Because of events over the last few years, Java applets no longer have a future on the web for the kind of application used here.

Work is currently in progress to replace the java applets that were on these pages with

This has the advantage that it is possible to have the result look and work the same way in any browser and on any device. To date the ones that have been completed have been tested with different browsers on windows and apple pc's, android and windows tablets and android phones.

Because of time commitments to other issues, it will take a while to complete the conversion from java applets to javascript.

Cuthbert Nyack. 2015-07-26.

For the Laplace transform used in the analysis of linear systems see:-

*Transient Response Introduction**1 pole Step Response**1 pole Ramp Response**1 pole 1 zero Step Response**2 Real poles Impulse Response**2 CC poles Impulse Response**2 Real poles Step Response**2 CC poles Step Response**2 poles Ramp Response**2 poles Sine Response**2 Real poles Modified Step Response**2 Real poles Modified 2 Step Response**2 Real poles 1 Real Zero Step Response**3 Real poles Step Response**3 Real poles Type 0 Impulse Response**3 Real poles Type 1 Impulse Response**3 Real poles 1 Zero Step Response**3 Real poles 0, 1, 2 Zeros Step Response**1 Real 2 CC poles Step and Impulse Response**4 Real poles Step Response**2 x Complex Conjugate Poles Step Response**1, 2, 3, 4 Real poles Sine Response**3 Real poles Step Response and Closed Loop Poles**Frequency Analysis Introduction**S Plane and Frequency Response**Bode Plot, Single Pole Zero Factors**Bode Plot, Quadratic Pole Zero Factors**Quick look at Bode Plots.**Bode Plot, 1 Pole, 1 Zero Factors**Nyquist Plot, 1, 2, 3 Real Poles**Bode Plot, 2 Real Poles, 1 Zero**Nyquist Plot, 2 Real Poles, 1 Zero**Bode Plot, 3 Real Poles**Bode Plot, 3rd order Polynomial**Bode Plot, 3 Real Poles, 1 Zero**Nyquist Plot, 3 Real Poles, 3 Real Poles, 1 Zero**Bode Plot, 3 Real Poles, 2 Complex Conjugate Zeros**Bode Plot, 3 Real Poles, Closed Loop Response**Nyquist Plot, 3 Real Poles, Closed Loop Response**Bode Plot, 3 Real Poles, Phase and Gain Margins**Nyquist Plot, 3 Real Poles, Phase and Gain Margins**Bode Plot, 1 Real Pole, 2 Complex Conjugate Poles**Nyquist Plot, 1 Real Pole, 2 Complex Conjugate Poles**Bode Plot, 4 Real Poles**Nyquist Plot, 4, 3 Real Poles**Bode Plot, 4 Real Poles, 2 Complex Conjugate Zeros**Nyquist Plot, 4 Real Poles, 2 Complex Conjugate Zeros**Bode Plot, 4th Order Polynomial**Bode Plot, 5 Real Poles**Nyquist Plot, 5 Real Poles**Routh Hurwitz Introduction**Routh Hurwitz, 3 Real Poles**Routh Hurwitz, 3 Real Poles, 2 Complex Conjugate Zeros**Routh Hurwitz, 3rd Order Polynomial**Routh Hurwitz, 4 Real Poles**Routh Hurwitz, 4 Real Poles, 2 Complex Conjugate Zeros**Routh Hurwitz, 4th Order Polynomial**Routh Hurwitz, 5 Real Poles**Routh Hurwitz, 5th Order Polynomial**Routh Hurwitz, 3 Real Poles and closed loop poles**Routh Hurwitz, 3rd Poly and closed loop poles**Routh Hurwitz, 4th Poly and closed loop poles**Root Locus Introduction**Angle Condition, Quick look at Root Locus for Pole Zero Configurations**Angle Condition, 1 Real Pole, 1 Real zero**Angle Condition, 2 Real Poles**Angle Condition, 2 Real Poles, Magnitude and Phase Surface Plots**Angle Condition, 2 Real Poles, 1 Real zero**Angle Condition, 3 Real Poles, type 0 and 1**Angle Condition, 3 Real Poles and root locus**Angle Condition, 3rd order Polynomial**Angle Condition, 3 Real Poles, Magnitude and Phase Surface Plots**Angle Condition, 3 Real Poles, 1 Real Zero**Angle Condition, 3 Real Poles, 1 Real Zero, Root Locus**Angle Condition, 3 Real Poles, 2 Real Zeros**Angle Condition, 3 Real Poles, 2 Complex Conjugate Zeros**Angle Condition, 1 Real Pole, 2 Complex Conjugate Poles, 2 Real Zeros**Angle Condition, 1 Real Pole, 2 Complex Conjugate Poles, 2 Complex Conjugate Zeros**Angle Condition, 4 Real Poles**Angle Condition, 2 Real Poles, 2 Complex Conjugate Poles**Angle Condition, 2 x 2 Complex Conjugate Poles**Angle Condition, 4 Real Poles, 1 real Zero**Angle Condition, 4 Real Poles, 2 real Zeros**Angle Condition, 2 Real Poles, 2 Complex Conjugate Poles, 1 real Zero**Angle Condition, 4 Real Poles, 2 Complex Conjugate Zeros**Angle Condition, 2 x 2 Complex Conjugate Poles, 2 Complex Conjugate Zeros**Angle Condition, 4th Order Polynomial**Angle Condition, 5 Real Poles**Angle Condition, 5 Real Poles, 1Real Zero.