CHARACTERISTICS AND STABILITY OF OPEN LOOP AND CLOSED LOOP SYSTEMS1.Aim of the experimentIn this experiment sensitivity and stability which are important properties for both open and closed loop control systems are studied.How the stability and sensitivity are changed experimentally , how they give response to the open and feedback control systems are also determined.2.Control SystemsAcontrol systemis a device, or set of devices to manage, command, direct or regulate the behavior of other device(s) or system(s).Industrial control systemsare used in industrial production. The most known and important control systems are open loop control systems and closed loop control systems.2.1 Open Loop Control SystemAs we stated previously, an open-loop control system is controlled directly, and only, by an inputsignal.For example oven just heat the meat but it can not check the quality of the meat after heating process. The basic units of this type consist only of an amplifier and a motor. The amplifier receives a low-level input signal and amplifies it enough to drive the motor to perform the desired job.The open-loop control system is shown in basic block diagram form in figure 2-1. With this system,the input is a signal that is fed to the amplifier. The output of the amplifier is proportional to theamplitude of the input signal. The phase (ac system) and polarity (dc system) of the input signaldetermines the direction that the motor shaft will turn. After amplification, the input signal is fed to themotor, which moves the output shaft (load) in the direction that corresponds with the input signal. Themotor will not stop driving the output shaft until the input signal is reduced to zero or removed. This system usually requires an operator who controls speed and direction of movement of the output byvarying the input. The operator could be controlling the input by either a mechanical or an electrical linkage.

2.2 Closed Loop Control System

Using that diagram we can understand what the closed loop is .1- There is an input, u(t), to the system, which we assume starts from rest. In the block diagram, that is represented by U(s).2- The output of the system, Y(s), is measured with a sensor that has a transfer function Ks. That transfer function could have a time constant, etc., but for now we will examine it as though it is a constant.3- There is an error, E(s), developed, particularly because the controlled system, G(s), cannot respond immediately and the feedback signal that is subtracted from the input to form the error is zero.4- The error that is developed acts through the proportional controller, Kp, to start to move the output of the system to where we want it to be.5- As the system continues to operate, the output of the system (described by G(s)) rises, reducing the error so that the control effort from the proportional controller gets smaller.6- Even though the error gets smaller, if the gain of the proportional controller is large it will still provide enough output to drive the system close to where we want it to be.This kind of system is referred to as aclosed loop system, since there is a feedback signal that "closes the loop" in the system.2.3 Sensitivity of Control Systems to Parameter VariationsConsider first the system with unity feedback represented in Figure 4.7a.

Assume that the open-loop transfer function H(s) is represented by the ratio of two polynomials, that is, H(s)=N(s)/D(s) . The zeros of D(s) represent theopen-loop system poles, and we say that the open-loop transfer function is stable if all the poles of H(s) are strictly in theleft half complex plane (none of them is on the imaginary axis).

The closed-loop transfer function of the feedback system in Figure 4.7a is

defines the characteristic equation of the closed-loop system with unity feedback.The zeros of the closed-loop characteristic equation represent the closed-loop systempoles. The open-loop characteristic equation is simply D(s) = 0 . Hence, the feedback changes the system characteristic equation and the system poles. It can happen that the open-loop system is unstable, but the closed-loop system is stable. it can happen that for all choices of the static element the closed-loop system remains unstable. In such cases, we should try to stabilize the system using a dynamic feedback element G(s). The corresponding closed-loop characteristic equation is given by

G(s) can be also chosen as a ratio of two polynomials. It should be pointed outthat system stabilization with a dynamic feedback element is more complicatedthan stabilization with a static feedback element.In summary,

which indicates that the relative change in the system output is proportional to therelative change in the system transfer function. The proportionality factor S(s)is called the system output sensitivity function. Due to the fact that |S(s)| = |1/(1+H(s))| < 1we can conclude that the impact of system parameter variations on the system output is relatively reduced by the factor of |S(s)| < 1 .For systems with non unity feedback, G(s) is not equal to 1 , we can follow the samederivations, and obtain the following form for the system output sensitivity function

