COMPENSATOR CONTINUED

The precise locations of the poles and zeros depend on both the desired characteristics of the closed loop response and the characteristics of the system being controlled. However, the pole and zero of the lag compensator should be close together so as not to cause the poles to shift right, which could cause instability or slow convergence. Since their purpose is to affect the low frequency behavior, they should be near the origin.

Both analog and digital control systems use lead-lag compensators. The technology used for the implementation is different in each case, but the underlying principles are the same. The transfer function is rearranged so that the output is expressed in terms of sums of terms involving the input, and integrals of the input and output. The reason for expressing the transfer function as an integral equation is that differentiating signals amplify the noise on the signal, since even very small amplitude noise has a high derivative if its frequency is high, while integrating a signal averages out the noise. This makes implementations in terms of integrators the most numerically stable.

ROBUST CONTROLLER

One particular approach to robust control controller design is the so-called sliding mode control methodology which is a particular type of Variable Structure Control System (VSCS). Variable Structure Control Systems are characterised by a suite of feedback control laws and a decision rule (termed the switching function) and can be regarded as a combination of subsystems where each subsystem has a fixed control structure and is valid for specified regions of system behaviour. The advantage is its ability to combine useful properties of each of the composite structures of the system. Furthermore, the system may be designed to possess new properties not present in any of the composite structures alone.

In sliding mode control, the VSCS is designed to drive and then constrain the system state to lie within a neighbourhood of the switching function. Its two main advantages are (1) the dynamic behaviour of the system may be tailored by the particular choice of switching function, and (2) the closed-loop response becomes totally insensitive to a particular class of uncertainty. Also, the ability to specify performance directly makes sliding mode control attractive from the design perspective.

PID CONTROLLER

Proportional-Integral-Derivative (PID) control is the most common control algorithm used in industry and has been universally accepted in industrial control. As the name suggests, PID algorithm consists of three basic coefficients; proportional, integral and derivative which are varied to get optimal response.

ProportionalResponse:

The proportional component depends only on the difference between the set point and the process variable. This difference is referred to as the Error term. The proportional gain (Kc) determines the ratio of output response to the error signal. For instance, if the error term has a magnitude of 10, a proportional gain of 5 would produce a proportional response of 50. In general, increasing the proportional gain will increase the speed of the control system response. However, if the proportional gain is too large, the process variable will begin to oscillate. If Kc is increased further, the oscillations will become larger and the system will become unstable and may even oscillate out of control.

LEAD LAG COMPENSATORS

Lead–lag compensators influence disciplines as varied as robotics, satellite control, automobile diagnostics, laser frequency stabilization, and many more. They are an important building block in analog control systems, and can also be used in digital control. Both lead compensators and lag compensators introduce a pole–zero pair into the open loop transfer function. The pole and zero are both typically negative. In a lead compensator, the pole is left of the zero in the complex plane, while in a lag compensator .

A lead-lag compensator consists of a lead compensator cascaded with a lag compensator.  The lead compensator provides phase lead at high frequencies. This shifts the poles to the left, which enhances the responsiveness and stability of the system. The lag compensator provides phase lag at low frequencies which reduces the steady state error. 

COMPARITIVE REPORT

Experimental comparison between a sliding mode controller and a classical controller for stabilizing and commanding a single-axis magnetic levitation system was investigated in this project. In general, the performance of the sliding mode controller was superior to the classical controller. The strategic importance of magnetic levitation systems is being rejuvenated. and we believe recent developments in robust and nonlinear control methods can be utilized to provide better performance than that afforded by traditional control methodologies. Out of all the three controllers designed, the phase lead controller and PID controller have turned out to be very sensitive to external disturbances. Any slight disturbance to the object will push the system to unstable state. Thus the position of equilibrium is a point. The sliding mode controller has a whole surface as its equilibrium region. It is for sure that this will give a better result than the other two. We conclude that sliding mode controller is the most robust and advantageous of all.

Using a reference detector and a signal detector separately will also lead to avoiding the change in the ambient light in the room where the kit is placed. Being a research topic, we found it so interesting and equally challenging to learn and implement the concepts. As a future scope of this project, we are planning to research on sliding mode controller and implement it. We are also having an idea of building a senseless magnetic levitation kit. We are also working on making the kit even more compact. There is a lot more areas to be explored in this topic of magnetic levitation, which we think will be even more interesting. We are very happy that this project has given us a good experience and made us learn a lot of new things.

SLIDING MODE CONTROLLER

Sliding mode techniques are one approach to solving control problems and are an area of increasing interest. This text provides the reader with an introduction to the sliding mode control area and then goes on to develop the theoretical results. Fully worked design examples which can be used as tutorial material are included. Industrial case studies, which present the results of sliding mode controller implementations, and are used to illustrate successful practical applications of the theory. In the formulation of any control problem there will typically be discrepancies between the actual plant and the mathematical model developed for controller design. This mismatch may be due to any number of factors and it is the engineer's role to ensure the required performance levels exist despite the existence of plant/model mismatches. This has led to the development of so-called robust control methods.

INTEGRAL AND DERIVATIVE RESPONSE

Integral Response

The integral component sums the error term over time. The result is that even a small error term will cause the integral component to increase slowly. The integral response will continually increase over time unless the error is zero, so the effect is to drive the Steady-State error to zero. Steady-State error is the final difference between the process variable and set point.

Derivative Response

The derivative component causes the output to decrease if the process variable is increasing rapidly. The derivative response is proportional to the rate of change of the process variable. Increasing the derivative time (Td) parameter will cause the control system to react more strongly to changes in the error term and will increase the speed of the overall control system response. Most practical control systems use very small derivative time (Td), because the Derivative Response is highly sensitive to noise in the process variable signal. If the sensor feedback signal is noisy or if the control loop rate is too slow, the derivative response can make the control system unstable.

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