Vibration suppression in multi-body systems by means of disturbance filter design methods

This paper addresses the problem of interaction in mechanical multi-body systems and shows that subsystem interaction can be considerably minimized while increasing performance if an efficient disturbance model is used. In order to illustrate the advantage of the proposed intelligent disturbance filter, two linear model based techniques are considered: IMC and the model based predictive (MPC) approach. As an illustrative example, multivariable mass-spring-damper and quarter car systems are presented. An adaptation mechanism is introduced to account for linear parameter varying LPV conditions. In this paper we show that, even if the IMC control strategy was not designed for MIMO systems, if a proper filter is used, IMC can successfully deal with disturbance rejection in a multivariable system, and the results obtained are comparable with those obtained by a MIMO predictive control approach. The results suggest that both methods perform equally well, with similar numerical complexity and implementation effort

Discrete Modeling and Sliding Mode Control of Piezoelectric Actuators

With the ability to generate fine displacements with a resolution down to sub-nanometers, piezoelectric actuators (PEAs) have found wide applications in various nano-positioning systems. However, existence of various effects in PEAs, such as hysteresis and creep, as well as dynamics can seriously degrade the PEA performance or even lead to instability. This raises a great need to model and control PEAs for improved performance, which have drawn remarkable attention in the literature. Sliding mode control (SMC) shows its potential to the control of PEA, by which the hysteresis and other nonlinear effects can be regard as disturbance to the dynamic model and thus rejected or compensated by its switching control. To implement SMC in digital computers, this research is aimed at developing novel discrete models and discrete SMC (DSMC)-based control schemes for PEAs, along with their experimental validation. The first part of this thesis concerns with the modeling and control of one-degree of freedom (DOF) PEA, which can be treated as a single-input-single-output (SISO) system. Specifically, a novel discrete model based on the concept of auto-regressive moving average (ARMA) was developed for the PEA hysteresis; and to compensate for the PEA hysteresis and improve its dynamics, an output tracking integrated discrete proportional-integral-derivative-based SMC (PID-SMC) was developed. On this basis, by making use of the availability of PEA hysteresis models, two control schemes, named “the discrete inversion feedforward based PID-SMC” and “the discrete disturbance observer (DOB)-based PID-SMC”, were further developed. To illustrate the effectiveness of the developed models and control schemes, experiments were designed and conducted on a commercially available one-DOF PEA, as compared with the existing ones. The second part of the thesis presents the extension of the developed modeling and control methods to multi-DOF PEAs. Given the fact that details with regard to the PEA internal configurations is not typically provided by the manufacturer, a state space model based on the black box system identification was developed for the three-DOF PEA. The developed model was then integrated in the output tracking based discrete PID-SMC, with its effectiveness verified through the experiments on a commercially available three-DOF PEA. The superiority of the proposed control method over the conventional PID controller was also experimentally investigated and demonstrated. Finally, by integrating with a DOB in the discrete PID-based SMC, a novel control scheme is resulted to compensate for the nonlinearities of the three-DOF PEA. To verify its effectiveness, the discrete DOB based PID-SMC was applied in the control experiments and compared with the existing SMC. The significance of this research lies in the development of the discrete models and PID-based SMC for PEAs, which is of great help to improve their performance. The successful application of the proposed method in the control of multi-DOF PEA allows the application of SMC to the control of complicated multi-inputs-multi-outputs (MIMO) systems without details regarding the internal configuration. Also, integration of the inversion based feedforward control and the DOB in the SMC design has been proven effective for the tracking control of PEAs

Optimized state feedback regulation of 3DOF helicopter system via extremum seeking

