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Nonlinear Characteristics and Dynamics of Hydraulic Servo Systems
Pressure lag, valve hysteresis, and fluid compressibility in servo hydraulic systems
To control servo hydraulic systems, you have to work with three types of non-linear behaviors. First, there is pressure lag, which is the time it takes for the hydraulic actuator to respond to control commands given to the valve, which reduces dynamic precision. In addition, valve hysteresis, which is the time it takes for the hydraulic actuator to settle to a new desired position, introduces repeatability errors in the actuator’s position. Lastly, fluid (especially air) compressibility introduces a lag behavior to the system, which can significantly reduce the stiffness of the hydraulic system, and therefore, the actuator’s motion. This is particularly problematic when there is greater than 1% air in the fluid. This stiffness loss also could reduce the fidelity of the motion desired by the actuator. Using the right type of proportional valve with appropriate dynamic response matched with proper degrees of fluid evacuation, these effects can be largely reduced.
Dynamics limitations of hydraulic systems: why cutoffs are between 50 to 300 Hz
The determination of the hydraulic systems dynamics cut-off frequency is based on the actuator’s inertia and how compressible fluids are. In hydraulic systems, the effective damping behavior of the system is further determined by the bulk modulus of the fluid and the resonance inertia (which is the inertia caused by the moving part of the system). When the frequency used in the hydraulic system surpasses 300 Hz, the fluid containment (which is typically a mineral oil and has a bulk modulus of between 15,000 to 25,000 bar) starts to oscillate and disrupts the accurate positioning of the system. This behavior is further governed by the response requirements and loss of phase/gain margins (as defined in ISO 10770-1). This is why most hydraulic actuators work at reasonably low frequencies of below 250
Practical PID Tuning Strategies for Servo Hydraulic Systems
Ziegler-Nichols or Model-based Relay Tuning on Electro-Hydraulic Actuators
When considering methods of tuning PID controllers on nonlinear servo hydraulic systems, certain trade-offs arise. One of the simplest methods is the Ziegler-Nichols method, which involves adjusting the proportional, integral, and derivative gains until sustained uniform oscillations occur. This method, while simple, has certain pitfalls associated with it. This method can induce instability in systems with high response and attack the service laws near the natural resonance. In contrast, the model based relay method involves injecting controlled oscillations to the system to determine and capture the dominant resonating modes which, in hydraulic systems, can be above 50 Hz, and then determining the stabilizing gain via the Nyquist criterion. This method can mitigate overshoot in applications involving pressure compensated valves, unlike the Ziegler-Nichols method. The Ziegler-Nichols method can be expected to reduce settling time by 40% when compared to the Ziegler-Nichols method for systems resonating about 150 Hz.
Tuning method Best for Stability risk Typical bandwidth gain
Ziegler-Nichols Low-frequency applications High in resonance zones ≤150 Hz
Model-based Relay High-dynamic electro-hydraulics Low with accurate modeling 200–300 Hz
When PID Tuning Fails: Recognizing Causes of Instability in High Gain Servo Hydraulic Systems PID Tuning
When fluid compressibility and hysteresis are present in a system, PID controllers will inevitably be unsuccessful. Excessive gains in the proportional control element will increase the set-point dead time, and result in limit cycles above 250 Hz. The changes in actuator load that occur in injection molding will result in a displacement of the actuator assembly of approximately 0.5 mm, and will result in integral control windup. This presents a serious problem and necessitates the use of gain scheduling or modification of the system. Valves with greater than 15% overlap will exhibit a considerable time delay, and result in instability. This will necessitate the use of friction compensation to the system or use of adaptive friction threshold control. Recent studies have shown
Compensation Techniques for Better Performance of Servo Hydraulic Systems
Feedforward Control with Bulk Modulus and Friction Compensation
Feedforward control not only improves performance but also allows anticipatory compensation for certain nonlinearities, as opposed to traditional practices that rely on feedback, and the subsequent loss of performance. Bulk modulus may vary through a ±15% range with temperature which causes fluid pressure-dependent stiffness shifts, and ultimately poor high-precision task location. The static friction of fluid leakage is also said to be in the range of 20% resistance of the total actuator resistance. Advanced controllers can be designed to model the fluid dynamic friction, and fluid dynamic compressibility, and provide a corrective control input prior to the error. This dual compensation helps in avoiding overshoot and reduces the time taken to stabilize injection molding machines by 37% while maintaining thermal transients with real time control accuracy to the order of microns.
Pole Placement to Maximize Damping: An ISO 10770-1 Based Design
In pole placement techniques, the damping ratio of the hydraulic servo system is maintained in the range of 0.6 to 0.8 to avoid resonance and instability. This is different from traditional tuning techniques, as a model-based approach to control the system in the area of its natural frequency. The placement of poles along the 45° angle of the s-plane transformed the system from an underdamped range of 0.3 to a critically damped range using an ISO 10770-1 compliant design. This involved calculating the system's hydraulic stiffness based on the geometry of the cylinder and the fluid, mapping the flow-pressure characteristics of the control valve to determine gain limits, and adjusting the feedback control to shift the poles below the 300 Hz instability threshold. The outcome was an impressive 92% reduction in vibrations in steel rolling mills, while still resulting in full ISO 10770-1 compliance with dynamic stiffness evaluation requirements.
Frequently asked questions
What does the term “pressure lag” mean in hydraulic servo systems?
In high-speed operations, valve actuation followed by response lags in the cylinder can decrease the overall dynamic precision of the system.
Why are hydraulic servo system bandwidths in the 50–300 Hz range?
Typically, actuator inertia in conjunction with fluid compressibility will create a resonance which will limit the bandwidth. Once the instability region is entered, the disturbances will start oscillating, resulting in the loss of system accuracy.
What are the benefits of Model-Based Relay Tuning (MBRT) in contrast to Ziegler-Nichols?
MBRT will aid in locating the different resonance modes of the system and also in calculating the stabilizing gain margins. This can be accomplished with smaller overshoot and improved response in terms of settling time.
What is the effect of using a feedforward control scheme?
Timing and accumulation of errors due to feedback are eliminated when a feedforward control scheme is used. This results in improved system performance with reduced overshoot and settling time.
What does pole placement mean in hydraulic servo systems?
This is a model-based control method to dampen the natural (and potentially unsafe) poles of a hydraulic servo system to maintain performance and system integrity.
