Design of hinfinity controller The main objective is the design of hinfinity speed controller K which attains stabilization of closed loop system with guaranteed performance. The infinity norm of the system G s exists if and only if G s is proper with no poles on the imaginary axis. Let a linear time invariant LTI system be represented by P, controller by K, control input by u and measured output by y. Reference commands, load disturbances, and sensor noise are represented by w, and tracking errors, performance variables, and actuator signals are represented by z [29].
Figure 4 shows the H-infinity control problem which indicates that the controller should be able to achieve a robust output in the presence of disturbances. Figure 4. Frequency domain loop shaping is attained by proper weights selection.
By selecting proper weights W1 for error signal e, W2 for control signal u and W3 for output signal y the solution of H infinity control problem can be achieved. Figure 5 shows the augmented state space representation of plant G with weights. Figure 5. Selection of weight filters A proper design of controller involves the suitable choice of weight filters. A simple low pass filter has been selected for W1. The low frequency gain of the low pass filter has been chosen for limiting overshoot.
As recommended by Christiansson and Lennartson [32] the other weights have been chosen as constants so that the order of the controller is made low. The choice of weights depends on the the coefficients of W1, W2, and W3.
The selection of coefficients is considered as an optimization problem and PSO has been used for this purpose. Steps involved in particle swarrm optimization of weight coefficients PSO is an optimization algorithm in which best solution is searched in every iteration thereby converges at a faster rate when compared with other optimization techniques.
The progression of algorithm is discussed in the following steps [34]. Figure 6 shows the basic block diagram of the hardware setup.
The functional block diagram of the experimental setup for the motor performance analysis on load is depicted in Figure 7. The phase voltages are sensed and the corresponding line voltages and the difference between them are calculated. The hall sensor signals are emulated from the zero crossing instants of back emf.
Figure 8 shows the convergence plot of PSO. Functional block diagram The transfer function of synthesized controller is given by Convergence plot of PSO Figure 9 shows the bode plot of controller.
The gain margin is The BLDC motor performance under loaded condition has been analyzed experimentally by a motor generator setup. The motor which acts as generator is loaded by delta connected resistors of 47 ohms, 10 W in each arm. The performance of the motor has been studied while starting, by suddenly applying the load with a DPST for duration of 10 seconds and removing the load after 10 seconds. Figure 9. Bode plot Figure Hardware immplementation Implementation of speed control of sensorless brushless DC motor drive using H-infinity … K.
Figure 11 shows the reference tracking with PI controller and Figure 12 shows that of prposed controller. From these two figures it is clear that proposed controller shows better reference tracking than PI controller. The controller parameters such as percentage overshoot, steady state error and settiling time are compared and tabulated in Table 1. Figure Reference tracking waveform with PI Figure A comparison has been made with PI and proposed controller strategy and the results are tabulated in Table 2 and Table 3.
From the results it can be inferred that H infinity controller with its weights optimized by PSO shows a reduction of 1. Also there is a reduction of settling time by 0. Thus the proposed controller strategy exhibits a better performance during disturbances in load. The current waveforms during the application and removal of load are shown in Figure The ripples in current waveform with the proposed control strategy are found to be less when compared with PI controller.
This results in less torque ripples thereby resulting in smoother operation of motor. The motor is loaded by coupling another BLDC motor which acts as a generator. A comparative study of the proposed and PI controller is conducted and results are tabulated. The performance parameters such as peak time, settling time, percentage overshoot and steady state error of both the controllers are studied.
The results show that the proposed controller strategy exhibits a robust performance in the presence of load disturbances. Assawinchaichote, and N. Soliman, E. Orman, K. Can, A. Lee, K. Kim, J. Lee, D. Lee, and K. Ko, J. Lee, S. Chung, and M. Ohishi, K. Ohnishi, K. Taniguchi, and M. Mozaffari Niapour, M. Tabarraie, and M. Venkat, and G. Mousmi, A. Abbou, and Y. Ramesh, G. Rao, J. Amarnath, S. Kamakshaiah, and B. Voultoury, and J.
Akin, and M. Srinivasan, and R. Shanmugam, and M. C motors, are indispensable controlling elements in automation systems. Depending on the applications, some of them are fixed speed and some of the variable speed drives. The variable speed drives, till a couple of decades back, had various limitations, such as poor efficiencies, larger space, lower speeds, etc. Direct currents DC motors have been used in variable speed drives for a long time. The versatile characteristics of dc motors can provide high starting torques which is required for traction drives.
Control over a wide speed range, both below and above the rated speed can be very easily achieved. The methods of speed control are simpler and less expensive than those of alternating current motors. There are different techniques available for the speed control of DC motors. The phase control method is widely adopted in which ac to dc converters are used to supply the dc motors, but has certain limitations mainly it generates harmonics on the power line and it also has poor p.
