Concepts

As we evolve, the demands of control methods grow. The modern control theory based on state space methods cannot meet those demands due to the fact that , it is very difficult to obtain the precise mathematical model of the processes (as they are non-linear, uncertain and time-varying in nature).

Predictive Control: To use a model to predict the future output of a process, achieve optimization and feedback correction.

General Predictor control strategies meet the demands to some extent but as the prediction algorithms are time consuming(reason: complex on-line computation), they are restricted to slow processes.

PFC (Predictive Function Control) has come up to cater to the demands of quick tracking control problems. It also follows the same principle of classical predictive control above.

Difference: In PFC, the structure of control variables is considered as a linear combination of a set of base functions. The control variables are obtained by evaluating the weight coefficients of the base functions' linear combination. The choice of base functions (generally step, ramp, parabola etc.) depends on the characteristics of the process and the desired set point. The key objective is the selection of base functions, predictive model, reference trajectory and coincidence points.

A conventional PID (proportional-integral-derivative) feedback controller will not work well in applications with long process deadtimes. Good control can be accomplished by employing the Smith Predictor control algorithm to address processes with significant transport delays or deadtimes.

Smith Predictor Control - It uses a process model to calculate predicted process change in response to a control action as if there is no deadtime. This change is added to the PID process variable so the controller is made to "believe" that the corrective action actually took effect immediately, and thus will not take additional action. With such a modification, the PID controller can be aggressively tuned so it can provide good control of its process variable.

PID Controller

Responds to an error signal in a closed control loop and attempts to adjust the controlled quantity to achieve the desired system response. Advantage of the PID controller is that it can be adjusted empirically by adjusting one or more gain values and observing the change in system response.
A digital PID controller is executed at a periodic sampling interval. It is assumed that the controller is executed frequently enough so that the system can be properly controlled.
Error signal is the difference between the desired setpoint and actual measured value of the controlled quantity. The sign of the error indicates the direction of change required by control input.

P term of the controller is formed by multiplying the error signaly by a P gain causing a controller response that is a function of the error magnitude. As error signal becomes larger, the P term becomes larges to provide more corrective action. The effect of P term tends to reduce the overall error as time elapses. P term effect reduces as the error approaches zero. In most cases, error gets very close to zero but does not converge. The result is a small steady state error.

I term is used to eliminate the small steady state errors. Running total of the error signal is computed and hence a small steady state error turns out to a large error over time. This accumulated error is multiplied by I gain to form the I term.

D term is used to enhance the speed of the controller. It responds to the rate of change of the error signal. Present error is subracted from the previous error and multiplied by a D gain factor and that becomes D term of the controller. Faster the change in error, D term produces more control output.

Faraday’s Law of Electromagnetic Induction:

This basic law, due to the genius of the great English chemist and physicist Michael Faraday (1791–1867), presents itself in two different forms:
1. A moving conductor cutting the lines of force (flux) of a constant magnetic field has a voltage induced in it.
2. A changing magnetic flux inside a loop made from a conductor material will induce a voltage in the loop.

In both instances the rate of change is the critical determinant of the resulting differential of potential.

Ampere-Biot-Savart’s Law of Electromagnetic Induced Forces

This basic law is attributed to the French physicists Andre Marie Ampere (1775–1836), Jean Baptiste Biot (1774–1862), and Victor Savart (1803–1862). In its simplest form this law can be seen as the “reverse” of Faraday’s law. While Faraday predicts a voltage induced in a conductor moving across a magnetic field, the Ampere-Biot-Savart law establishes that a force is generated on a currentcarrying conductor located in a magnetic field.

Lenz’s Law of Action and Reaction

Both Faraday’s law and Ampere-Biot-Savart’s law neatly come together in Lenz’s law written in 1835 by the Estonian-born physicist Heinrich Lenz (1804–1865).
Lenz’s law states that electromagnetic-induced currents and forces will try to cancel the originating cause.

For example, if a conductor is forced to move cutting lines of magnetic force, a voltage is induced in it (Faraday’s law). Now, if the conductors’ ends are closed together so that a current can flow, this induced current will produce (according to Ampere-Biot-Savart’s law) a force acting upon the conductor. What Lenz’s law states is that this force will act to oppose the movement of the conductor in its original direction.

Here in a nutshell is the explanation for the generating and motoring modes of operation of an electric rotating machine! This law explains why when a generator is loaded (more current flows in its windings cutting the magnetic field in the gap between rotor and stator), more force is required from the driving turbine to counteract the induced larger forces and keep supplying the larger load. Similarly Lenz’s law explains the increase in the supply current of a motor as its load increases.

Kalman Filter

The Kalman filter is a set of mathematical equations that provides an efficient computational (recursive) means to estimate the state of a process, in a way that minimizes the mean of the squared error.

The filter is very powerful in several aspects:
It supports estimations of past, present, and even future states, and it can do so even when the precise nature of the modeled system is unknown.