Richard Burton

Modeling and Robust Discrete-Time Sliding-Mode Control Design for a Fluid Power Electrohydraulic Actuator (EHA) System

This paper studies the design of a robust discrete-time sliding-mode control (DT-SMC) for a high precision electrohydraulic actuator (EHA) system. Nonlinear friction in the hydraulic actuator can greatly influence the performance and accuracy of the hydraulic actuators, and it is difficult to accurately model the nonlinear friction characteristics. In this paper, it is proposed to characterize the frictions as an uncertainty in the system matrices. Indeed, the effects of variations of the nonlinear friction coefficients are considered as norm-bounded uncertainties that span a bounded region to cover a wide range of the real actuator friction. For such a discrete-time dynamic model, for the EHA system with system uncertainty matrices and a nonlinear term, a sufficient condition for existence of stable sliding surfaces is proposed by using the linear matrix inequality approach. Based on this existence condition, a DT-SMC is developed such that the reaching motion satisfies the discrete-time sliding mode reaching condition for uncertain systems. Simulation and experimental studies on the EHA system illustrate the effectiveness and applicability of the proposed method.

An Empirical Discharge Coefficient Model for Orifice Flow

Abstract In fluid power systems, flow control is mainly achieved by throttling the flow across valve orifices. Lumped parameter models are generally used to model the flow in these systems. The basic orifice flow equation, derived from Bernoullis equation of flow, is proportional to the orifice sectional area and the square root of the pressure drop and is used to model the orifice coefficient of proportionality. The discharge coefficient, Cd, is often modeled as being constant in value, independent of Reynolds number. However, for very small orifice openings, Cd varies significantly and can result in substantial error if assumed constant. In this situation, modelers usually revert to graphs or look—up tables to determine Cd. This paper provides a closed form model for Cd as a function of the Reynolds number which can be applied to different types of orifices. Based on this model, a technique to evaluate flow given an orifice area and pressure drop without having to use iteration is introduced.

Modelling of Orifice Flow Rate at Very Small Openings

Abstract Modelling hydraulic control systems that contain flow modulation valves is highly influenced by the accuracy of the equation describing flow through an orifice. Classically, the basic orifice flow equation is expressed as the product of cross-sectional area, the square root of the pressure drop across the orifice and a “flow discharge coefficient”, which is often assumed constant. However, at small Reynolds numbers (such the case of valve pilot stage orifices), the discharge coefficient of the flow equation is not constant. Further, the relationship between the flow cross-sectional area and the orifice opening are extremely complex due to clearances, chamfers, and other factors as a result of machining limitations. In this work, a novel modification to the flow cross-sectional area is introduced and the resulting closed form of the flow equation is presented. As a secondary benefit, an analytical form of the orifice flow gain and flow pressure coefficient can be obtained. This closed form equation greatly facilitates the transient and steady state analysis of low flow regions at small or null point operating regions of spool valve.

Effect of Controller in Reducing Steady-State Error due to Flow and Force Disturbances in the Electrohydraulic Actuator System

Abstract This paper pertains to the nonlinear control of a high-precision hydrostatic actuation system known as the Electro- Hydraulic Actuator (EHA). It describes the action of the controller in reducing the steady state error resulting from flow and force disturbances. The EHA uses inner-loop pump velocity feedback to achieve an unprecedented level of accuracy for a hydrostatic system. A published mathematical model of the EHA is reviewed and expanded to produce an equation that predicts the response of the EHA to both desired inputs as well as flow and force disturbances. This equation suggests that the use of a proportional outer-loop controller should result in steady-state error as a result of these disturbances, but that a PI outer-loop controller should eliminate the steady-state error. Experimental results from a prototype of the EHA demonstrate that due to the nonlinear friction present in the actuator, the use of a conventional proportional or PI controller is not sufficient to effectively deal with these disturbances. However, a nonlinear proportional outer-loop controller does result in a substantial performance improvement in regards to disturbance rejection for positional accuracy. Experiments conducted on the prototype using the nonlinear controller reveal that it is capable of a positional accuracy of 1 μm for a load of 20 kg.

High Precision Hydrostatic Actuation Systems for Micro- and Nanomanipulation of Heavy Loads

In this paper reports on an important finding, that is, hydrostatic actuation systems are able to manipulate heavy loads with submicron precision and a large stroke. In this relation, the design of a high-precision hydrostatic actuation system referred to as the ElectroHydraulic Actuator (EHA) is presented. A laboratory prototype of this system has achieved an unprecedented level of performance by being able to move a large load of 20 Kg with a precision of 100 nm and a stroke of 12 cm. This level of performance places the hydrostatic actuation concept in competition with piezoelectric platforms in terms of positional accuracy. Experimental results from this prototype are reported and analyzed.

