ioviewer.m

function ioviewer( sys )

do = true;
switch sys
    case '1'
        % System 1: Mass Spring
        tra = tf( 5, [1 0 5] );
        w = 0.3;
        t = 0:0.01:40;
        ylbl = 'Output (m)';
        ttl = 'Input vs Output System 1, w=0.3';

    case '2'
        % System 2: Electronic Circuit
        tra = tf(1, [40 22 3]);
        w = 0.2;
        t = 0:0.1:100;
        ttl = 'Input vs Output System 2, w=0.2';
        ylbl = 'Output ( V )';

    case '3a'
        % System 3a: Feedback Control Systems
        %transfer function = tf(forward, loop);
        S = 1; C= tf( [96 56 8], [1 0] ); L = 0; P = tf( 12.5, [12 7 1] ); M = 1;
        tra = S * feedback ( C * feedback( P, L ), M );
        w = 20;
        t = 0:0.001:0.5;
        ttl = 'Input vs Output System 3a, w=20';
        ylbl = 'Output (units)';
    case '3b'
        % System 3b: Feedback Control Systems
        S=1; C= 0.5 * tf( [6 1], [1 1] ); L = tf( [0.08 0], 1 ); P = tf( 12.5, [12 7 1] ); M = 1;
        tra = S * feedback ( C * feedback( P, L ), M );
        w = 0.1;
        t = 0:0.1:100;
        ttl = 'Input vs Output System 3b, w=0.1';
        ylbl = 'Output (units)';
    case '4'
        % System 4: Wien Bridge Oscillator
        K = 3; R1 = 10*10^3; R2 = R1; C1 = 10*10^-9; C2 = C1;
        tra = K * tf( [ R2*C1 0 ], [ R1*R2*C1*C2 R1*C1+R2*C2+R2*C1 1 ] );
        w = 10^4;
        t = 0:(1*10^-5):(2*10^-3);
        ttl = 'Input vs Output System 4, w=10^4';
        ylbl = 'Output (units)';
    otherwise
        display( 'Sorry, invalid system name.' );
        do = false;
end
    
if( do )
    sn = sin( t*w );
    [x,t] = lsim( tra, sn, t );
    [z,t] = step( tra, t );
    subplot( 2, 3, [1:3] );
    plot( t, sn, ':', t, x );
    title( ttl );
    xlabel( 'Time (s) ');
    ylabel( ylbl );
    legend( 'Input', 'Output' );
    subplot( 2, 3, [4:5] );
    nyquist( tra );
    subplot( 2, 3, 6 );
    bode( tra );
end

modass.m

function modelass( sys )
switch sys
    case '1'
        % System 1: Mass Spring
        sys1_tf = tf( 5, [1 0 5] );
        subplot( 1, 2, 1 );
        [x, t ] = step( sys1_tf, [0:0.1:4] );
        % Time domain of output.
        o = 1 - cos( sqrt( 5 ) * t );
        plot( t, x, t, o, '*' );
        xlabel('Time (s)');
        ylabel('Output (m)');
        title('Response of System 1 to a Step Input');
        legend( 'Simulated Response', 'Theoretical Response', 'Location', 'SouthEast' );
        subplot( 1, 2, 2 )
        bode( sys1_tf );

    case '2'
        % System 2: Electronic Circuit
        sys2_tf = tf(1, [40 22 3])
        subplot( 1, 2, 1 );
        [x,t] = step( sys2_tf );
        % Time domain
        o = 1/3  + ( ( 5/3 )* exp( ( -3/10 ) * t ) ) - 2 * exp( -(1/4) * t );
        plot( t, x, t, o, '*' );
        title( 'Response of System 2 to a Step Input' );
        xlabel( 'Time (s)' );
        ylabel( 'Output (V)' );
        legend( 'Simulated Response', 'Theoretical Response', 'Location', 'SouthEast' );
        subplot( 1, 2, 2 );
        bode( sys2_tf );
    case '3a'
        % System 3a: Feedback Control Systems
        %transfer function = tf(forward, loop);
        S = 1; C= tf( [96 56 8], [1 0] ); L = 0; P = tf( 12.5, [12 7 1] ); M = 1;
        sys3a_tf = S * feedback ( C * feedback( P, L ), M );
        subplot( 1, 2, 1 );
        [x,t] = step( sys3a_tf );
        % Time domain
        o = 1-exp(-100*t);
        plot( t, x, t, o, '*' );
        title( 'Response of System 3a to a Step Input' );
        xlabel( 'Time (s)' );
        ylabel( 'Output (Units)' );
        legend( 'Simulated Response', 'Theoretical Response', 'Location', 'SouthEast' );
        subplot( 1, 2, 2 );
        bode( sys3a_tf );
    case '3b'
        % System 3b: Feedback Control Systems
        S=1; C= 0.5 * tf( [6 1], [1 1] ); L = tf( [0.08 0], 1 ); P = tf( 12.5, [12 7 1] ); M = 1;
        sys3b_tf = S * feedback ( C * feedback( P, L ), M );
        % Graphs
        subplot( 1, 2, 1 );
        [x,t] = step( sys3b_tf );
        % Time domain
        o = (25/29) * (1 - exp(-(3/4)*t) .* (cos((7/4)*t) + (3/7)*sin((7/4)*t)));
        plot( t, x, t, o, '*' );
        title( 'Response of System 3b to a Step Input' );
        xlabel( 'Time (s)' );
        ylabel( 'Output (Units)' );
        legend( 'Simulated Response', 'Theoretical Response' );
        subplot( 1, 2, 2 );
        bode( sys3b_tf );
    case '4'
        % System 4: Wien Bridge Oscillator
        K = 3; R1 = 10*10^3; R2 = R1; C1 = 10*10^-9; C2 = C1;
        tra = K * tf( [ R2*C1 0 ], [ R1*R2*C1*C2 R1*C1+R2*C2+R2*C1 1 ] );
        minreal(tra);
        % Graphs
        t = [0:0.000001:0.002];
        subplot( 1, 2, 1 );
        [x,t] = step( tra, t );
        plot( t, x );
        title( 'Response of System 4 to a Step Input' );
        xlabel( 'Time (s)' );
        ylabel( 'Output (V)' );
        legend( 'Simulated Response' );
        subplot( 1, 2, 2 );
        bode( tra );
end