Continuous Path Regulator for Exact Time-Position Trajectory Control
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Solution Overview
Problem
Existing control systems, such as PID controllers, often result in suboptimal performance due to overdamping, underdamping, and oscillation when transitioning between control signal states, particularly in systems requiring simultaneous control of time and position, like robotics and flight path management.
Innovation Solution
A Continuous Path Regulator (CPR) system that defines a trajectory using mathematical equations to precisely control spatial and temporal dimensions, utilizing splines and higher-order polynomial equations to ensure accurate transition signals, with each segment expressed as a function of time, allowing for exact determination of position and velocity at any given time.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If PID controller is used for control signal transition, then the control system is simple and reliable, but the transition time is variable and accuracy is reduced due to overdamping, underdamping, and oscillation
Solution Approach 1:
The patent transforms the control approach by changing from a first-order PID controller to a higher-order continuous path regulator that uses polynomial equations (second-order, third-order, or higher) to define the control signal trajectory. This parameter change in the mathematical model order enables exact control of both position and time, eliminating the approximation errors and damping issues inherent in PID controllers while maintaining system reliability.
2Ease of manufacture
If PID controller is used for control signal transition, then the control system is simple to implement, but the transition accuracy is suboptimal due to first-order approximation
Solution Approach 1:
The patent introduces dynamic adjustment of the control signal trajectory by using higher-order polynomial equations that can adapt to varying start and end states. The continuous path regulator dynamically calculates the optimal trajectory parameters (coefficients of polynomial equations) based on the specific transition requirements, enabling high-precision control while maintaining computational efficiency through systematic mathematical formulations.
3Measurement precision
If higher-order control system is used instead of PID, then control accuracy is improved, but system complexity increases
Solution Approach 1:
The patent segments the control signal transition into distinct mathematical phases using piecewise polynomial functions. Each segment of the trajectory is defined by a specific polynomial equation with calculated coefficients, allowing the complex higher-order control to be broken down into manageable, computationally efficient segments. This segmentation reduces the overall system complexity while maintaining high-precision control through systematic mathematical decomposition.
4Manufacturing precision
If trajectory control with time parameter is implemented, then simultaneous position and time control is achieved, but the control system complexity increases
Solution Approach 1:
The patent creates a universal control framework where a single continuous path regulator handles both position and time control simultaneously through higher-order polynomial equations. This multi-functional approach eliminates the need for separate control systems for spatial and temporal parameters, reducing overall system complexity while achieving precise simultaneous control of both dimensions through unified mathematical modeling.
Data Source
AI summary
A solution to a system of simultaneous equations where an exact mathematical solution to a multivariate signal path or physical trajectory problem includes time and allows a control regulator to maintain high accuracy simultaneously over multiple variables such as but not limited to distance, velocity, and time. In a flight vehicle, for example, the regulator maintains with high accuracy the position of the vehicle in X, Y, and Z at exactly the time required over the entire trajectory making its position highly predictable at any time.