**Angle Condition, 5 Real Poles, 2 Real Zeros.**Angle Condition, 5 Real Poles, 2 Complex Conjugate Zeros.**Angle Condition, 3 Real Poles, 2 Complex Conjugate Poles, 2 Complex Conjugate Zeros**Angle Condition, 1 Real Poles, 2 x 2 Complex Conjugate Poles, 2 Complex Conjugate Zeros**Angle Condition, 5th Order Polynomial**Magnitude Condition, 3 Real Poles**Magnitude Condition, 3 Real Poles, 1 Real Zero**Magnitude Condition, 3 Real Poles, 1 Real Zero, Contour Plot**Distance Velocity Lag and Nonminimum Phase introduction**Distance Velocity Lag, Transient Response and Bode Plot**Distance Velocity Lag, Transient Response and Nyquist Plot**Distance Velocity Lag, Transient Response and Root Locus**NonMinimum Phase, Transient Response**NonMinimum Phase, Bode Plot**NonMinimum Phase, Root Locus**Compensator Introduction**Compensator Controller Comparison**Second Order Phase Lead Compensator**Second Order Phase Lag Compensator**Second Order Phase Lag Compensator, Root Locus**Second Order Phase Lag Lead Compensator**Second Order Lead, Lag and LagLead Ramp Response.**Second Order LagLead compensator, Root Locus.**Third Order Phase Lead Compensator.**Third Order Phase Lag Compensator.**Third Order Phase Lag Lead Compensator.**Third Order Lead, Lag and LagLead Ramp Response.**Comparison of Compensators for 2 poles.**Comparison of Lead Compensator and PD Control.**Comparison of Lag Compensator and PI Control.**Comparison of Compensators for 3 poles.**Introduction**P Control 1st, 2nd, 3rd and 4th order**First Order P, P + I Control, Step Response**First Order P, P + I Control, Ramp Response**First Order P, P + I Control, Disturbance**First Order P, P + I Control, Bode Plot**First Order P, P + I Control, Nyquist Plot**First Order P + I Control, Root Locus**Second Order P + D Control, Step Response**Second Order P + D Control, Ramp Response**Second Order P + D Control, Disturbance Response**Second Order P + D Control, Bode Plot**Second Order P + D Control, Nyquist Plot**Second Order P + D Control, Root Locus**Second Order Tachometer Control(Velocity Feedback), Step Response**Second Order Tachometer Control, Ramp Response**Second Order Tachometer Control, Bode Plot**Second Order PID Control, Step Response, Bode, Nyquist, Rootlocus, Routh Hurwitz**Second Order PID Control, Step response.**Second Order PID Control, Controller Outputs**Second Order PI, PD, PID Control, Ramp Response**Second Order PI, PD, PID Control, Parabolic Response**Second Order PI, PD, PID Control, Disturbance Response**Second Order PI, PD, PID Control, Bode Plot**Second Order PI, PD, PID Control, Nyquist Plot**Second Order PI, PD, PID Control, Root Locus**Second Order PID Control, Root Locus**Third Order PD Control**Third Order PD Control, Bode Plot**Third Order PD Control, Nyquist Plot**Third Order PD Control, Root Locus**Third Order PID Control**Third Order PID Control, Bode Plot**Third Order PID Control, Nyquist Plot**Third Order PID Control, Root Locus**Second Order I-PD Control**Optimal Control Introduction.**Optimal Control P, PD Control.**Optimal Control PI Control.**Optimal Control PID Control.**Optimal Control Lead Compensator.**Optimal Control Lag Compensator.**Optimal Control 2 Step input.**Optimal Control Ramp to Step input.**Optimal Control Cos to Step input.**Optimal Control Exponential input.**State Vector Introduction.