Statistics Calculator++ vs PIDTune

Simplify your statistics with Statistics Calculator++ Perform powerful statistical analysis without needing a manual. Enter your data easily using "Add X," "Add Y," and "Add Z" buttons, and let Statistics Calculator++ handle the rest. Analyze results in a clear table, including sum, mean, standard deviation, quartiles, and more. Visualize your data with box and whisker plots and histograms. Powerful regression analysis: Choose from linear, logarithmic, exponential, power, and quadratic regressions. The intuitive interface simplifies selecting models and calculating predictions for x and y values. View residuals, residual sum of squares, and how the regression model fits your data in a graph. Save and import data with ease: Store multiple data lists and use them in calculations effortlessly. Import data directly from Microsoft Excel or Apple Numbers. Plus, your data is always saved within the app, so you never lose it. More than just statistics: Probability distributions: Normal, Student's t, Chi-Squared, F, Binomial, Poisson, Geometric, Beta, and Gamma. Confidence intervals and hypothesis tests: Step-by-step explanations for common statistical tests. Advanced calculations: Fraction manipulation, angle conversions, permutation/combination, LCM/GCD, prime factorization, quadratic solver, system of linear equations solver, rectangular/polar conversions, dice rolling. Statistics Calculator++ is a powerful and user-friendly tool for: Students Scientists Engineers Anyone who needs statistical analysis Download Statistics Calculator++ today and experience the simplicity of powerful statistics!

PID Tuner uses the IMC (Internal Model Control) method to calculate PID tuning parameters. I’ve tried a lot of tuning methods over the years and have found this one to be the best. The app is written for the iPad to show all the information on one page. The program calculates: PID Parameters: Controller Gain (Kc) Integral Time (Ti) Derivative Time (Td) For process types First Order with Dead Time (FO) Second Order with Dead Time (SO) Integrating or Long Time Constant with Dead Time (I) For controller types Parallel (non-interacting) c(s) = Kc (1 + 1/(Ti s) + Td s) Series (interacting) c(s) = Kc (Ti s + 1)/(Ti s)(Td s + 1) For controller modes PID PI You can either enter the process gain (Kp) directly or enter the changes in the controlled virable (CV) and manipulated variable (MV). Tuning aggression is adjusted using the slider to set the closed loop time constant to the process time constant ratio (λ/Ƭ). The closed loop time constant (λ) is the time the controller is expected to reach set point (plus the dead time (ϴ)). Setting the closed loop time constant to process time constant ratio (λ/Ƭ) to 1.0 will make the MV change to its final value and allow the process to settle out to the setpoint. Setting (λ/Ƭ) greater than 1.0 will give a slower responce. Setting (λ/Ƭ) less than 1.0 will cause the MV to make a larger change and then reduce to its final value. Tight tuning would be to set the close loop time constant to the dead time. Use the Integrating Process type (Ƭ = ∞) for both integrating processes or processes with long time constants. These processes use the maximum slope as the process gain. Tuning aggression for these processes is determined by setting the closed loop time constant to the dead time ratio (λ/ϴ). Once again, setting the closed loop time constat to the dead time gives tight control. References: “Probably the test simple PID tuning rules in the World,” Sigurd Skogestad, Jounal of Process Control, July 3, 2001 “Consider the generalized IMC-PID method for PID controller tuning of time-delay processes,” Y. Lee, S. Park, M. Lee, Hydrocarbon Processing, January 2006