Robust control stability using the error loop

The paper briefly formulates the error loop as a tool for designing robust stability control systems in front of structured and unstructured uncertainties. The error loop indicates that a tool for accommodating such uncertainties is the noise estimator, which is the unique feedback channel from plant to control. It is shown that the causality constraint preventing perfect cancellation of causal uncertainties (unknown disturbance), makes also control law to play a role, offering a further degree of freedom. Employing asymptotic expansions of the closed-loop transfer functions, simple, explicit design formulae derive from stability inequalities: they relate closed-loop eigenvalues to model parameter and requirements. A simple example is provided from a ball and beam plan

Proportional electro-hydraulic valves: from analogue to digital control

Proportional electro-hydraulic valves are ubiquitous as flow actuators in hydraulic systems. Flow regulation is the result of the accurate positioning of a spool driven by a solenoid and a position sensor, usually a Linear Variable Differential Transformer. The overall control consists of two hierarchical loops: the inner loop is the solenoid current regulator with a closed-loop bandwidth close to 1 kHz. A model-based digital regulator of this kind has been presented elsewhere: requirements and performance are here reminded. The outer loop is a position tracking control, in charge of an accurate positioning of the spool with respect to the valve openings. The paper addresses the outer loop and concentrates on the conversion of an existing industrial analogue controller into a digital one. The analogue controller is a nonlinear proportional, integrative and derivative controller including a second-order derivative, and is capable of recovering a dead-band hysteresis. The digital conversion provides the necessary position derivatives through a state predictor, in order to withstand the 5-kHz Nyquist limit of the power supplier. As such it departs from traditional conversions dating back to more than ten years ago. The digital control law is fed by the state predictions and repeats the analogue control law with some improvements. Preliminary experiments prove that the conversion repeats and improves analogue performance. Some flaws of the resulting digital controller are outlined and discussed in view of a model-based conversion.

Proportional electro-hydraulic valves: from analogue to digital control

Proportional electro-hydraulic valves are ubiquitous as flow actuators in hydraulic systems. Flow regulation is the result of the accurate positioning of a spool driven by a solenoid and a position sensor, usually a Linear Variable Differential Transformer. The overall control consists of two hierarchical loops: the inner loop is the solenoid current regulator with a closed-loop bandwidth close to 1 kHz. A model-based digital regulator of this kind has been presented elsewhere: requirements and performance are here reminded. The outer loop is a position tracking control, in charge of an accurate positioning of the spool with respect to the valve openings. The paper addresses the outer loop and concentrates on the conversion of an existing industrial analogue controller into a digital one. The analogue controller is a nonlinear proportional, integrative and derivative controller including a second-order derivative, and is capable of recovering a dead-band hysteresis. The digital conversion provides the necessary position derivatives through a state predictor, in order to withstand the 5-kHz Nyquist limit of the power supplier. As such it departs from traditional conversions dating back to more than ten years ago. The digital control law is fed by the state predictions and repeats the analogue control law with some improvements. Preliminary experiments prove that the conversion repeats and improves analogue performance. Some flaws of the resulting digital controller are outlined and discussed in view of a model-based conversion.

Digital current regulator for proportional electro-hydraulic valves featuring unknown disturbance rejection

Solenoid current regulation is well-known and standard in any proportional electro-hydraulic valve. The goal is to provide a wide-band transfer function from the reference to the measured current, thus making the solenoid a fast and ideal force actuator within the limits of the power supplier. The supplier is usually a Pulse Width Modulation (PWM) amplifier fixing the voltage bound and the Nyquist frequency of the regulator. Typical analogue regulators include three main terms: a feedforward channel, a proportional feedback channel and the electromotive force compensation. The latter compensation may be also accomplished by integrative feedback. Here the problem is faced through a model-based design (Embedded Model Control), on the basis of a wide-band embedded model of the solenoid which includes the effect of eddy currents. To this end model parameters must be identified. The embedded model includes a stochastic disturbance dynamics capable of estimating and correcting the electromotive contribution together with the model parametric uncertainty, variability and state dependence. The embedded model which is fed by the measured current and the supplied voltage becomes a state predictor of the controllable and disturbance dynamics. The control law combines a reference generator, state feedback and disturbance rejection to dispatch the PWM with the appropriate duty cycle. Modeling, identification and control design are outlined together with experimental result. Comparison with an existing analogue regulator is also provided

Embedded Model Control calls for disturbance modeling and rejection

Robust control design is mainly devoted to guaranteeing the closed-loop stability of a model-based control law in the presence of parametric uncertainties. The control law is usually a static feedback law which is derived from a (nonlinear) model using different methodologies. From this standpoint, stability can only be guaranteed by introducing some ignorance coefficients and restricting the feedback control effort with respect to the model-based design. Embedded Model Control shows that, the model-based control law must and can be kept intact in the case of uncertainty, if, under certain conditions, the controllable dynamics is complemented by suitable disturbance dynamics capable of real-time encoding the different uncertainties affecting the ‘embedded model', i.e. the model which is both the design source and the core of the control unit. To be real-time updated the disturbance state is driven by an unpredictable input vector, the noise, which can only be estimated from the model error. The uncertainty-based (or plant-based) design concerns the noise estimator, so as to prevent the model error from conveying uncertainty components (parametric, cross-coupling, neglected dynamics) which are command-dependent and thus prone to destabilizing the controlled plant, into the embedded model. Separation of the components in the low and high frequency domain by the noise estimator itself allows stability recovery and guarantee, and the rejection of low frequency uncertainty components. Two simple case studies endowed with simulated and experimental runs will help to understand the key assets of the methodolog

Disturbance rejection in a current regulator for proportional electro-hydraulic valves

Current regulation of solenoids is well-known and standard in any proportional electro-hydraulic valve. The goal is to provide a wide band transfer function from the current reference to the measured current, thus making the solenoid a fast and ideal force actuator for the position control within the limits of the power supplier. The latter is a Pulse Width Modulation (PWM) amplifier fixing the voltage limit and the Nyquist frequency of the regulator. Typical analogue regulators include three main terms: a feedforward channel, a proportional feedback channel and the electromotive force compensation fed by an estimate of the plunger velocity. The latter may be replaced by an integrative feedback. Here the problem is faced through a model based design (Embedded Model Control), based on a wide-band embedded model of the solenoids which includes also the effect of the eddy currents. To this end the model must be identified. The Embedded Model includes a disturbance dynamics capable of completing and correcting the electromotive contribution with parametric uncertainty, variability and state dependence. The embedded model fed by the measured current and the supplied voltage becomes a state estimator of the controllable and disturbance dynamics. The control law combines reference generator, state feedback and disturbance rejection to dispatch PWM with the appropriate duty cycle. Modelling, identification and control design are outlined together with regulator performance