Proportional-integral compensator

This is the speed controller block that consists of both a PID (proportional integral derivative, a type of programming) controller and an acceleration compensator. The required speed reference signal is compared with the actual speed signal obtained from the motor model (section 2). The error signal is then fed to both the PID controller... 

On the other hand, conventional control approaches also rely on models, but they are usually not built into the controller itself. Instead the models form the basis of simulations and other analysis methods that guide in the selection of control loops and suggest tuning constants for the relatively simple controllers normally employed [PI, PID, I-only. P-only, lead-lag compensation, etc. (P = proportional, PI = proportional-integral, PID = proportional-integral-derivative)]. Conventional control approaches attempt to build the smarts into the system (the process and the controllers.) rather than only use complex control algorithms. 

The simplest control algorithm to calculate the compensating action of the variable is called proportional control. It is the first component of a more complex algorithm called a proportional integral derivative. As its name suggests, the command to the actuator is calculated in proportion to the error, as shown in the following equation ... 

If the tracked outputs coincide with the measured ones (i.e. z = y), which is the most studied case in the literature [10], the construction of the estimator-based controller is a straightforward task [20]. In fact, the robustness of the controller can be significantly improved by using a proportional-integral (PI) estimator that eliminates the output mismatch [7, 9, 22, 24, 25]. In this case, the modeling error compensation is performed in the fast estimation loop [21] and not in the slow control loop. The situation is more complex when the tracked and measured outputs do not coincide. In this case, the controller and estimator structure might be interlaced in a nontrivial maimer. 

This type control is actually a combination of two previously discussed control modes, proportional and integral. Combining the two modes results in gaining the advantages and compensating for the disadvantages of the two individual modes. 

Whereas the heat flux DSC measures the temperature difference between the sample and the reference sample, power-compensated DSCs are based on compensation of the heat to be measured by electrical energy. Here the sample and the reference are contained in separate micro-furnaces, as shown in Figure 10.6(b). The time integral over the compensating heating power is proportional to the enthalpy absorbed by or released from the sample. 

Semiconductor based devices are the integrated circuit temperature transducers which, in a limited temperature range, may produce an easy-to-read output proportional to temperature and may also be used for thermocouple compensation. 

As experimentally demonstrated above, in the complexation thermodynamics involving cationic species as guests and ionophores as hosts, the entropic change TAAS, induced by altering cation, ligand, or solvent, is proportional to the enthalpic change AAH. This correlation immediately leads to an empirical Eq. 14 with a proportional coefficient a, integration of which affords an extrathermodynamic relationship between TAS and AH. Thus, Eq. 15 is the quantitative expression of the observed compensation effect ... 

The fundamental building block has been the proportional plus integral plus derivative (PID) controller whereby the proportional term would adjust the manipulated variable to correct for a deviation between measurement and target or setpoint the integral term would continue the action of the proportional term over time until the measurement reached the setpoint and the derivative term would compensate for lags in the action in the measurement in responding to actions of the manipulated variable. The classic equation is ... 

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