Open-loop Crossover Frequency Research Articles

Disturbance rejecting PID-FF controller design of a non-ideal buck converter using an innovative snake optimizer with pattern search algorithm

The optimal design of a proportional-integral-derivative controller with two cascaded first-order low-pass filters (PID-FF) for non-ideal buck converters faces significant challenges, including effective disturbance rejection, robustness to parameter variations, and the mitigation of high-frequency signal noise, with existing approaches often struggling and leading to suboptimal performance in practical applications. This study addresses these challenges by introducing a constraint on the open-loop crossover frequency to mitigate high-frequency noise and ensuring the controller prioritizes maintaining constant output voltage and robust responsiveness to input voltage and load current variations. This study also introduces an innovative metaheuristic algorithm, the opposition-based snake optimizer with pattern search (OSOPS), designed to address these limitations. OSOPS enhances the Snake Optimizer (SO) by integrating opposition-based learning (OBL) and Pattern Search (PS), thereby improving its exploration and exploitation capabilities. The proposed algorithm design includes a crossover frequency constraint aimed at counteracting high-frequency noise and ensuring robust performance under diverse disturbances. The efficacy of the OSOPS algorithm is demonstrated through rigorous statistical box plot analysis and convergence response comparisons with the original SO algorithm. Additionally, we systematically compare the performance of the OSOPS-based PID–FF–controlled non-ideal buck converter system against systems utilizing the original SO algorithm and the classical pole placement (PP) method. This evaluation encompasses transient and frequency responses, disturbance rejection, and robustness analysis. The results reveal that the OSOPS-based system outperforms the SO- and PP-based systems with 14.21 % and 32.10 % faster rise times, along with 15.38 % and 84.95 % faster settling times, respectively. The OSOPS and SO systems also exhibit higher bandwidths, exceeding the PP-based system by 18.74 % and 17.03 %, respectively. By addressing the key challenges in PID-FF controller design for non-ideal buck converters, this study provides a substantial advancement in control strategy, promising enhanced performance in practical applications.

Optimal Control Approach to Design a Three-Loop Autopilot for a Tactical Missile

Conventionally, the Three-Loop Autopilot is dominated by three main parameters namely the damping factor, time constant and the open-loop crossover frequency, to achieve the desired performance. In developing the autopilot gains, the same gains as the conventional approach can also be obtained using the general optimality theory. The basic idea of setting the design parameters and the feedback gains using methods of optimal control revolves around the proper selection of the performance index for which the control is optimized. In this paper, an explicit formula for autopilot gains is driven by taking into account the relations between the desired performance and the open-loop frequency, phase margin and time constant without the need to adjust the LQR weights. Since each set of design parameters selection doesn’t guarantee the existence of the optimal control law, the optimization criteria for the three-loop autopilot are derived to know the set of design parameters for which the control is optimized. Finally, an optimal criterion to select the design parameters and therefore the autopilot gains is developed, where the time constant is set to the designer objective while the open-loop crossover frequency and the phase margin as design constraints.

A Nonlinear Integrator Based on the First-Order Reset Element

This work proposes a novel nonlinear Proportional-Integral (PI) controller, which utilizes a generalized first-order reset element. The proposed element can achieve similar magnitude-characteristics as its linear counterpart but with less phase lag at the open-loop crossover frequency (i.e. the control bandwidth), according to a sinusoidal-input describing function (SIDF) analysis. The same can be achieved with an existing reset-based integrator, the Clegg integrator (CI). However, it is known that a Proportional-CI (PCI) element can excessively generate higher-order harmonics of its input, which are neglected in the SIDF-analysis. Furthermore, a PCI can cause a limit cycle when placed in closed-loop with certain types of plants. The novel PI controller proposed in this work can prevent the limit cycle and can reduce the generation of higher-order harmonics, while retaining the beneficial phase advantage that is associated with existing reset-based PI controllers.

Pole Placement-Based Current Control Method for CSI-Fed PMSM Drive With Eliminating Capacitor Voltage Sampling

This article proposes a pole placement based current control method for the current source inverter (CSI) fed permanent magnet synchronous machine (PMSM) drive with eliminating capacitor voltage sampling. Firstly, a generalized <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> -order feedback form of motor current and CSI output current is proposed in the stationary <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\alpha \beta$</tex-math></inline-formula> frame, for the arbitrary pole placement of the control plant. With the proposed pole placement method, the resonance frequency is moved closer to the Nyquist frequency and the resonance peak is damped. On this basis, a linear controller is proposed in the synchronous <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$dq$</tex-math></inline-formula> frame for the high-performance current control of PMSM. Moreover, the control parameter selection method is presented based on the consideration of open-loop crossover frequency and phase margin (PM). In this way, the desired PM and enough gain margin (GM) can be achieved, thus guaranteeing the stability and robustness of the system. Finally, the effectiveness of the proposed method is verified by lab-scaled experiments.

