Unity feedback control system

A unity-feedback control system has a nominal plant transfer function... 

The analysis of feedback control systems can often be facilitated by conversion to an equivalent unity feedback system, i.e. a feedback loop in which the feedback path is represented by a steady-state gain of unity. There are two principal cases to consider. 

A unity feedback computer control system, has an open-loop pulse transfer function... 

In the simplest scenario, we can think of the equation as a unity feedback system with only a proportional controller (i.e., k = Kc) and G(s) as the process function. We are interested in finding the roots for different values of the parameter k. We can either tabulate the results or we can plot the solutions s in the complex plane—the result is the root-locus plot. 

Here are some useful suggestions regarding root locus plots of control systems. In the following exercises, we consider only the simple unity feedback closed-loop characteristic equation ... 

Based on the linearized models around the equilibrium point, different local controllers can be implemented. In the discussion above a simple proportional controller was assumed (unity feedback and variable gain). To deal with multivariable systems two basic control strategies are considered centralized and decentralized control. In the second case, each manipulated variable is computed based on one controlled variable or a subset of them. The rest of manipulated variables are considered as disturbances and can be used in a feedforward strategy to compensate, at least in steady-state, their effects. For that purpose, it is t3q)ical to use PID controllers. The multi-loop decoupling is not always the best strategy as an extra control effort is required to decouple the loops. 

Fig. 7.38. Unity feedback system equivalent to the control loop shown in Fig. 7.37 when the dynamics of the feedback path are not significant...

Fig. 7.86. Equivalent unity feedback block diagram of control system illustrated in Fig. 7.42 including non-linear element...

The above simple analysis highlights an important issue in process dynamics the influence of positive and negative feedback on system s stability. Instability can occur in recycle systems due to positive feedback when the gain is larger than unity. We may give as example the recycle of energy developed by an exothermal reaction in an adiabatic PFR for feed preheating. Instability may occur because of the exponential increase in reaction rate with the temperature when this cannot be properly controlled (Bildea Dimian, 1998). Another example is the recycle of impurities in a plant with recycles, whose inventory cannot be kept at equilibrium by the separation system (Dimian et al., 2000). 

As a specific example to study the characteristics of the controller, the problem involving four modes of longitudinal oscillations is considered herein. The natural radian frequency of the fundamental mode, normalized with respect to 7ra/L, is taken to be unity. The nominal linear parameters Dni and Eni in Eq. (22.12) are taken from [1], representing a typical situation encountered in several practical combustion chambers. An integrated research project comprising laser-based experimental diagnostics and comprehensive numerical simulation is currently conducted to provide direct insight into the combustion dynamics in a laboratory dump combustor [27]. Included as part of the results are the system and actuator parameters under feedback actions, which can... 

There is a possibility that concern over the new feedback loop and system instability has overshadowed the improvement in potentiostatic control when F = 1. This change is not readily apparent in the graphs, but the low-frequency, long-time value of Eg/Vj is unity in the presence of faradaic current. After the instability is cured, the dependence of potential on current will be more evident than it is now. 

Optical oscillators, commonly referred to as lasers, are optical feedback systems in which two fundamental conditions must be satisfied for stable oscillation at the lasing wavelength the round-trip gain must be unity, and the round-trip phase must be an integer multiple of 2ti radians. Consequently there are two fundamental elements in any optical fiber laser, i.e., a source of optical in, and an optical feedback path either or both may be in fiber. For the purposes of this article optical fiber lasers will be defined as lasers in which the optical gain element is an optical fiber amplifier. Extra elements may be added to facilitate coupling of optical energy in and out of the laser cavity, or to control the temporal and spectral characteristics of the laser. 

---