In this paper, an optimized state feedback regulation of a 3 degree of freedom (DOF) helicopter is designed via extremum seeking (ES) technique. Multi-parameter ES is applied to optimize the tracking performance via tuning State Vector Feedback with Integration of the Control Error (SVFBICE). Discrete multivariable version of ES is developed to minimize a cost function that measures the performance of the controller. The cost function is a function of the error between the actual and desired axis positions. The controller parameters are updated online as the optimization takes place. This method significantly decreases the time in obtaining optimal controller parameters. Simulations were conducted for the online optimization under both fixed and varying operating conditions. The results demonstrate the usefulness of using ES for preserving the maximum attainable performance

Performance-driven control of nano-motion systems

The performance of high-precision mechatronic systems is subject to ever increasing demands regarding speed and accuracy. To meet these demands, new actuator drivers, sensor signal processing and control algorithms have to be derived. The state-of-the-art scientific developments in these research directions can significantly improve the performance of high-precision systems. However, translation of the scientific developments to usable technology is often non-trivial. To improve the performance of high-precision systems and to bridge the gap between science and technology, a performance-driven control approach has been developed. First, the main performance limiting factor (PLF) is identified. Then, a model-based compensation method is developed for the identified PLF. Experimental validation shows the performance improvement and reveals the next PLF to which the same procedure is applied. The compensation method can relate to the actuator driver, the sensor system or the control algorithm. In this thesis, the focus is on nano-motion systems that are driven by piezo actuators and/or use encoder sensors. Nano-motion systems are defined as the class of systems that require velocities ranging from nanometers per second to millimeters per second with a (sub)nanometer resolution. The main PLFs of such systems are the actuator driver, hysteresis, stick-slip effects, repetitive disturbances, coupling between degrees-of-freedom (DOFs), geometric nonlinearities and quantization errors. The developed approach is applied to three illustrative experimental cases that exhibit the above mentioned PLFs. The cases include a nano-motion stage driven by a walking piezo actuator, a metrological AFM and an encoder system. The contributions of this thesis relate to modeling, actuation driver development, control synthesis and encoder sensor signal processing. In particular, dynamic models are derived of the bimorph piezo legs of the walking piezo actuator and of the nano-motion stage with the walking piezo actuator containing the switching actuation principle, stick-slip effects and contact dynamics. Subsequently, a model-based optimization is performed to obtain optimal drive waveforms for a constant stage velocity. Both the walking piezo actuator and the AFM case exhibit repetitive disturbances with a non-constant period-time, for which dedicated repetitive control methods are developed. Furthermore, control algorithms have been developed to cope with the present coupling between and hysteresis in the different axes of the AFM. Finally, sensor signal processing algorithms have been developed to cope with the quantization effects and encoder imperfections in optical incremental encoders. The application of the performance-driven control approach to the different cases shows that the different identified PLFs can be successfully modeled and compensated for. The experiments show that the performance-driven control approach can largely improve the performance of nano-motion systems with piezo actuators and/or encoder sensors

Design, control and error analysis of a fast tool positioning system for ultra-precision machining of freeform surfaces

