WASHOUT CONTROL FOR MANUAL OPERATIONS
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WASHOUT CONTROL FOR MANUAL OPERATIONS
Applied Electronics & Instrumentation
DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING
COLLEGE OF ENGINEERING
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It is known that limitations of human accuracy in manual manipulation hinder the quality of work performed by human operators of manual control systems. Indeed, movements of operators are apt to cause undesirable vibrations in manual control systems. In this paper, I propose a new operator-support control scheme for suppressing harmful oscillatory motions in such systems without disturbing human operator’s manipulation. The proposed scheme is based on the fact that steady state blocking zeros of a feedback controller do not affect the steady-state control input. A finite-dimensional feedback controller with steady-state blocking zeros, called a washout controller in this paper, plays the central role in support for operator’s manipulation. However, the dynamics of a manual control system may become different significantly from its initial model used for the design of an initial washout controller when it is applied to the manual control system. Such difference can result in poor performance of operator-support control. In order to improve it, an iterative procedure is presented for redesign of washout controllers based on closed-loop subspace identification. Closed-loop identification is performed to refine the model for the control design, and then a more sophisticated washout controller is obtained using the identified model. The effectiveness of the proposed scheme is demonstrated by an experiment on manual control of an inverted pendulum
THIS PAPER concerns operator-support control for a class of manual control systems. The operator-support control is useful to human operators for manipulation of unstable objects. Riding a bicycle and piloting an aircraft are typical examples of manual operations of unstable objects. In manual control systems, a crucial issue underlies undesirable vibration caused by quivering movements of human operators, due to limitations of human accuracy in manual manipulation. Therefore, it is important to suppress undesirable vibration effectively during manual manipulation in order to improve control performance
and to reduce operators’ workload.
In operator-support control, it is important not to hinder manual manipulation intended by human operators. There are several methods of suppressing harmful vibration in manual control systems without disturbing manual manipulation, example, a feedback configuration of delayed feedback control and washout filters . An attractive feature of these schemes is that the feedback controller has steady-state blocking zeros. Steady-state blocking zeros mean that the closed-loop system has a blocking zero at zero frequency. Therefore, a feedback controller with steady-state blocking zeros does not affect the steady-state control input. In other words, such a controller can eliminate a steady-state bias which can disturb operator’s manipulation
An operator-support control scheme has been developed based on the technique used in delayed feedback control.Although it has unveiled the effectiveness of the steady-state blocking zeros, the design procedure of the operator-support control scheme is burdensome due to infinite-dimensionality of the closed-loop system which is inherited from delayed feedback control The washout filter can be regarded as a high pass filter for eliminating the steadystate input. Washout filter aided controllers have been applied to many real-life systems, e.g., power systems. In this paper, we will propose a finite-dimensional feedback controller with steady-state blocking zeros, called a washout controller. The proposed washout controller is an extension of washout filter aided controllers in the sense that less conservative conditions for controllers is given. The proposed operator-support control scheme is that a washout controller is added to a manual control system as an auxiliary feedback loop.
However, it is difficult to obtain a good initial model of a manual control system used for the design of a washout controller due to uncertainty and inherent nonlinearity of human operation. Therefore, the initial model of a manual control system may contain large modeling errors. To overcome it, we adopt the iterative procedure as follows: we will carry out closed-loop identification of the manual control system compensated by the initial washout controller, in order to obtain a better model of the manual control system used for the redesign of a washout controller. Particularly, we will use the SSARX method for closed-loop identification. It is known as a closed-loop subspace identification method. To demonstrate the effectiveness of the proposed operatorsupport control scheme, an experiment on manual control of an inverted pendulum is performed. The system has a pendulum attached to a moving cart whose movement is controlled by a human operator’s manipulation such that the pendulum is activelybalanced and remains standing. The result of the experiment demonstrates that the proposed scheme successfully suppresses undesirable vibration in the manual control system. This paper is organized as follows. First, in Section II, operator-support control for suppressing harmful vibration in manual control systems without disturbing manual manipulation is presented. Then, we propose a washout controller for the operator-support control scheme. In Section III, we give a parameterization of washout controllers in the case of continuous time and discrete time. In Section IV, we propose an iterative design method of washout controllers for operator-support control. In Section V, we show experimental results which illustrate the effectiveness of the proposed scheme.
