Nonlinear control laws often need to be implemented with digital hardware. Use of digital control systems leads to communication/processing delays which are widely neglected in control of mechanical systems. This paper proposes a discrete approach to feedback linearization that considers these commonly overlooked delays in design. The proposed approach is shown to both improve the performance and remove the need for continuous derivative terms. In feedback linearization control systems, designed in the continuous domain, derivative terms are required to speed up the control response of mechanical systems, but disadvantageously cause high sensitivity to noise. The proposed approach was used to design a feedback linearization control system for a common turning maneuver of an unmanned helicopter in yaw. At this maneuver, the helicopter centroid motion and pitch rotational speed are almost zero. Governing differential equations of the helicopter at this maneuver are nonlinear and coupled. A feedback linearization law was proposed to curb nonlinearity and, a discrete control system, considering the inevitable delay due to the use of digital control systems, was adopted to complete the control law. This innovative approach resulted in less sensitivity to noises and performance boost. Practical limits in terms of control input, rotor speed, sampling frequency and noises of the gyroscope, the tachometer and the acceleration sensor were taken into account in this research. The results show that the proposed control system leads to fast and smooth yaw turns even at a high pitch angle (close to vertical) or in the case of being hit by external objects.

This article first reviews the position control of piezoelectric actuators, particularly charge-based sensorless control systems, which often include a charge estimator as a key component. The rest of the paper is about charge estimators for piezoelectric actuators. Two of the most recent/effective types of these estimators utilise either a sensing capacitor (type I in this paper) or a sensing resistor (type II); the latter (and the newer) type is broadly known as a digital charge estimator. Some experimental results in the literature show that, with the same loss in excitation voltage, a considerably higher amount of charge can be estimated with a type II estimator in comparison with a type I estimator; therefore, the superiority of type II estimators was acknowledged. In order to re-assess this conclusion, this paper equitably compares type I and II estimators through analytical modelling and experimentation. The results indicate that type II estimators have only a slight advantage in estimating higher amounts of charge, if both type I and II estimators are designed appropriately. At the same time, type II estimators have disadvantages; e.g., the resistance of type II estimators has to be tuned to suit different excitation frequencies. This research concludes that capacitor-based (type I) charge estimators for piezoelectric actuators, with pertinent design and implementation, can be still the prime solution for many charge estimation problems despite claims in the literature in the last decade.

This paper focuses at charge estimators of piezoelectric actuators with a sensing capacitor. They have been claimed in the literature to be outperformed by their newly emerged competitors, charge estimators with a sensing resistor, widely known as digital charge estimators. This paper proposes a digital implementation of capacitor-based estimators and compares them with resistor-based ones both analytically and experimentally. Although, the sensing capacitors are normally bulkier than the sensing resistors used in newer resistor-based estimators; a resistor-based estimator needs to have a variable resistance to deal with different excitation frequencies satisfactorily; this is a major drawback which does not exist in capacitor-based estimators. Both capacitor-based and resistorbased estimators, if designed appropriately, are quite comparable in terms of voltage drop and range of measurable charge. This research concludes that capacitor-based estimators, with right design and implementation, can be still of wide use in nanopositioning.