Lab Manual: CE107 Engine Speed Control

Design of a Proportional Controller for Air Driven Engine

By: Anthony Docimo

Joseph Miller Matthew Grosse Timothy Priestly

Instructors:

Dr. Raul Ordonez Dr. Ravi P. Ramachandran

Dr. Stephanie Farrell

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Overview of the CE107 Engine Speed Controller The CE107 Engine Speed Control Apparatus demonstrates the problems encountered in regulating the speed of rotating machines under varying load conditions, in particular, problems with non-linear control systems. Some typical examples of such systems are:

¾ An electrical generator being driven by a prime mover. In the case of the generator, a prime mover such as an internal combustion engine or turbine, provide the input energy to be converted into the output electrical energy. To maintain certain output voltage or frequency levels from the generator under varying power loads, the prime mover speed must be kept within the specified limits. This is accomplished by varying the fuel to the prime mover as operating conditions change.

¾ The 'Cruise Control' on a motor vehicle. This device allows the user to select

a desired speed at the beginning of a long journey. A feedback control system overrides the manual accelerator setting to maintain the vehicle’s speed, irrespective of whether the road is level or inclined or declined.

The apparatus is designed for control and analysis using an external control element. The primary objective of the apparatus is to regulate the engine speed by manipulating the position of the motorized valve under varying load conditions. All power supplies to drive the system and sensor signal conditioning circuits are fully buffered and contained within the base of the CE107. The circuits are accessed via the 2mm sockets mounted on the front panel.

Figure 1: Front Panel of CE107 Engine Speed Control Apparatus

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The CE107 is composed of three individual systems, which are:

a. The Engine, Flywheel and Load Assembly b. The Air Supply c. The Motorized Valve

a. The Engine, Flywheel and Load Assembly The engine comprises a four-cylinder 2-stroke compressed air motor. Air has been chosen as the fuel (prime mover) for safety reasons. Each cylinder of the engine consists of a piston, a cylinder, a crank, a flywheel, and connecting rod. The cylinders are connected in tandem such that they effectively provide a single common shaft along which the output power is transmitted to the Main Flywheel and Generator.

Figure 2: Overview of Engine Air is provided to each cylinder by an inlet manifold located above the assembly. The four cylinders connected in tandem achieve the rotation, each offset by 90o, and this is done to ensure that there is a power stroke from each of the cylinders every 90o. The cylinders provide power strokes in the sequence 1-3-4-2. Although each cylinder is equipped with a small flywheel, an additional flywheel is connected to the shaft. The purpose of this flywheel is to increase the inertia of the system, and also to increase the time constant. The flywheel consists of a series of holes that are located around the perimeter of the flywheel. This is done so that as the engine shaft rotates the holes are detected by an

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optical sensor, which consists of a light emitting diode and phototransistor. As the flywheel spins and cuts the beam of the optical sensor it will cause a series of electrical pulses to be generated. The frequency of the generated pulses is proportional to the actual speed of the shaft. Internal conditioning circuits convert this frequency into an analogue signal voltage. The calibration is such that the speed range of 0-2500 RPM produces an analogue output voltage of 0 –10V at the Tachometer (ω) Output Socket mounted on the front panel. A permanent Magnet DC Generator is also mounted on the engine shaft. The purpose of this component is to apply a variable load to the engine. The Generator Load Control Socket inputs a DC signal in the range of 0-10V; this allows the load to be varied from no load to full l oad. This feature is useful to test the controller’s robustness to disturbances. b. The Air Supply Compressed air to the engine is supplied from an adjacent airline or compressor. The actual air inlet is via a Filter/ Pressure/ Regulator/ Lubrication Reservoir assembly located at the rear of the front panel. The pressure supplied to the Control Regulator is indicated by the Primary Pressure Gauge. The range is 0-7 bar (0-100 psi). c. The Motorized Air Valve The pressure of the air stream supplied to the engine is controlled in the CE107 by a servo motor driven Control Pressure Regulator. The assembly consists of a pressure regulator, in which the screw adjustment of the control spring is driven through a gear system by an electric servomotor. The angular position of the screw is sensed using a multi -turn potentiometer. Internal circuitry conditions and calibrates the signal to produce an analogue signal in the range of +10V for fully open to –10V for fully closed. The voltage applied to the servomotor is proportional to the voltage at the Servo Motor Ampli fier input socket. If 0V are applied at the input, the motor will be stationary. A positive voltage applied opens the valve, while a negative voltage will close the valve. Overview of Input/ Output Signals Input

¾ Generator Load Control 8 Inputs a DC signal in the range of 0-10V

¾ Valve motor Ampli fier

8 0V at the input, the motor will be stationary 8 + voltage opens the valve 8 - voltage closes the valve

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Output

¾ Air valve position (θ) 8 + 10 Volts for fully open 8 -10 Volts for fully closed

¾ Tachometer Output (ω)

8 Calibration is such that a speed range of 0-2500 RPM produces an analogue output of 0-10V

Also there is a connection for a ground terminal. Theory: Air Supply Valve: Modeling We will begin by examining the valve that is used to supply air to the system. The valve input operates an electric motor, which turns at a rate proportional to the input voltage. The equation modeling the dynamics of the system is given by:

ugdt

dx1=

where x is the valve position, u is the input voltage, and g1 is the drive valve motor gain. This system works by having the valve position adjust the tension F on a control spring, which in turn acts upon a diaphragm in the valve. If the tension is increased, then additional air flows through an inlet and through the main valve. This allows the outlet pressure on the valve to increase. The outlet pressure Po, exerts an opposite force on the diaphragm which acts against the input tension. When the control spring tension and outlet are in equilibrium the airflow through the valve stabilizes. Engine and Load: Modeling The air from the valve applies a pressure Po to the engine piston. This applied force is transformed into an engine torque τe at the engine crankshaft. This means that the engine torque τe is proportional to the pressure supplied by the valve oee Pg=τ

where ge is the gain of the engine and crank assembly. The engine torque is used to supply engine load, friction losses and to accelerate the engine flywheel inertia I. Identifying the engine speed ω we can write the following equation:

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−

−

=

Torque

Frictional

Torque

Load

Torque

Engine

MomentumFlywheel

ofchangeofRate

_

___

or

fledt

dI τττω −−=

τf is proportional to the engine speed, τf = bω τl is proportional to the load demand voltage dl, τf = gldl Valve Position and Speed Sensor Characteristics There are two output variables; the valve position x and engine speed ω are measured by speed sensing circuits. The valve position sensor is a potentiometer, which gives a voltage yx proportional to the actual valve position. xky vx ⋅=

An opto-electric sensor and the perforations on the flywheel sense the engine speed. The pulses from the sensor are converted into a voltage yω, which is proportional to the engine speed. ωω ⋅= sky

Understanding the complete models of the systems we can represent the equations in the Laplace Domain. For the valve:

)()( 1 sus

Gsy x =

All valves are subjected to some static friction in the drive gear. This friction, which is referred to as stiction, requires that a certain initial voltage be applied to before the valve will begin to move. This gives rise to a non-linear gain characteristic for G1, with a dead band about zero. This concept can be seen in Figure 3.

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Figure 3: Non-Linear Gain Characteristic (Dead Band) For the engine:

)(1

)(1

)( 2 sdsT

Gsy

sT

Gsy l

lx +

−+

=ω

The constant G2 is the gain of the system, which is the output voltage over the input voltage. Here the input voltage will be the absolute value of the peak voltage of the step input, while the output voltage will be the absolute value of the peak voltage measured at the terminal (ω) of the motor. The value T is the pole of the system, which is obtained by analyzing the output voltage waveform from the step input. CE107 Block Diagram Development It was observed that there was a non-linear effect associated with the gain of the air valve motor. To reduce the effects of the non-linear gain we will implement the method

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of local feedback. The following figure illustrates the feedback loop with a gain k1 that is used to make the actual valve position yx correspond to the desired valve position yr.

Figure 4: Block Diagram of Motorized Valve Control From the block diagram shown it can be seen that if the signal u required to overcome the deadband is D, then the error to overcome the deadband will be given by:

1k

De =

Since we have a deadband that is constant, we can minimize the error greatly by choosing a large k1. Cascade Control Cascade control systems are widely used in industry control systems practice. The aim is to start with the inner most blocks of the system, place them under control and then work your way out to the next level of control.

K1 Air

Valve Engine Σ K2 Σ

e1(t) e2(t)

Master Controller

Slave Controller

re(t)

rv(t)

ye(t)

yv(t)

- - u(t)

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Figure 5: Overall Block Diagram of CE107 The engine speed control system is an example of a process in which we must first control the control the actuator (the air valve) before the system (the engine) can be controlled. The cascade control consists of an inner loop (slave control) which controls the valve position yx to a reference position yxr. The outer loop (master controller) controls the engine speed yω. The outer loop is termed the master control because it supplies the reference valve position, which the inner (slave) loop must follow. Approach: To determine the constants for the models of the system we must first develop a controller for the slave loop. The controller of the slave loop will be a simple proportional controller since the system to be controlled is a simple DC motor, which is a stable system. The gain for the proportional controller will be found by using the error formula stated in the theory section. To obtain the gain of the controller, one can divide the voltage level required to make the motor spin by the error. Once a controller for the slave loop is developed, one can begin by calculating the gain and poles of the engine. Because of the physical constraints in this system, frequency response methods are not suitable for system identifications, so we may identify a first order model of the engine by examining its step response. Note that to derive this model we will use the engine without load or disturbances. Having found a model of the system, design a controller for the system that will minimize error, using the method of your choice. Implementation: Once your controller has been designed you will now be able to implement into the software that was provided. You will begin by initializing a reference speed. The program will then obtain the actual speed and determine the error. The error then will alter the effect on the controller hopefully yielding the desired speed. This process will keep repeating. Figure 5 shows the overall flow diagram of the system. Refer to Figure 4 for signal names.

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(Lab 1: Understanding the CE107/120 and basic control theory.) Objective: To design a proportional controller for the air driven engine so that the speed of the output shaft remains constant regardless of varying pressure changes in the air inlet line. With no control the motor speed will increase as the manual air inlet pressure is increased. Our controller will be able to override any manual pressure change, similar to cruise control in a motor vehicle. Set up: Set up as seen in Fig. 6 CE 120: -Set gains in km and kp to 1 -Set the function generator to DC, offset to middle position, with level set

to approximately 2 volts CE 107: - With the Air ON/OFF valve in the off position, turn on main air to 80

psi. Procedure:

1. Connect main air line to motor. 2. Turn Primary Pressure Regulator knob completely counter clockwise. 3. Turn on Air ON/OFF valve on CE107 4. Turn Primary Pressure Regulator knob clockwise until the pressure reading is

approximately 70psi. 5. Redo with the different gains in kp and km and determine if the system oscillates to

reach steady state. Results:

kp km Oscillate (y/n) 1 1 2 2 3 3 6 6

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Using the following block diagram develop the transfer function for the system and explain why the system may or may not oscillate with higher gain sets.

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Fig 6

kp

km