The second method is pwm technique, which has got better advantages over the phase control. In our proposed project, a 5 H. The pulse width modulation can be achieved in several ways.
By varying resistor pot only we can control the speed of motor states that simple and easy method. The project proposed is a real time working project, and this can be further improvised by using more no. This concept of speed control or adjustment should not be taken to include the natural change in speed which occurs due to change in the load on the shaft. Any given piece of industrial equipment may have its speed change or Adjusted mechanically by means of stepped pulleys, sets of change gears, variable speed friction clutch mechanism and other mechanical devices.
Historically it is proved to be the first step in transition from non adjustable speed to adjustable speed drive. The electrical speed control has many economical as well as engineering advantages over mechanical speed control The nature of the speed control requirement for an industrial drive depends upon its type. Some drives may require continues variation of speed for the whole of the range from zero to full speed or over a portion of this range , while the others may require two or more fixed speeds 1.
Field windings connections for the three types Of DC motors have been shown in fig. Hence, name flux or field control method. The flux of DC motor can be changed by changing with help of a shunt field rheostat.
Since in relatively small, shunt field rheostat has to carry only a small, so that rheostat is small in size. The connection diagram for this type of speed control is shown in fig1. Field rheostat V Fig. As the supply voltage is normally constant, the voltage across the armature is varied by inserting a variable rheostat or controller resistance in series with the armature circuit as shown in fig1.
For a load of constant torque, speed is approximately proportional to the potential difference. Across the armature current characteristics in fig. This method is very wasteful, expensive and unsuitable for rapidly changing loads because for a given value of Rt, speed will change with load.
A more stable operation can be obtained by using a diverter across the armature in addition to armature control resistance. Now, the changes in armature current will not be so effective in changing the potential difference across the armature.
The connection diagram for this type of speed control arrangement is shown in fig. The armature will be approximately proportional to these different voltages.
The intermediate speeds can be obtained by adjusting the shunt field regulator. The field of the motor M1 is permanently connected across the DC supply lines whose speed control can be done. The other motor M2 is directly connected to Generator G. The voltage of generator can be varied from zero to upto its maximum value by means of field regulator. It should be remembered that motor set always runs in the same direction. The addition of a flywheel whose function is to reduce fluctuations in the Power demand from the supply circuit.
The chief advantage of system is its overall efficiency especially at right loads. It has the outstanding merit of giving wide speed Control from maximum in one direction through zero to the maximum in the opposite direction and of giving a smooth acceleration. In view of this, the demand for dc motors would continue undiminished even in figure. A brief discussion regarding the dc motor applications is given below. Speed of the shunt motors may be regulated in two ways: first, by inserting resistance in series with the armature, thus decreasing speed: and second, by inserting resistance in the field circuit, the speed will vary with each change in load: in the latter, the speed is practically constant for any setting of the controller.
This latter is the most generally used for between synchronous motors and dc shunt motors. It is because the construction of high performance poly phase induction motor with large number of poles is difficult. The decreasing speed with increase in load torque or vice versa has only a marginal effect on the power taken by the series motor. However for traction purposes , series motor is the only choice.
Therefore series motors are widely used in all types of electric vehicles, eletrictrains, streetcars, battery powered tools, automotive starter motors etc. With the increase in the load speed of the machine decreases. DC shunt motor maintains almost constant speed from no load to full load.. Therefore such type of compound motors are used for loads requiring heavy starting torque which are likely to be reduced to zero A compound motor with weak series field has its characteristics approaching that of a shunt motor.
Weak series field causes more drooping speed torque characteristics than with an ordinary shunt motors. Such compound motors with steeper characteristics, are used where load fluctuates between wide limits intermittently. They are also used in feedback and the freewheeling functions of converters and snubbers.
Fig 2. In the forward biased condition, the diode can be represented by a junction offset drop and a series-equivalent resistance that gives a positive slope in the V-I characteristics.
The typical forward conduction drop is 1. This drop will cause conduction loss, and the device must be cooled by the appropriate heat sink to limit the junction temperature. In the reverse-biased condition, a small leakage current flows due to minority carriers, which gradually increase with voltage. If the reverse voltage exceeds a threshold value, called the breakdown voltage, the device goes through avalanche breakdown, which is when reverse current becomes large and the diode is destroyed by heating due to large power dissipation in the junction.
The modern era of solid- state power electronics started due to the introduction of this device in the late s. Basically, it is a trigger into conduction device that can be turned on by positive gate current pulse but once the device is on, a negative gate pulse cannot turn it off. The thyristors have been widely used in dc and ac drives, lighting, heating and welding control. The dc current gain of a power transistor is low and varies widely with collector current and temperature.