This thesis was previously held under moratorium from 03/12/19 to 03/12/21Freeform surfaces are widely found in advanced imaging and illumination systems, orthopaedic implants, high-power beam shaping applications, and other high-end scientific instruments. They give the designers greater ability to cope with the performance limitations commonly encountered in simple-shape designs. However, the stringent requirements for surface roughness and form accuracy of freeform components pose significant challenges for current machining techniques—especially in the optical and display market where large surfaces with tens of thousands of micro features are to be machined. Such highly wavy surfaces require the machine tool cutter to move rapidly while keeping following errors small. Manufacturing efficiency has been a bottleneck in these applications. The rapidly changing cutting forces and inertial forces also contribute a great deal to the machining errors. The difficulty in maintaining good surface quality under conditions of high operational frequency suggests the need for an error analysis approach that can predict the dynamic errors. The machining requirements also impose great challenges on machine tool design and the control process. There has been a knowledge gap on how the mechanical structural design affects the achievable positioning stability. The goal of this study was to develop a tool positioning system capable of delivering fast motion with the required positioning accuracy and stiffness for ultra-precision freeform manufacturing. This goal is achieved through deterministic structural design, detailed error analysis, and novel control algorithms. Firstly, a novel stiff-support design was proposed to eliminate the structural and bearing compliances in the structural loop. To implement the concept, a fast positioning device was developed based on a new-type flat voice coil motor. Flexure bearing, magnet track, and motor coil parameters were designed and calculated in detail. A high-performance digital controller and a power amplifier were also built to meet the servo rate requirement of the closed-loop system. A thorough understanding was established of how signals propagated within the control system, which is fundamentally important in determining the loop performance of high-speed control. A systematic error analysis approach based on a detailed model of the system was proposed and verified for the first time that could reveal how disturbances contribute to the tool positioning errors. Each source of disturbance was treated as a stochastic process, and these disturbances were synthesised in the frequency domain. The differences between following error and real positioning error were discussed and clarified. The predicted spectrum of following errors agreed with the measured spectrum across the frequency range. It is found that the following errors read from the control software underestimated the real positioning errors at low frequencies and overestimated them at high frequencies. The error analysis approach thus successfully revealed the real tool positioning errors that are mingled with sensor noise. Approaches to suppress disturbances were discussed from the perspectives of both system design and control. A deterministic controller design approach was developed to preclude the uncertainty associated with controller tuning, resulting in a control law that can minimize positioning errors. The influences of mechanical parameters such as mass, damping, and stiffness were investigated within the closed-loop framework. Under a given disturbance condition, the optimal bearing stiffness and optimal damping coefficients were found. Experimental positioning tests showed that a larger moving mass helped to combat all disturbances but sensor noise. Because of power limits, the inertia of the fast tool positioning system could not be high. A control algorithm with an additional acceleration-feedback loop was then studied to enhance the dynamic stiffness of the cutting system without any need for large inertia. An analytical model of the dynamic stiffness of the system with acceleration feedback was established. The dynamic stiffness was tested by frequency response tests as well as by intermittent diamond-turning experiments. The following errors and the form errors of the machined surfaces were compared with the estimates provided by the model. It is found that the dynamic stiffness within the acceleration sensor bandwidth was proportionally improved. The additional acceleration sensor brought a new error source into the loop, and its contribution of errors increased with a larger acceleration gain. At a certain point, the error caused by the increased acceleration gain surpassed other disturbances and started to dominate, representing the practical upper limit of the acceleration gain. Finally, the developed positioning system was used to cut some typical freeform surfaces. A surface roughness of 1.2 nm (Ra) was achieved on a NiP alloy substrate in flat cutting experiments. Freeform surfaces—including beam integrator surface, sinusoidal surface, and arbitrary freeform surface—were successfully machined with optical-grade quality. Ideas for future improvements were proposed in the end of this thesis.Freeform surfaces are widely found in advanced imaging and illumination systems, orthopaedic implants, high-power beam shaping applications, and other high-end scientific instruments. They give the designers greater ability to cope with the performance limitations commonly encountered in simple-shape designs. However, the stringent requirements for surface roughness and form accuracy of freeform components pose significant challenges for current machining techniques—especially in the optical and display market where large surfaces with tens of thousands of micro features are to be machined. Such highly wavy surfaces require the machine tool cutter to move rapidly while keeping following errors small. Manufacturing efficiency has been a bottleneck in these applications. The rapidly changing cutting forces and inertial forces also contribute a great deal to the machining errors. The difficulty in maintaining good surface quality under conditions of high operational frequency suggests the need for an error analysis approach that can predict the dynamic errors. The machining requirements also impose great challenges on machine tool design and the control process. There has been a knowledge gap on how the mechanical structural design affects the achievable positioning stability. The goal of this study was to develop a tool positioning system capable of delivering fast motion with the required positioning accuracy and stiffness for ultra-precision freeform manufacturing. This goal is achieved through deterministic structural design, detailed error analysis, and novel control algorithms. Firstly, a novel stiff-support design was proposed to eliminate the structural and bearing compliances in the structural loop. To implement the concept, a fast positioning device was developed based on a new-type flat voice coil motor. Flexure bearing, magnet track, and motor coil parameters were designed and calculated in detail. A high-performance digital controller and a power amplifier were also built to meet the servo rate requirement of the closed-loop system. A thorough understanding was established of how signals propagated within the control system, which is fundamentally important in determining the loop performance of high-speed control. A systematic error analysis approach based on a detailed model of the system was proposed and verified for the first time that could reveal how disturbances contribute to the tool positioning errors. Each source of disturbance was treated as a stochastic process, and these disturbances were synthesised in the frequency domain. The differences between following error and real positioning error were discussed and clarified. The predicted spectrum of following errors agreed with the measured spectrum across the frequency range. It is found that the following errors read from the control software underestimated the real positioning errors at low frequencies and overestimated them at high frequencies. The error analysis approach thus successfully revealed the real tool positioning errors that are mingled with sensor noise. Approaches to suppress disturbances were discussed from the perspectives of both system design and control. A deterministic controller design approach was developed to preclude the uncertainty associated with controller tuning, resulting in a control law that can minimize positioning errors. The influences of mechanical parameters such as mass, damping, and stiffness were investigated within the closed-loop framework. Under a given disturbance condition, the optimal bearing stiffness and optimal damping coefficients were found. Experimental positioning tests showed that a larger moving mass helped to combat all disturbances but sensor noise. Because of power limits, the inertia of the fast tool positioning system could not be high. A control algorithm with an additional acceleration-feedback loop was then studied to enhance the dynamic stiffness of the cutting system without any need for large inertia. An analytical model of the dynamic stiffness of the system with acceleration feedback was established. The dynamic stiffness was tested by frequency response tests as well as by intermittent diamond-turning experiments. The following errors and the form errors of the machined surfaces were compared with the estimates provided by the model. It is found that the dynamic stiffness within the acceleration sensor bandwidth was proportionally improved. The additional acceleration sensor brought a new error source into the loop, and its contribution of errors increased with a larger acceleration gain. At a certain point, the error caused by the increased acceleration gain surpassed other disturbances and started to dominate, representing the practical upper limit of the acceleration gain. Finally, the developed positioning system was used to cut some typical freeform surfaces. A surface roughness of 1.2 nm (Ra) was achieved on a NiP alloy substrate in flat cutting experiments. Freeform surfaces—including beam integrator surface, sinusoidal surface, and arbitrary freeform surface—were successfully machined with optical-grade quality. Ideas for future improvements were proposed in the end of this thesis