The Inverse Optimal Control Problem for a Three-Loop Missile Autopilot

The performance characteristics of the autopilot must have a fast response to intercept a maneuvering target and reasonable robustness for system stability under the effect of un-modeled dynamics and noise. By the conventional approach, the three-loop autopilot design is handled by time constant, damping factor and open-loop crossover frequency to achieve the desired performance requirements. Note that the general optimal theory can be also used to obtain the same gain as obtained from the conventional approach. The key idea of using optimal control technique for feedback gain design revolves around appropriate selection and interpretation of the performance index for which the control is optimal. This paper derives an explicit expression, which relates the weight parameters appearing in the quadratic performance index to the design parameters such as open-loop crossover frequency, phase margin, damping factor, or time constant, etc. Since all set of selection of design parameters do not guarantee existence of optimal control law, explicit inequalities, which are named the optimality criteria for the three-loop autopilot (OC3L), are derived to find out all set of design parameters for which the control law is optimal. Finally, based on OC3L, an efficient gain selection procedure is developed, where time constant is set to design objective and open-loop crossover frequency and phase margin as design constraints. The effectiveness of the proposed technique is illustrated through numerical simulations.

Optimization of three-loop missile autopilot gain under crossover frequency constraint

Abstract The open-loop crossover frequency is pointed as an important parameter for practical autopilot design. Since different gain designs may achieve the same open-loop crossover frequency, it should be neither considered as a performance objective of the optimal autopilot design-schemes nor neglected. Besides, the main assignment of the autopilot is to drive the missile to track the acceleration commands, so the autopilot gain design should be evaluated directly according to the resultant tracking performance. For this purpose, an optimal design methodology of the three-loop missile autopilot is introduced based on constraint optimization technique, where the tracking performance is established analytically as the design objective and the open-loop crossover frequency is formed as inequality constraint function, both are manipulated in terms of stable characteristic parameters of the autopilot closed-loop. The proposed technique is implemented with the assistance of a numerical optimization algorithm which automatically adjusts the design parameters. Finally, numerical simulation results are provided to demonstrate the effectiveness and feasibility of the proposed approach compared with that in some references.

Role of motion cues in straight-line driving of an agricultural vehicle

Driving simulators open new opportunities for research in a wide range of areas including human factors and ergonomics. The main concern regarding driving simulator research is the validity of the results. In order to obtain the same driving behaviours as those in a real world experiment, it is necessary to provide the driver with the same sensory cues that he/she uses in real world driving. Therefore, one would like to know which sensory cues are used by the human driver. This study investigates the effect of motion cues in straight-line driving of a tractor. Field experiments were conducted in which experienced tractor drivers drove a tractor in parallel swathing mode with the help of a lightbar guidance system. Driving simulator experiments were then performed in which experienced tractor drivers drove in two sessions: in one session motion cues were provided whereas in the other session motion cues were not delivered. Analysis showed that in the absence of motion cues, the drivers significantly increase their control activity and their performance deteriorates. It is also shown that drivers are unable to respond to the full range of disturbances on the tractor and the guidance system and that they automatically reduce the open-loop crossover frequency by reducing their gain, in order to avoid high tracking errors. In the presence of motion cues, drivers adopted a more relaxed driving style by reducing their gain and lead time constant. Using a multi-loop feedback control scheme it is shown that if the driver uses both tractor lateral deviation and yaw rate as feedback variables, he/she can drive the tractor without any lag or lead equalization. The results show that driving simulators for agricultural vehicles require a motion subsystem to allow valid duplication of the real field driving in parallel swathing mode. The implications of the results of this study for developers of guidance systems are also discussed.

Design of optimal robust fixed-structure controllers using the quantitative feedback theory approach

A simple optimization algorithm is proposed for designing fixed-structure controllers for highly uncertain systems. The method can be used to automate the loop-shaping step of the quantitative feedback theory (QFT) design procedure and guarantees robust stability and performance to the feedback loop for all parameters in the plant's uncertainty set. To avoid over-designing the system, the algorithm can be used to minimize either the asymptotic gain, the open-loop crossover frequency or the 3 dB bandwidth of the closed-loop system (nominal or worst case). The proposed algorithm is illustrated with a design example involving a hydraulic actuator, carried out within a computer aided design (CAD) environment (‘StdQFT’ toolbox) which has been developed by the authors. Some preliminary results of this work appeared in 2002 [1].