2.4 Stability of Control SystemsThe system stability is a great problem in feedback system.But in open loop system it is not a problem so open loop system construction is easier than closed loop system.If we analyze the transfer functions of both systems we can easily see that K (Gain) value of open loop system does not change but in closed loop system it changes thats why we have problems about stability in closed loop systems.A feedback control system must be stable as a prerequisite for satisfactory control.Consequently, it is of considerable practical importance to be able to determine underwhich conditions a control system becomes unstable

Definition of stability

Before we proceed, we introduce the following definition for unconstrained linearsystems. Notice that the term unconstrained is used to refer to the ideal situation wherethere are no physical limits on the output variable.Definition of stability. An unconstrained linear system is said to be stable if the outputresponse is bounded for all bounded inputs. Otherwise, it is said to be unstable.Characteristic equationConsider the general block diagram, which is discussed in the previous chapter. Usingblock diagram algebra that was developed in the previous chapter, we obtain

The stability characteristics of the closed-loop response will be determined by the polesof the transfer functions GSP and GLoad. These poles are common for both transferfunctions (because they have common denominator) and are given by the solution of theequation1+G c G mG v Gp =0 is called the characteristic equation for the generalized feedback system.A feedback control system is stable if all the roots of its characteristic equation havenegative real parts (i.e. are to the left of the imaginary axis).If any root of the characteristic equation is on or to the right of the imaginary axis (i.e. ithas real part zero or positive), the feedback system is unstable. Figure 1 providesgraphical interpretation of this stability criterion. The qualitative effects of these roots onthe transient response of the closed-loop system are shown in Figure 2. The left portion of each part of this figure shows representative root locations in the complex plane. Thecorresponding figure on the right shows the contributions these poles make to the closedloop response to a step change in the set point. Similar responses would occur for a step change in load.

The root locations also provide an indication of how rapid the transient response willbe. A real root at s = p1 corresponds to a closed-loop time constant of 1 = 1/p1. Thus, real roots close to the imaginary axis result in slow responses. Similarly, complex roots near the imaginary axis correspond to slow response modes. The further the complex roots are away from the real axis, the more oscillatory the transient response will be.

Remarks

GOL= G c G mG v Gp is called open-loop transfer function because it relatesthe measurement indication ym to the set point if the feedback loop is broken just beforethe comparator G OL y sp = ymNote that the same characteristic equation occurs for both load and set-point changessince the term, 1+GOL, appears in the denominator of both terms in Equation (1). Thus, if the closed-loop system is stable for load disturbances, it will also be stable for set-pointchanges.

2.5 Closed-Loop versus Open-Loop Control SystemsClosed-loop control shows a closed-loop action (closed control loop); can counteract against disturbances (negative feedback); can become unstable, i.e.thecontrolled variable does not fade away, but grows (theoretically) to an infinite value.

Open-loop control shows an open-loop action (controlled chain); can only counteract againstdisturbances, for which it has been designed; other disturbances cannot be removed; cannot become unstable - as long as the controlled object is stable.The open and closed loop system describes the two primary types of CNC control systems. Open and closed loop describes the control process of a system. Open loop refers to a system where the communication between the controller system and the motor is one way. Check the image to the right. As you can see the process for a open loop system is simple. After the user decides what he/she wants to do and generates the g-code or some sort of work file, the NC software then create the necessary step and direction signals to perform the desired task. The computer relays this information to the controller which then energizes the motor/s. After the motor moves to the desired position, there is no feedback to the controller system to verify the action.In the CNC industry, open loop systems use stepper motors. However, just because a system uses stepper motors does not mean the system is an open loop system. Stepper motors may be outfitted with encoders to provide position feedback just like servo motors.

Stepper motors are able to operate in an open loop system while servo motors are not, for CNC applications at least. Because stepper motors do not require feedback hardware, the price for an open loop CNC system is much cheaper and simpler than a closed loop system. This makes it more affordable for hobbyists tobuild their own CNC machine.There are drawbacks to the open loop system. Because there is no feedback to the controller, if the motor does not operate as instructed there is no way for the system to know. The controller system will continue performing the next task as if there is no problem until a limit switch is tripped or the operator resets the machine.