The gain is increased to a high value in the Darlington connection, as shown in Fig2. The shunt resistances and diode in the base-emitter circuit help to reduce collector leakage current and establish base bias voltages.
A transistor can block voltage in the forward direction only asymmetric blocking. The feedback diode, as shown, is an essential element for chopper and voltage-fed converter applications. Double or triple Darlington transistors are available in module form with matched parallel devices for higher power rating. Power transistors have an important property known as the second breakdown effect. This is in contrast to the avalanche breakdown effect of a junction, which is also known as first breakdown effect.
When the collector current is switched on by the base drive, it tends to crowd on the base-emitter junction periphery, thus constricting the collector current in a narrow area of the reverse-biased collector junction.
This tends to create a hot spot and the junction fails by thermal runaway, which is known as second breakdown.
The rise in junction temperature at the hot spot accentuates the current concentration owing to the negative temperature coefficient of the drop, and this regeneration effect causes collapse of the collector voltage, thus destroying the device.
Two stage Darlington transistor with bypass diode 2. If the gate voltage is positive and beyond a threshold value, an N-type conducting channel will be induced that will permit current flow by majority carrier electrons between the drain and the source. Although the gate impedance is extremely high at steady state, the effective gate-source capacitance will demand a pulse current during turn-on and turn-off. The device has asymmetric voltage- blocking capability, and has an integral body diode, as shown, which can carry full current in the reverse direction.
The diode is characterized by slow recovery and is often bypassed by an external fast-recovery diode in high-frequency applications.
Many designers view IGBT as a device with MOS input characteristics and bipolar output characteristic that is a voltage-controlled bipolar device. It combines the best attributes of both to achieve optimal device characteristics. The IGBT is suitable for many applications in power electronics, especially in Pulse Width Modulated PWM servo and three-phase drives requiring high dynamic range control and low noise.
IGBT improves dynamic performance and efficiency and reduced the level of audible noise. It is equally suitable in resonant-mode converter circuits. Optimized IGBT is available for both low conduction loss and low switching loss. It has a very low on-state voltage drop due to conductivity modulation and has superior on-state current density.
So smaller chip size is possible and the cost can be reduced. Low driving power and a simple drive circuit due to the input MOS gate structure. It can be easily controlled as compared to current controlled devices thyristor, BJT in high voltage and high current applications. Wide SOA. It has superior current conduction capability compared with the bipolar transistor.
It also has excellent forward and reverse blocking capabilities. The collector current tailing due to the minority carrier causes the turnoff speed to be slow. There is a possibility of latchup due to the internal PNPN thyristor structure.
The IGBT is suitable for scaling up the blocking voltage capability. In case of Power MOSFET, the on-resistance increases sharply with the breakdown voltage due to an increase in the resistively and thickness of the drift region required to support the high operating voltage. In contrast, for the IGBT, the drift region resistance is drastically reduced by the high concentration of injected minority carriers during on-state current conduction.
The forward drop from the drift region becomes dependent upon its thickness and independent of its original resistivity. Thus by varying the pulse-width, we can vary the average voltage across a DC motor and hence its speed. Ymax The circuit of a simple speed controller for a mini DC motor, such as that used in tape recorders and toys, is shown in Fig2. The heat dissipation problem often results in large heat sinks and sometimes forced cooling.
PWM amplifiers greatly reduce this problem because of their much higher power conversion efficiency. The PWM power amplifier is not without disadvantages. The desired signal is not translated to a voltage amplitude but rather the time duration or duty cycle of a pulse. This is obviously not a linear operation.
But with a few assumptions, which are usually valid in motor control, the PWM may be approximated as being linear i. The linear model of the PWM amplifier is based on the average voltage being equal to the integral of the voltage waveform. The duty cycle must be recalculated at each sampling time. Pulse width modulation technique PWM is a technique for speed control which can overcome the problem of poor starting performance of a motor. PWM for motor speed control works in a very similar way.
Instead of supplying a varying voltage to a motor, it is supplied with a fixed voltage value such as 12v which starts it spinning immediately. The wave forms in the below figure to explain the way in which this method of control operates. In each case the signal has maximum and minimum voltages of 12v and 0v.
By varying the mark space ratio of the signal over the full range, it is possible to obtain any desired average output voltage from 0v to12v. The motor will work perfectly well, provided that the frequency of the pulsed signal is set correctly, a suitable frequency being 30Hz. Pulse Width Modulation Waveforms 2. Block Diagram of an Analogue PWM Generator The simplest way to generate a PWM signal is the intersective method, which requires only a saw tooth or a triangle wave form easily generated using a simple oscillator and a comparator.
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