Optimal Narrow-Band Disturbance Filter for PZT-Actuated Head Positioning Control on a Spinstand

Narrow-band position error at midfrequencies around the open-loop crossover frequency cannot be effectively reduced by using a conventional peak filter, because the attenuation of sensitivity gains has to be traded off with the associated decrease of phase margin. This paper presents a general second-order filter that can reject narrow-band disturbances at any frequency range. The filter zero is designed to minimally degrade the closed-loop system stability and obtain a smooth sensitivity curve around the disturbance frequency. The paper presents a nonlinear optimization procedure for selecting the filter parameters so that the statistical position error is minimized. Experimental results of a piezoelectrically actuated head positioning control system on a spinstand demonstrate that the add-on filter can further reduce the midfrequency nonrepeatable runout of the position error signal by 8% and preserve the stability margin of the original feedback control system

HYBRID DESIGN METHOD OF NONLINEAR CONTROLLERS: AVOIDING BIFURCATIONS

a hybrid design method of pulse energy conversion system (PECS) nonlinear controllers is proposed in this paper. The hybrid method makes possible to avoid bifurcation phenomena in controller dynamics at the design stage. Application of the proposed method allows to eliminate an uncertainty of switching frequency to system open loop crossover frequency ratio choice, to estimate designed controller quality indices (overshoot, settling time and steady-state error) taking into consideration its essentially nonlinear nature and to guarantee bifurcation phenomena absence with high probability. An example of this hybrid method application is demonstrated for the DC-DC buck converter controller design.

Suppressing sensitivity hump in HDD dual-stage servo systems

In Hard disk drive (HDD) single-stage servo system that uses voice coil motor as the sole actuator, the sensitivity hump appears unavoidable due to the Bode’s integral theorem, resulting in amplification of disturbances at frequencies higher than the open-loop gain crossover frequency. This paper studies the sensitivity transfer function limitation in HDD dual-stage servo system. A compensation method for the micro-actuator dynamics, termed as “near-perfect modeling” (NPM), is proposed to generate an effective compensated plant model with zero relative degree in order to suppress the sensitivity hump of the dual-stage servo loop. Therefore, high-frequency disturbances would not be amplified by the servo loop. Experimental results show that the sensitivity hump of dual-stage servo loop can be reduced to very close to 0 dB without amplification of the corresponding measurement noise.

ヘッドサスペンション駆動形マイクロアクチュエータを用いた二段アクチュエータの高帯域化(S62-1 機構・制御(1),S62 情報機器コンピュータメカニクス)

Dual-stage actuators sometimes have a serious problem that the driving force of microactuators excites VCM vibration. To avoid the problem, we designed a suspension-drive piezoelectric micro-actuator to have high resonant frequency and small mass. We installed the microactuator in one of Fujitsu's 3.5-inch commercial drives for evaluation of the dual-stage servo system. The dual-stage actuator system achieved the openloop crossover frequency of 4 kHz.

Servo bandwidth and positioning accuracy design for high track density disk drives

Possibility of achieving positioning accuracy to meet the areal density of 40 Gb/in/sup 2/ has been studied. Stationary and nonstationary position errors are shown, and the servo design approaches have been proposed. A precise model of head-positioning system has been developed, and the required open loop servo bandwidth is estimated using the model. The experimental results using 2.5-inch HDD show that 750 Hz to 1 kHz servo bandwidth (open loop crossover frequency) is effective to achieve 40 nm positioning accuracy during track-following to meet 60 kTPI for 40 Gb/in/sup 2/.

Why modern controllers can go unstable in practice

This paper demonstrates the importance of analyzing proposed modern control system designs with classical frequency response techniques. When classical constraints such as open-loop crossover frequency are ignored, apparently robust modern control designs may go unstable for relatively innocuous plant perturbations. Modern control system designs of successively more complex plants are analyzed to reveal some problems that may occur in the design of real systems and to show how these problems can be solved so that modern control methods will be more useful to practical'control system designers.

Effects of Display Gain on Human Operator Information Processing Rate in a Rate Control Tracking Task

A single-axis rate control tracking experiment was conducted to determine the sensitivity of transinformation (information processing rate in bits/s) to display gain, display type (pursuit or compensatory), and forcing function bandwidth. Four other performance measures were also derived: relative error, relative noiseless error, relative remnant, and system open-loop crossover frequency. It was shown that human information processing rates increased to a maximum and then decreased as a function of both display gain and forcing function bandwidth. In general, little difference in transinformation performance was noted between pursuit and compensatory displays.

Acceleration Stress Effects on Pilot Performance and Dynamic Response

Several brief studies were conducted to assess the effects of a wide range of acceleration environments, varying from zero gravity to high sustained accelerations, on pilot performance and dynamic response. The results indicated that the control performance decrements observed at high sustained accelerations were attributable to decreased pilot gains and corresponding reductions in open-loop system crossover frequency. Limited results for extreme vibratory accelerations suggested that performance deterioration was associated with a reduction in pilot lead equalization (and a corresponding reduction in open-loop crossover). Under short-term weightless conditions, performance in a simulated control task was appreciably poorer than under comparable 1 g conditions for one of two sets of simulated vehicle dynamics investigated. The reason was attributed primarily to increased pilot excitation of the vehicle's lightly damped short-period mode. Soviet data, available from Voskhod flights, indicated that cosmonauts did not perform as well in a simulated control system as during ground training sessions.