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Shaping the Loop Frequency Response
Published in Boris J. Lurie, Paul J. Enright, Classical Feedback Control with Nonlinear Multi-Loop Systems, 2020
Boris J. Lurie, Paul J. Enright
In Section 4.3 we will discuss physical constraints on the high-frequency loop gain. However, first we need to clarify the definitions of the term “feedback bandwidth.” In the literature and in the professional language of control engineers, this term may have any of the following three interpretations indicated in Figure 4.22:The crossover frequency fb, i.e., the bandwidth of the loop gain exceeding 0 dB. In this book, this definition for feedback bandwidth is accepted.The frequency fM, where |M|=1/2, i.e., 20 log |M| ≈ −3 dB. This frequency is the tracking system 3 dB bandwidth mentioned in Section 3.1. The 3 dB frequency is typically from 1.3fb to 1.7fb.The frequency up to which the loop gain retains a specified value (e.g., the bandwidth of 30 dB feedback). This bandwidth is also called the bandwidth of functional feedback.
Controller Adjustments
Published in Norman A. Anderson, Instrumentation for Process Measurement and Control, 2017
The total loop gain is the product of the gain of the control loop, exclusive of the controller, multiplied by the gain of the controller. Assume that Step 6 gave a proportional band of 50%, i.e., a controller gain of 2. Since total loop gain is 1, the gain of the loop exclusive of the controller must be 1 divided by 2, or 0.5. To produce a damped response the total gain must be less than 1, and since the controller is the only part of the loop that can be adjusted, its gain must be less than 2 (i.e., a proportional band greater than 50%). The response that is usually desirable approximates Curve A for the proportional-only controller in Figure 12-1. This response, called quarter-amplitude dampening, causes each cycle to have an amplitude of one-quarter that of the previous cycle. A total loop gain of 0.5 will result in quarter-amplitude dampening. This, in the above example, the controller should have a gain of 1, or a proportional band setting of 100 percent. If the control loop has a much lower gain, the loop is said to be overdamped. Although the loop will be stable, excessive offset will result (see Curve C). A loop gain of 1 will yield Curve A. A loop gain greater than 1 will yield continuous cycling of increasing amplitude. This procedure should give satisfactory results in a proportional-only controller.
Amplifier Basics
Published in Bang-Sup Song, Micro CMOS Design, 2017
The Bode plots for the feedback loop gain and the closed-loop gain are included in the figure with other important parameters. Again, the stability is determined by the excess phase delay of the loop gain at the unity loop-gain frequency ωk. PM can be estimated as in Equation (1.20). This configuration has a noninverting gain of ~1/f, and the input resistance is high as the input looks into the opamp input. Although all opamps reject common-mode signals, one drawback of this noninverting amplifier is the input common-mode swing. For good PM greater than 60°, the nondominant pole ωp2 should be placed at far higher frequencies than ωk in this example.
Output-only identification of self-excited systems using discrete-time Lur'e models with application to a gas-turbine combustor
Published in International Journal of Control, 2022
Juan A. Paredes, Yulong Yang, Dennis S. Bernstein
In view of these diverse applications, it is of interest to construct models of SES based on response data. To this end, a candidate model structure is the Lur'e model, where linear dynamics are connected in feedback with a static nonlinear function (Khalil, 2002). The ability of Lur'e models to exhibit self-oscillation has been widely studied (Aguilar et al., 2009; Chatterjee, 2011; Ding, 2010; Mees & Chua, 1979; Risau-Gusman, 2016; Stan & Sepulchre, 2007; Zanette, 2017), and self-excited discrete-time systems are considered in Rasvan (1998), D'Amico et al. (2002), Gentile et al. (2011). As shown in Paredes et al. (2021), a Lur'e model exhibits self-excited behaviour when the linear dynamics are asymptotically stable, the nonlinear feedback function is sigmoidal, and the loop gain is sufficiently high. In effect, high loop gain renders the zero equilibrium unstable, driving the state to the saturation region, where the system operates as an open-loop system driven by a step input. A washout filter (an asymptotically stable transfer function with a zero at 1 and thus zero asymptotic step response) drives the state of the open-loop asymptotically stable dynamics back into the linear region, which yields an oscillatory response.
Robust fractional-order [proportional integral derivative] controller design with specification constraints: more flat phase idea
Published in International Journal of Control, 2021
Zhenlong Wu, Jairo Viola, Ying Luo, YangQuan Chen, Donghai Li
It is widely known that the flat phase constraint can guarantee a constant open-loop phase around a given gain crossover frequency. It leads to insensitivity to the loop gain variations for the closed-loop system (Luo & Chen, 2012). When the loop gain has an extreme variation, the flat phase constraint system may not handle with the loop gain variations well. Therefore, the ‘more flat phase’ idea is proposed to design fractional-order controllers and its exact definition will be introduced by Equation (17) in Section 2. The high order derivative of the open-loop phase as the core of the ‘more flat phase’ idea can be applied to enhance the iso-damping property of system response. The more flat phase constraint means the open-loop phase is more likely to be a constant and less sensitive to the loop gain variations.
An Algorithm for DSTATCOM with Optimized Values of PI Gain Using Adaptive Internal Model
Published in Electric Power Components and Systems, 2021
Jayadeep Srikakolapu, Sabha Raj Arya, Rakesh Maurya, Ramakanta Mehar
The fundamental frequency extractors play an important role in control scheme of DSTATCOM. In addition, achieving precise and fast dynamic behavior of DSTATCOM under unbalance and harmonic distortions is also needed [8]. During dynamic condition for a three-phase system, DSTATCOM is able to get good control with synchronous reference frame (SRF) PLL in its control. Severe effect on the performance of DSTATCOM due to distortions is unavoidable with SRF PLL. Synchronous reference frame based and P-Q theory-based schemes are used in constructing a basic three-Phase-Phase Locked Loop (PLL) [9]. The incapability of harmonic mitigation in few control algorithms has planted the advancement of various PLLs. Dual second order generalized integrator (DSOGI) [10], Moving average PLL (MA-PLL), third-order sinusoidal integrator (TOSSI) [11], are presented for detection of fundamental components in Stationary Reference Frame (SRF), Double Synchronous Reference Frame (DSRF), Decoupled Double Synchronous Reference Frame (DDSRF) [12], Modified Synchronous Reference Frame PLL (MSRF-PLL), and auto adjustable synchronous reference frame PLL (ASRF-PLL) are few types of d-q based PLLs. Loop gain plays a key role in the stability of these systems [13]. Online frequency estimation of a periodic signal but not necessarily sinusoidal signal using Notch filter provides adaptive ness to the system and its application has improved the system stability during dynamic conditions [14].