^{1}

The gas turbine is a power plant, which produces a great amount of energy for its size and weight. Its compactness, low weigh, and multiple fuels make it a natural power plant for various industries such as power generation or oil and gas process plants. In any of these applications, the performance and stability of the gas turbines are the end products that strongly influence the profitability of the business that employs them. Control and analyses of gas turbines for achieving stability and good performance are important so that they have to operate for prolong period. Effective control system design usually benefits from an accurate dynamic model of the plant. Characteristic component parts of the system are considered in this model. Gas turbine system is described by specified thermodynamic equations that can be used for defining its model. This paper introduces an optimal LQG/LTR control method for a gas turbine. Analysing the gas turbine dynamic in time and frequency domain by using proposed control compared to PID controller is followed. Applying this optimal control method can provide good performance and stability for the component parts of system.

The object of a control system is to make the outputs behave in a desired way by manipulating the plant inputs [

In some practical circumstances, the dynamics of controlled plant may not be exactly modeled, and there may be system disturbances and measurement noises in the plant. The LQG/LTR controller can provide good performance and guaranteed stability in the face of such noises [

The system to be investigated is a gas turbine. Various approaches such as Fuzzy [

Next sections are concerned with a general description of the gas turbine system, definition of its model, LQG/LTR method, and introducing state space model and simulation results. Matlab mfile commands are used for this idea. PID (Proportional Integrated Derivative) control [

Gas turbines are designed for many different purposes. In the petroleum industry, they are commonly used to drive compressors for transporting gas through pipelines or generators that produce electrical power. The gas turbine is a constant flow cycle with a constant addition of heat energy. It is commonly referred to as the Brayton cycle [

The design of any gas turbine must meet essential criteria based on operational considerations such as high efficiency, high reliability and thus high availability, ease of service, ease of installation and commission, flexibility to meet various service and fuel needs, conformance with environmental standards, and auxiliary and control systems. The two factors, which most effect high turbine efficiencies, are pressure ratios and temperature. High-pressure ratios and turbine inlet temperatures improve efficiencies on the simple cycle gas turbine. It should also be noted that the very high-pressure ratios tend to reduce the operating range of the turbine compressor [

Auxiliary systems and control systems must be designed carefully, since they are often responsible for the downtime in many units. Control systems provide acceleration time and temperature time controls for startups as well as control various antisurge valves. At operating speeds they must regulate fuel supply and monitor vibrations, temperatures, and pressures throughout the entire range [

Gas turbine system is described by nonlinear mathematical equations that used thermodynamic principle rules such as conservation of total mass, energy, and ideal gas equation [

Nonlinear state equations of gas turbine system in [

The compressor pressure ^{2}),

Other parameters state by specific nonlinear dynamic equations same as these at [

The state space model of gas turbine is defined with 5 inputs as

The system dynamic equations can be expressed as follows

Linear quadratic Gaussian or LQG problem is a method based on optimal control theory. The main results of this theory are stated in this section. But fuller details can be referred to [

Suppose the plant is generally described by the dynamic equations in the form of state-space representation as follows:

The solution to the LQG problem is prescribed by the seperation principle, which states that the optimal result is achieved by adopting the following procedure. First obtain an optimal estimate

The solution to the first subproblem that of estimating the state is given by Kalman filter theory. Figure

The Kalman filter.

The second subproblem is to find the control signal which will minimize the cost:

By substitute (

From Figure

The equation of the combined Kalman filter-optimal state feedback scheme is

Since both the optimal state feedback regulator and the Kalman filter have such good properties, it might be expected that LQG compensator would generally yield good robustness and performance. Unfortunately, this is not the case and the LQG designs can exhibit arbitrarily poor stability margins [

The LQG loop transfer function can be made to approach filter transfer function with its guaranteed stability margins if

The state space detailed model of gas turbine at a given operation point helps to understand the dynamic behavior of system. A nonlinear model can capture the dynamic behavior of gas turbine system [

The MS5002D mechanical drive gas turbine is used to drive a centrifugal load compressor to compress treated gas and deliver export gas at 90 bar pressure for export via pipeline. The gas turbine is that part of the mechanical drive gas turbine, exclusive of control and protection devices, in which fuel and air are processed to produce shaft horsepower. Gas turbine axial air compressor has 17 stages with 10.75 : 1 pressure ratio. The output shaft speed is 4670 rpm with 32.5 MW output power. Combustion section has 12 multiple combustors with reverse flow type.

Control of the gas turbine in providing the shaft horse power required by the operation or process is accomplished using parameters such as fuel flow, compressor inlet pressure, compressor discharge pressure, shaft speed, compressor inlet temperature, and turbine inlet or exhaust temperature [

The SPPEDTRONIC MARK VI turbine control is the current state of the art control for General Electric turbine. It contains a number of control protection and sequencing systems designed for reliable and safe operation of the gas turbine [

Control of the turbine is done mainly by startup, speed, acceleration, synchronization, and temperature control. Figure

Simplified control schematic.

Operating conditions of the turbine are sensed and utilized as feedback signals to the SPEEDTRONIC control system. There are three major control loops—startup, speed, and temperature, which may be in control during turbine operation. These loops command fuel stroke reference (FSR), the command signal for fuel. The outputs of these control loops are connected to a minimum value select algorithm as shown in Figure

Matlab mfile commands used for simulating gas turbine system [

The gain matrix of state feedback controller

where

Analysis the gas turbine dynamic in time and frequency domain by using LQG/LTR control method and with compare to PID controller is flowed. Step response, impulse response and principal gain consider for simulation. Figure

Step response of the compressor pressure (a), turbine temperature (b), and rotational speed (c) respect to compressor mass flow rate.

Step response of the compressor pressure (a), turbine temperature (b), and rotational speed (c) respect to compressor mass flow rate for LQG/LTR and PID control.

Simulation results for rotational speed and turbine temperature by using impulse function as input to

Impulse response of the rotational speed (a) and turbine temperature (b) respect to power.

Impulse response of the turbine temperature respect to mass flow rate of compressor.

The structure singular value can be used to analyze the ability of a given design on achieves robust performance [

Singular value diagram of main system (a) and return ratio at input for LQG/LTR controlled system.

This paper introduces the gas turbine systems. Control and satisfactory performances are important concept for this system. By using thermodynamic equations, a nonlinear dynamic model is specified to study control objects. A gas turbine type is considered and its control system is described. Analyses the system is followed by making LTI state space model obtained of linearization nonlinear dynamic model and apply suggested LQG/LTR optimal control method. By LQG/LTR controller, and set parameters of this control by specified procedure, simulation results in time and frequency domain are achieved. To compare results, we use PID control method for described system model.

System analysis shows response of uncontrolled dynamics and effect of LQR, LQG, and LQG/LTR controller designed and PID control. LQG/LTR controller improved principal gain diagram to attain good performance. With LTR method a satisfactory return ratio is recovered at the plant input.

Settling times of system characteristic component parts by using LQG/LTR controller are shorter, and stability of system makes it better by applying this optimal control method.