Adaptive optimal control of under-actuated robotic systems using a self-regulating nonlinear weight-adjustment scheme: Formulation and experimental verification

This paper formulates an innovative model-free self-organizing weight adaptation that strengthens the robustness of a Linear Quadratic Regulator (LQR) for inverted pendulum-like mechatronic systems against perturbations and parametric uncertainties. The proposed control procedure is devised by using an online adaptation law to dynamically adjust the state weighting factors of LQR's quadratic performance index via pre-calibrated state-error-dependent hyperbolic secant functions (HSFs). The updated state-weighting factors re-compute the optimal control problem to modify the state-compensator gains online. The novelty of the proposed article lies in adaptively adjusting the variation rates of the said HSFs via an auxiliary model-free online self-regulation law that uses dissipative and anti-dissipative terms to flexibly re-calibrate the nonlinear function's waveforms as the state errors vary. This augmentation increases the controller's design flexibility and enhances the system's disturbance rejection capacity while economizing control energy expenditure under every operating condition. The proposed self-organizing LQR is analyzed via customized hardware-in-loop (HIL) experiments conducted on the Quanser's single-link rotational inverted pendulum. As compared to the fixed-gain LQR, the proposed SR-EM-STC delivers an improvement of 52.2%, 16.4%, 55.2%, and 42.7% in the pendulum's position regulation behavior, control energy expenditure, transient recovery duration, and peak overshoot, respectively. The experimental outcomes validate the superior robustness of the proposed scheme against exogenous disturbances