Many do it yourselfers run into trouble by overloading their machine and losing steps with the open loop system. This can ruin the piece or be harmful to the machine or user. However, if the system is constructed properly and not overloaded, there is no reason an open loop system should not function properly.

3. Construction of the Experiments3.1 Open Loop Construct of DC Motor Position

Part a and b) Here maximum value of potentiometer is always 180 degree. As an input and output voltage values are r,y respectively.Amp #1

Gain 1Gain 10Gain 100

LEFT HAND SIDEVout = - 4.89vVout = 4.83vVout = - 5.05v

Vin = - 0.46Vin = - 0.02vVin = 0.12v

RIGHT HAND SIDEVout = 4.95vVout = - 4.88vVout = 4.98v

Vin = 0.44vVin = 0.03vVin = - 0.13v

Part C )We also found for the gain = 1.So I noted it here.GAIN 1GAIN 10GAIN 50GAIN 100

Angle = 60 degreeShaft did not give any response.I mean it did not move.If we change the shaft by hand t changes (+,-)10 degreeIt always moved.Continous motion.It always moved.Continous motion.But here it is faster than gain = 50s.

Vout = 1.97 vVout = 1.51 vVout = 1.92 vVout = 1.93 v

Angle = - 60 degreeShaft did not give any response.I mean it did not move.If we change the shaft by hand t changes (+,-)30 degreeIt always moved.Continous motion.It always moved.Continous motion.But here it is faster than gain = 50s.

Vout = - 1.71 vVout = - 1.73 vVout = - 1.78 vVout = - 1.73 v

Answer the following questions:Motor position did not reach to the zero degree from the 60 degree.Because in open loop systems control mechanism does not check the input values and does not correct them.If there is disturbances there is no correction.If there are disturbances in the system closed loop usage gives more advantage.So motor position is not corrected and did not come back to zero degree.Due to former information we learnt in lecture we can easily determine that this is the expected result.3.2 Closed Loop Construct of DC Motor Position

Part a and b) Gain = 1Gain = 10Gain = 100

RightVout = 3.68v 120 degreeVout = 4.71v155 degreeVout = 4.83v160 degree

Vin = 5vVin =5vVin = 4.84v

LeftVout = - 1.7v290 degreeVout = - 4.80v185 degreeVout = -4.9v182 degree

Vin = - 5vVin = - 5vVin = -4.95v

Part c)

GAIN 10GAIN 50GAIN 100

Angle = 60 degreeIf we change the shaft by hand t comes back to zero degree.If we change the shaft by hand t comes back to zero degree.But faster than gain = 1.If we change the shaft by hand t comes back to zero degree.But faster than gain = 10.

Vout = 1.82 vVout = 1.79 vVout = 1.81 v

Angle = - 60 degreeIf we change the shaft by hand t comes back to zero degree.If we change the shaft by hand t comes back to zero degree.But faster than gain = 1.If we change the shaft by hand t comes back to zero degree.But faster than gain = 10.

Vout = - 1.54 vVout = - 1.58 vVout = - 1.52 v

Answer the following questions:The rotating shaft had never been changed or small changes were occured but we did not note them. Feed back mechanism decreases the voltage error and stabilize the system and if we increase the gain rotating shaft gets more stable which means that its position does not change easily by hand.We expect this situation because we inserted the feed back mechanism into the system to sum the error and the system became more stable.

Deadband

Gain 185 Degree

Gain 100100Degree

Gain 505Degree

TF = Cxinverse of (SI-A)xB+DFrom this we can easily calculate the transfer function of the DC motor.TF= 3.5/(0.196xSxS)+(1)Where Km= 3.5 Ncm/A , and Tm= 19.6 msP(s)=1+0.0196(SxS)Open loop TF = 0.0196(S^2)CONCLUSIONConclusion is done in the Answer the following questions part.