Fluid Bulk Modulus: Comparison of Low Pressure Models

ABSTRACT Fluid bulk modulus is a fluid property that has been studied extensively over the past. The numerical value of this property depends on the operating conditions, the amount of entrained air/gas, and the way compression is applied and to some extent, the mathematical form it is defined. In a companion paper, an extensive review of fluid bulk modulus was presented. From this review, it was established that many models for fluid bulk modulus in the low pressure range (below critical pressure) have been forwarded. However, many of these models are based on assumptions that have not been explicitly defined. This paper considers these models and attempts to quantify the underlying assumptions. In addition some modification to these models are proposed in order to compare their prediction in the case where air/gas in entrained, for example. The paper concludes by categorizing the models into two groups and recommending the best model that can be used for each group. Finally some problems which observed in the models are discussed and future work for solving these problems presented.

Neural networks and hydraulic control—from simple to complex applications

Abstract The control of hydraulic servo-systems has been the focus of intense research over the past decades. The highly non-linear behaviour of these devices makes them ideal subjects for applying different types of sophisticated controllers. This paper considers the application of neural networks to the control of hydraulic servo-systems subjected to either non-linear friction or highly coupled loads. Three applications are considered: a very simple quasi-open-loop pattern follower, a proportional-integral-derivative (PID) multiple-gain neural controller and a neural-based controller for a very complex multiple-input multiple-output system. A major factor in these applications is the fact that the neural network controllers have been applied to real-time control of experimental systems. In all cases, these controllers showed superior performance over conventional-type PID controllers.

Experimental Identification of a Flow Orifice Using a Neural Network and the Conjugate Gradient Method

An experimental approach of using a neural network model to identifying a nonlinear non-pressure-compensated flow valve is described in this paper. The conjugate gradient method with Polak-Ribiere formula is applied to train the neural network to approximate the nonlinear relationships represented by noisy data. The ability of the trained neural network to reproduce and to generalize is demonstrated by its excellent approximation of the experimental data. The training algorithm derived from the conjugate gradient method is shown to lead to a stable solution.

Viscous Damping Coefficient and Effective Bulk Modulus Estimation in a High Performance Hydrostatic Actuation System using Extended Kalman Filter

Abstract Increasing demands on reliability and safety of fluid power devices have brought much attention to methods for improving condition monitoring of these devices. Whereas faults in hydraulic systems were detected only when limit values of measurable output signals were transgressed, recently, attempts have been made to detect them earlier and to locate them better by the use of measurable signals. The Extended Kalman Filter can be used for real-time estimation of parameters in system models. Changes in model parameters may be tracked and, in turn, be used for determining the condition of the system. In this paper, the Extended Kalman Filter (EKF) is applied to a novel hydrostatic actuation system referred to as the Electrohydraulic Actuator (EHA). A state space model of the EHA is developed and the Extended Kalman Filter is used to estimate unmeasurable but critical parameters such as viscous damping coefficient of the actuator and the effective bulk modulus of the system. The proof of concept of applying the EKF for parameter and state is demonstrated through both simulation and experimental evidence. Changes in the viscous damping coefficient at the actuator at a known temperature may be good indication that the fluid is degrading or that the dynamic seal of the actuator is experiencing wear. The effective bulk modulus has a large impact on the system response, affecting the natural frequency and stability and can have implications on the safety of operation. These two parameters cannot be measured directly and hence need to be estimated. Based on this estimation, corrective actions may be taken in safety critical applications for the EHA such as Flight Surface Actuation.

Frequency Domain Modelling and Identification of 2D Digital Servo Valve

Abstract The 2D digital servo valve studied here is a two-stage valve designed by using both rotary (angular) and linear motions of a spool. The rotary motion is driven by a stepper motor operating under continual angular displacement control, while the linear motion of the spool is actuated by hydraulic servo control with feedback of the spools displacement, which is achieved by a unique “servo screw”. The modelling of the 2D valve is based on linear theory and is further verified by the special experiments. Because of the extremely large hydraulic natural frequency, the control of the 2D valve is identified as being that of a first-order-system. The relation between the time constant and the structural parameters is established, accounting for the non-linearity of the pilot hydraulic bridge. For the continual control of the stepper motor, a mathematical model considering the rotary motion, the rotating magnetic field and the angular control signal is established. In order to prevent the stepper motor from losing steps, the rate of the control signal is limited to a certain range. As a result, this may cause a non-linearity and, consequently, the deformation of the waveform when the input sinusoid wave is of large amplitude and high frequency. By utilizing the method of the description function, the effect of limiting the rate of the control signal is approximated as a first-order-system and the relation between the time constant and the amplitude and frequency is presented. The dynamic characteristics of the stepper motor are to a large extent dependent upon the way the power is supplied. For a constant current supply, the stepper motor can be classified as a second-order-system. The factors affecting the natural frequency and damping ratio are clarified. Finally, the frequency response of the 2D digital valve is experimentally measured and compared with theoretical results. Both theoretical and experimental results show that the 2D digital valve has a fairly high frequency response, especially when the valve operates near the central position. For a 25% full scale input signal, the 2D digital servo valve has at least 300 Hz under the gain of–3 dB.