Design and Simulation of Voltage Amplidyne System using Robust Control Technique

In this paper, modelling designing and simulation of a simple voltage amplidyne system is done using robust control theory. In order to increase the performance of the voltage amplidyne system with H optimal control synthesis and H optimal control synthesis via-iteration controllers are used. The open loop response of the voltage amplidyne system shows that the system can amplify the input 7 times. Comparison of the voltage amplidyne system with H optimal control synthesis and H optimal control synthesis via-iteration controllers to track a desired step input have been done. Finally, the comparative simulation results prove the effectiveness of the proposed voltage amplidyne system with H optimal control synthesis controller in improving the percentage overshoot and the settling time.


1.
Introduction An amplidyne is an electromechanical amplifier invented prior to World War II by Ernst Alexanderson. It consists of an electric powered motor riding a DC generator. The signal to be amplified is carried out to the generator's field winding, and its output voltage is an amplified reproduction of the field current. The amplidyne is used in enterprise in excessive power servo and manage systems, to increase low power manage signals to control powerful electric powered motors. An amplidyne incorporates an electric powered motor which turns a generator on the identical shaft. Unlike an ordinary motor-generator, the cause of an amplidyne isn't always to generate a consistent voltage but to generate a voltage proportional to an Input current, to modify the input. The motor affords the power, turning the generator at a constant velocity, and the signal to be amplified is applied to the generator's field winding.

2.
Mathematical Modelling of the system

Figure 1 Voltage amplidyne system
The Motor Side Assume The stator current is constant therefore the magnetic flux is constant The motor torque is proportional to the armature current and the flux The voltage vb is proportional to the angular speed of the motor Applying KVL to the motor circuit The field current is constant therefore the flux is constant The generated voltage is proportional to the angular speed, flux and field current Substituting Equation (10) in to Equation (12) yields: The transfer function between the input angular speed and the output current is The transfer function between the input motor voltages to the output load voltage is found by combining Equation (9) The parameters of the system is shown in Table 1 below.

The Proposed Controllers Design2 3.1 H  Optimal Control Synthesis Controller Design
H  optimal control synthesis solve the smallgain infinity-norm robust control problem; i.e., find a stabilizing controller F (s) for a system P (s) such that the closed-loop transfer function satisfies the infinitynorm inequality.
The block diagram of the system with H  optimal control synthesis controller is shown in Figure  2 below Figure 2 Block diagram of the system with H  optimal control synthesis controller An important use of the infinity-norm control theory is for direct shaping of closed-loop singular value Bode plots of control systems. In such cases, the system P (s) will typically be the plant augmented with suitable loop-shaping filters.
The H  optimal control synthesis controller transfer function is  

H fOptimal Control Synthesis via iteration Controller Design
H  optimal control synthesis via -iteration compute the optimal Hcontroller using the loopshifting two-Riccati formulae. The output is the optimal " " for which the cost function can achieve  under a preset tolerance.
    The search of optimal stops whenever the  relative error between two adjacent stable  solutions is less than the tolerance specified. For most practical purposes, the tolerance can be set at 0.01 or 0.001. The block diagram of the system with H  optimal control synthesis via -iteration controller is shown in Figure 3 below  The simulation result shows that the amplidyne output voltage is 210 volt which amplifies the voltage 7 times.

Comparison of the Proposed Controllers for Tracking a Desired Step Amplidyne Voltage
The Simulink model of the voltage amplidyne system with H  optimal control synthesis and H  optimal control synthesis via -iteration controllers are shown in Figure 6 below Figure 6 Simulink model of the voltage amplidyne system with H  optimal control synthesis and H  optimal control synthesis via -iteration controllers The simulation result of the voltage amplidyne system with H  optimal control synthesis and H  optimal control synthesis via -iteration controllers for tracking a desired step (from 0 to 220 V) input is shown in Figure 7 below.

Figure 7 Simulation result
The performance data of the rise time, percentage overshoot, settling time and peak value is shown in Table 2.

Conclusion
In this paper, a simple voltage amplidyne system is designed using a DC motor generator combination.
In order to improve the performance of the system, a robust control technique with H  optimal control synthesis and H  optimal control synthesis via -iteration controllers are used. The open loop response of the system shows that a 7 time's amplification voltage is gained. The comparison of the proposed controllers is done to track a desired step amplified voltage and the results proves that the system with H  optimal control synthesis controller improves the settling time and the percentage overshoot than the system with H  optimal control synthesis via iteration controller.