf(num,den) creates a continuous-time transfer function with numerator(s) and denominator(s) specified by num and den.  tf= 𝒔 𝒔 𝟐 +𝟒𝒔+𝟓

CONTROL SYSTEM DESIGN by using MATLAB Creation of Transfer Functions num=[1 0]; den=[1 4 5]; h=tf(num,den) stepplot(h) tf= 𝒔 𝒔 𝟐 +𝟒𝒔+𝟓

CONTROL SYSTEM DESIGN by using MATLAB Example 2 Transfer Function Model with One-Input Two-Outputs Create the one-input, two-output transfer function H(s)= 𝒔+𝟏 𝒔 𝟐 +𝟐𝒔+𝟐 1 𝑠 with input current and outputs torque and angle velocity. To do this, enter num = {[1 1] ; 1}; den = {[1 2 2] ; [1 0]}; h = tf(num,den) stepplot(h)

1: 𝒔+𝟏 𝒔 𝟐 +𝟐𝒔+𝟐 2: 𝟏 𝑺

Second-Order Transfer Function from Damping and Natural Frequency

CONTROL SYSTEM DESIGN H(s)= 𝛚𝐨^𝟐 𝐬 𝟐 +𝟐𝛇𝛚𝟎𝐬+𝛚𝐨^𝟐 Example 3 Second-Order Transfer Function from Damping and Natural Frequency Create a tf model that represents a second-order system with known natural frequency and damping ratio. Solve the followıng second order TF. eq. Wher: wo=3 and zeta is considered underdamped ? zeta = 0.25; w0 = 3; h = tf(w0^2,[1,2*zeta*w0,w0^2]) stepplot(h) H(s)= 𝛚𝐨^𝟐 𝐬 𝟐 +𝟐𝛇𝛚𝟎𝐬+𝛚𝐨^𝟐

zeta = 0; w0 = 3; h = tf(w0^2,[1,2*zeta*w0,w0^2]) stepplot(h,'r') hold on zeta = 1; i = tf(w0^2,[1,2*zeta*w0,w0^2]) stepplot(i)

zeta = 0.25; w0 = 3; h = tf(w0^2,[1,2*zeta*w0,w0^2]) stepplot(h,'r') hold on zeta = 2; i = tf(w0^2,[1,2*zeta*w0,w0^2]) stepplot(i)

CONTROL SYSTEM DESIGN Multiple-Input Multiple-Output Transfer Function Model Specify the discrete MIMO transfer function Use MATLAB to explain the following 4 MIMO systems as a Multiple input Multiple output transfer function? with common denominator d (z) = z + 0.3 and sample time of 0.2 seconds. num = {1 [1 0];[-1 2] 3}; ts = 0.2; den=[1 0.3]; h=tf(num,den,ts) stepplot(h)

CONTROL SYSTEM DESIGN State-space models are models that use state variables to describe a system. Example 5 Convert State-Space Model to Transfer Function -Compute the transfer function of the state-space model with the following data. sys = ss([-2 -1;1 -2],[1 1;2 -1],[1 0],[0 1]); a=tf(sys) stepplot(a)

CONTROL SYSTEM DESIGN Example 1 Pole-Zero Plot of Dynamic System Plot the poles and zeros of the continuous-time system num=[2 5 1]; den=[1 2 3]; h=tf(num,den) sgrid pzmap(h) pole(h) zero(h) grid on