**Second Order, Product State Vector, Step Response and Bode Plot**Second Order, Partial Fraction State Vector, Step Response and Bode Plot**Second Order, Companion Matrix State Vector, Step Response and Bode Plot**Second Order, Product State Vector, Pole Placement**Second Order, Companion Matrix State Vector, Pole Placement**Third Order, Product State Vector, Step Response and Bode Plot**Third Order, Product State Vector, Sine Response and Bode Plot**Third Order, Partial Fraction State Vector, Step Response and Bode Plot**Third Order, Companion Matrix State Vector, Step Response and Bode Plot**Third Order, Companion Matrix State Vector, Sine Response and Bode Plot**Third Order, Product State Vector, Pole Placement Step Response and Bode Plot**Third Order, Product State Vector, Pole Placement Step Response and Root Locus**Third Order, Companion Matrix State Vector, Pole Placement**Third Order 3RP1Z, Companion Matrix State Vector, Step Response and Bode Plot**Multi Input, Introduction**Multi Input, Root Locus, Step and Sine Response**Nonlinear Introduction.**First Order, On Off Control, Step Response and Bode Plot**Second Order, On Off Control, Step Response and Bode Plot**Second, Third Order, Saturation, Step Response and Bode Plot**Second Order, Nonlinear Oscillator, Frequency and Amplitude dependence.**Second order Cubic Nonlinearity, Step Response**Third order Cubic Nonlinearity, Step, Sine Response**Second Order, Dead Band, Step Response and Bode Plot**Second Order, Back Lash and Describing Function**Second Order, Van Der Pol Limit Cycles**Second Order, Nonlinear Pendulum, Chaotic Response**Second Order 2RP, Phase Plane**Second Order 2RP1Z, Phase Plane**Third Order 3Rp, Phase Plane**First Order Type Zero, P Control Step and Ramp response**First Order Type Zero, P Control Sine and Impulse response**First Order Type One, P Control Step and Ramp response**First Order Type One, P Control Sine and Impulse response**First Order Type Zero, PI Control Closed loop Pole Zero locations.**First Order Type Zero, PI Control Step and Ramp response, Z Transfer Function**First Order Type Zero, PI Control Step and Ramp response, Finite Difference Trapezoidal Approximation**First Order Type Zero, PI Control Frequency response, Z Transfer Function and Finite Difference Approximation**Second Order Type Zero, P Control Step Response and Bode Plot**Second Order Type Zero, P Control Step Response and Root Locus**Third Order Type Zero, P Control Step Response and Bode Plot**Third Order Type Zero, P Control Step Response and Root Locus**Second Order Type Zero, PD Control Root Locus**Second Order Type Zero, PD Control Step and Ramp response, Z Transfer Function**Second Order Type Zero, PD Control Step and Frequency response, Z Transfer Function**Second Order Type Zero, PD Control Step Response and Root Locus, Z Transfer Function**Second Order Type Zero, PD Control Step and Ramp response, Finite Difference Approximation**Second Order Type Zero, PD Control Step and Frequency response, Finite Difference Approximation**Second Order Type Zero, PD Control Step Response and Root Locus, Finite Difference Approximation**Second Order Type Zero, PID Control Step and Ramp response, Finite Difference Approximation**Second Order Type Zero, PID Control Step Response and Bode Plot, Finite Difference Approximation**Second Order Type Zero, PID Control Step Response and Root Locus, Finite Difference Approximation**Second Order Type Zero, PID Control Root Locus**Second Order Type One, Lead Compensator Ramp response, Finite Difference Approximation**Second Order Type One, Lead Compensator Step Response and Bode Plot, Finite Difference Approximation**Second Order Type One, Lead Compensator Step Response and Root Locus, Finite Difference Approximation**Second Order Type One, Lag Compensator Ramp response, Finite Difference Approximation**Second Order Type One, Lag Compensator Step Response and Bode Plot, Finite Difference Approximation**Second Order Type One, Lag Compensator Step Response and Root Locus, Finite Difference Approximation**Second Order Type One, LagLead Compensator Ramp response, Finite Difference Approximation**Second Order Type One, LagLead Compensator Step Response and Bode Plot, Finite Difference Approximation**Second Order Type One, LagLead Compensator Step Response and Root Locus, Finite Difference Approximation*

For the Z transform used in the analysis of sampled systems see:-