Adaptive PID Controller Gain Scheduling for Valve Positioners
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Solution Overview
Problem
Conventional PID controllers exhibit slow oscillations and vibrations when used in high dynamic systems like valve positioners with high flow rate spools and high-speed actuator devices, despite advancements in microprocessors.
Innovation Solution
A modified PID controller method that adjusts gain terms based on specific conditions, including rate of change and error magnitude, to generate a manipulated variable by combining proportional, integral, and derivative terms, with the integral gain term applied only when the actuator is stationary or moving slowly and the derivative gain term applied when the error rate is negative.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If standard PID control is used in high dynamic systems, then the control accuracy is improved, but slow oscillations and vibrations occur
Solution Approach 1:
The patent applies dynamics by making the gain terms adaptive rather than fixed. The proportional gain Kp, integral gain Ki, and derivative gain Kd are dynamically adjusted based on the current operating state of the system, specifically based on the error magnitude and its rate of change. This allows the controller to optimize performance across different operating conditions and avoid oscillations that occur with fixed gains in high dynamic systems.
Solution Approach 2:
The patent changes the parameters of the PID controller by introducing state-dependent gain scheduling. The gain terms are modified as functions of the error e and its derivative de/dt, transforming the standard PID control into a nonlinear adaptive controller. This parameter change enables the system to maintain stability while achieving accurate control by adjusting the controller characteristics according to the current error state.
2Measurement precision
If integral gain term is continuously applied, then steady state error is corrected, but integral windup occurs causing oscillations
Solution Approach 1:
The patent applies preliminary anti-action by preventing integral windup before it occurs. The integral gain Ki is made conditional and is only applied when the error magnitude exceeds a threshold value. By anticipating the conditions that lead to integral windup and preventing the integral term from accumulating under those conditions, the system avoids the harmful oscillations that would otherwise result from excessive integral action.
Solution Approach 2:
The patent makes the integral gain dynamic rather than constant. The integral term is activated only when needed (when error > threshold) and deactivated when the error is small, preventing the continuous accumulation that causes integral windup. This dynamic adjustment of the integral gain based on the current error state corrects steady state errors when necessary while avoiding the oscillations caused by excessive integral action.
3Stability of the object's composition
If derivative gain term is always applied, then overshoot and oscillation are reduced, but noise and vibrations are amplified
Solution Approach 1:
The patent applies preliminary anti-action by preventing the derivative term from amplifying noise before it becomes problematic. The derivative gain Kd is made conditional and is only applied when the rate of change of error |de/dt| exceeds a threshold. By anticipating conditions where derivative action would be beneficial (rapid error changes) and suppressing it when noise would dominate (small error changes), the system reduces overshoot without amplifying noise and vibrations.
Solution Approach 2:
The patent makes the derivative gain dynamic by conditioning its application on the magnitude of the error rate of change. The derivative term is activated only when |de/dt| > threshold, transforming it from a continuous noise-amplifying term into a selective damping mechanism. This dynamic approach allows the derivative action to reduce overshoot and oscillation when needed while avoiding the amplification of high-frequency noise during steady-state operation.
Data Source
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AI summary
A method and device for controlling a process variable based upon a set point is disclosed. A process variable is measured, and a proportional gain term is assigned to a manipulated variable that is based upon a product of a proportional gain coefficient and an error magnitude between the process variable and the set point. An integral gain term is added to the manipulated variable under a first set of conditions, and a proportional gain term is added to the manipulated variable under a second set of conditions different from the first set of conditions. The sum of the proportional gain term, the integral gain term, and the derivative gain term is output, resulting in the process variable being responsively adjusted thereto.