Hybrid active force control for fixed based rotorcraft

Disturbances are considered major challenges faced in the deployment of rotorcraft unmanned aerial vehicle (UAV) systems. Among different types of rotorcraft systems, the twin-rotor helicopter and quadrotor models are considered the most versatile flying machines nowadays due to their range of applications in the civilian and military sectors. However, these systems are multivariate and highly non-linear, making them difficult to be accurately controlled. Their performance could be further compromised when they are operated in the presence of disturbances or uncertainties. This dissertation presents an innovative hybrid control scheme for rotorcraft systems to improve disturbance rejection capability while maintaining system stability, based on a technique called active force control (AFC) via simulation and experimental works. A detailed dynamic model of each aerial system was derived based on the Euler–Lagrange and Newton-Euler methods, taking into account various assumptions and conditions. As a result of the derived models, a proportional-integral-derivative (PID) controller was designed to achieve the required altitude and attitude motions. Due to the PID's inability to reject applied disturbances, the AFC strategy was incorporated with the designed PID controller, to be known as the PID-AFC scheme. To estimate control parameters automatically, a number of artificial intelligence algorithms were employed in this study, namely the iterative learning algorithm and fuzzy logic. Intelligent rules of these AI algorithms were designed and embedded into the AFC loop, identified as intelligent active force control (IAFC)-based methods. This involved, PID-iterative learning active force control (PID-ILAFC) and PID-fuzzy logic active force control (PID-FLAFC) schemes. To test the performance and robustness of these proposed hybrid control systems, several disturbance models were introduced, namely the sinusoidal wave, pulsating, and Dryden wind gust model disturbances. Integral square error was selected as the index performance to compare between the proposed control schemes. In this study, the effectiveness of the PID-ILAFC strategy in connection with the body jerk performance was investigated in the presence of applied disturbance. In terms of experimental work, hardware-in-the-loop (HIL) experimental tests were conducted for a fixed-base rotorcraft UAV system to investigate how effective are the proposed hybrid PID-ILAFC schemes in disturbance rejection. Simulated results, in time domains, reveal the efficacy of the proposed hybrid IAFC-based control methods in the cancellation of different applied disturbances, while preserving the stability of the rotorcraft system, as compared to the conventional PID controller. In most of the cases, the simulated results show a reduction of more than 55% in settling time. In terms of body jerk performance, it was improved by around 65%, for twin-rotor helicopter system, and by a 45%, for quadrotor system. To achieve the best possible performance, results recommend using the full output signal produced by the AFC strategy according to the sensitivity analysis. The HIL experimental tests results demonstrate that the PID-ILAFC method can improve the disturbance rejection capability when compared to other control systems and show good agreement with the simulated counterpart. However, the selection of the appropriate learning parameters and initial conditions is viewed as a crucial step toward this improved performance

Precise Trajectory Tracking of Multi-Rotor UAVs Using Wind Disturbance Rejection Approach

This paper discusses the resilience of the UAV quadrotor to wind disturbances. An unknown input-state observer is presented that uses the Lipschitz method to estimate the internal states and disturbances of the quadrotor and compensate for them by varying the velocities of the four rotors. The observer intends to use existing sensor measurements to estimate the unknown states of the quadrotor and reconstruct the three-dimensional wind disturbances. The estimated states and external disturbances are sent to the PD controller, which compensates for the disturbances to achieve the desired position and attitude, as well as robustness and accuracy. The Lipschitz observer was designed using the LMI approach, and the results were validated using Matlab/Simulink and using the Parrot Mambo mini quadrotor