Stability margin

Time-Delay Compensation Time delays are a common occurrence in the process industries because of the presence of recycle loops, fluid-flow distance lags, and dead time in composition measurements resulting from use of chromatographic analysis. The presence of a time delay in a process severely hmits the performance of a conventional PID control system, reducing the stability margin of the closed-loop control system. Consequently, the controller gain must be reduced below that which could be used for a process without delay. Thus, the response of the closed-loop system will be sluggish compared to that of the system with no time delay. 

SBWR power density is a low 42 kW/liter. BWRs are typically -50 kWAiter and about half the power density of PWRs. Low power density means more thermal and hydrodynamic stability margins. Vessel embrittlement, which has not been a problem for BWRs, is even less concern for the SBWR. 

In the operation of BWRs, especially when operating near the threshold of instability, the stability margin of the stable system and the amplitude of the limit cycle under unstable condition become of importance. A number of nonlinear dynamic studies of BWRs have been reported, notably in an International Workshop on Boiling Water Reactor Stability (1990). The following references are mentioned for further study. 

Polymers designed with this technique have a number of important aspects in common with proteins. First of all, the transition from a liquid-like globule into a frozen state occurs as a first order phase transition. Further, the frozen state itself has an essential stability margin, which is determined by the design parameters. As in real proteins, neither a large variation of temperature or other environmental conditions, nor a mutational substitution of several monomers leads to any change in basic state conformation. In this respect the ability of sequence design to capture certain essential characteristics of proteins seems quite plausible. 

Explicit RK Chap. 4, Sect. 4.5. Limited stability, marginally more efficient than EX. Easy to program. 

Quantitative models and numerical computations are and will continue to be central in the implementation of model-predictive feedback controllers. Unfortunately, numerical computations alone are weak or not robust in answering questions such as the following How well is a control system running Are the disturbances normal Why is derivative action not needed in a loop What loops need dead time compensation, and should it be increased or reduced Have the stability margins of certain loops changed and, if so, how should the controllers be automatically retuned ... 

The following example illustrates how a cold-shot reactor is designed to maximize conversion while satisfying stability margins. 

Advanced fluid bearings with broad stability margins, high-speed capability, and self-sustained operation... 

Schneider A, Zeidis I, Zimmermann K. Comparison of body shap>es of walking machines in regards to stability margins. In Proceedings of the third international conference on climbing and walking robots 2000. p. 275- 1. 

The core is divided into two orifice zones. The outer zone of fuel assemblies, located near the core periphery, has more restrictive orifices than the inner zone, so flow to the higher power fuel assemblies is increased. The orificing of all fuel assemblies increases the flow stability margin. 

Analysis results using the gap / and the maximum stability margin b ... 

Tci = dfci. In this simplified form, the tuning rules will be on a comparable level with the Ziegler-Nichols and Cohen-Coon rules in terms of ease of use, with the added benefit of having several different performance levels for the user to choose from along with their respective stability margins. 

To apply the new timing rules, the user must first identify the process dynamics in terms of JC, T and d. Then, a value for the normalized desired closed-loop time constant Td must be selected. This choice of fd would be dictated by the desired response speed of the closed-loop system (i.e. Ta = (5fci -f- l)d) with due consideration for the acceptable stability margins. This information is available for both PI and PID settings in Table 7.1 and Figures 7.1-7.4. With the selected value for fd and the value identified for i = 7, the normalized controller parameters Kc, f/, fo) are calcidated from Table 7.1. The final step is to evaluate the actual controller parameters for implementation according to Equations (7.11), (7.15) and (7.21), i.e. Kc = -,Ti = dfj TD — dfu-... 

Figure 7.1 PID stability margins as a function of L (dashed TcI = 4 dash-dotted fci — 2 dotted fd = 1.33 solid with o fd = 1 solid with Td = 0.8 solid Td — 0.67). Upper diagram gain margins lower diagram phase margins...

In order to examine the stability margins of the integrating plus delay process under feedback control with a PID controller, the actual open-loop transfer function is formulated as follows... 

With our tuning rules, if we choose C = 1 and 0 = 3, then Kc = 0.466 and f/ = 7.19. Therefore, for this particular choice of closed-loop performance, our tuning rules correspond almost exactly to those presented by Tyreus amd Luyben (1992). The key benefit with our timing rules is that different values for 0, depending on the control objective and desired stability margins, may be selected and used to eaisily calculate the corresponding PID controller parameters. 

Li, G, Yue, H., Zhou, M. Wei, J. (2014). Probabilistic assessment of oscillatory stability margin of power systems incorporating wind farms. International Journal of Electrical Power Energy Systems, 58(0) 47-56. 

IMO. 2009. Stability and Seakeeping Characteristics of Damaged Passenger Ships in a Seaway When Returning to Port by Own Power or Under Tow, A survey of residual stability margin. Submitted by Germany, SLF 521811, London, 26 October 2009. 

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