Projectile Motion Calc 與 PIDTune 使用情況與統計

Projectile Motion Calculator is a physics/math calculator designed to find Horizontal velocity, Vertical velocity, Time of flight, Range of the projectile, or Maximum height quickly and easily. Features: - Instant calculation - Results are copyable to other apps - Formulas are included as references - Supports up to 16 decimal places - Supports various units for each input Projectile motion is a form of motion experienced by an object or particle (a projectile) that is thrown near the Earth's surface and moves along a curved path under the action of gravity only (in particular, the effects of air resistance are assumed to be negligible). This curved path was shown by Galileo to be a parabola. The study of such motions is called ballistics, and such a trajectory is a ballistic trajectory. The only force of significance that acts on the object is gravity, which acts downward, thus imparting to the object a downward acceleration. Because of the object's inertia, no external horizontal force is needed to maintain the horizontal velocity component of the object. Taking other forces into account, such as friction from aerodynamic drag or internal propulsion such as in a rocket, requires additional analysis. A ballistic missile is a missile only guided during the relatively brief initial powered phase of flight, and whose subsequent course is governed by the laws of classical mechanics. Projectile motion equations: - Horizontal velocity component: vx = v * cos(θ) - Vertical velocity component: vy = v * sin(θ) - Time of flight: t = 2 * vy / g - Range of the projectile: R = 2* vx * vy / g - Maximum height: ymax = vy^2 / (2 * g) Thanks for your support and do visit nitrio.com for more apps for your iOS devices.

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PIDTune

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