A control system is a device or set of devices to manage, command, direct or regulate the behavior of other devices or systems.
There are two common classes of control systems, with many variations and combinations logic or linear controls, and feedback or non linear controls. There is also fuzzy logic which attempts to combine some of the design simplicity of logic with the utility of linear control. Some devices or systems are inherently not controllable.The term "control system" may be applied to the essentially manual controls that allow an operator, for example, to close and open a hydraulic press, perhaps including logic so that it cannot be moved unless safety guards are in place.
An automatic sequential control system may trigger a series of mechanical actuators in the correct sequence to perform a task. For example various electric and pneumatic transducers may fold and glue a cardboard box, fill it with product and then seal it in an automatic packaging machine.
In the case of linear feedback systems, a control loop, including sensors control algorithms and actuators, is arranged in such a fashion as to try to regulate a variable at a setpoint or reference value. An example of this may increase the fuel supply to a furnace when a measured temperature drops PID controllers are common and effective in cases such as this. Control systems that include some sensing of the results they are trying to achieve are making use of feedback and so can, to some extent, adapt to varying circumstances. Open loop systems do not make use of feedback, and run only in pre-arranged ways.
2.2 Manual control systems
Manual controls are used to control on/off state, speed, direction, or other parameters. The force driving or actuating the controls may be electrical, hydraulic, pneumatic, or manual. Manual controls provide flexibility to the user to control the way in which a particular parameters work during data analysis. There are many types of manual controls. Examples include an electrical control system, hydraulic control system, and a pneumatic control. An electrical control system is designed to control the current flow for safety. An electrical control system is available for applications in motors such as motor starters, control panels, or controllers. An electrical motor control is used in industrial automation. A hydraulic control system monitors the signals from the PLC and determines the braking mode from this data.
Fig.1 BLOCK DIAGRAM OF A MANUAL CONTROL SYSTEM
Suppose the manual control system depicted in the dashed rectangle in Fig. 1 can be described by the nonlinear differential equation:
where x(t)is the state vector, is u(t) the auxiliary input vector for operator-support control, and y(t) is the measured output. f and g are assumed to be unknown smooth functions. The task of a human operator is to maintain the output y(t) within a neighborhood of y his/her desirable operating point by means of the regulation of the amount of operation v(t).
On the manual control system, we make several assumptions as follows. The operating point y is assumed to be a constant which is determined by the human operator. Assume that any numerical information of y is not available a priori for operator- support control since no one but the human operator can understand it. Moreover, it is assumed that there exists an equilibrium point of the manual control system for u(t)=0, v(t) = ¯v and y(t)=y .
That is, there exists a unique x¯ such that
2.3 Operator support control
A crucial problem with the manual control system is that the measured output may vibrate due to limitations of human accuracy and the nonlinear nature of the human operator. Our goal is to suppress the vibration. To this end, we will introduce an operator-support control scheme for manual control by means of feedback connection of an automatic controller to the manual control system (see Fig. 1). Let the automatic controller be represented as the following state space model:
Wherew(t) is the state vector of the controller and the control input u(t) is applied to the manual operation v(t) . The automatic controller is designed to locally stabilize the unknown equilibrium point in the manual control system (1) without changing its equilibrium point . In otherwords, the stabilization should be achieved by unbiased input, i.e.w(t)=0, when y(t)-y=0. When the closed-loop system is stabilized, if the control input converges to a nonzero u, the human operator is forced to change his/her desired operation to u . In this way, the human operator is required to compensate the manual operation in order to eliminate the biased input u. This additional requirement imposes a burden of the human operator. Toavoid it, operator-support control should be designed such that and . From the assumption, however, the reference is y not available for any automatic controller. Hence, the controller is required to stabilize the uncertain operating point. This may be satisfied if the coefficients of the controller satisfy the condition that there exists a such that
for constant y
STABILIZATION OF UNKNOWN OPERATING POINT
A salient feature of our control problem is stabilization of the unknown operating point. The feedback controller (2) is designed so that the unknown y is locally asymptotically stabilized. The design is carried out based on the linearized model of the manual control system. In the vicinity of the unknown y , the manual control system is linearized as
(The parameters of the state-space model will be identified by methods in Section IV.) Define . Then, the closed-loop system of P(s) and (2) is depicted in Fig. 2, where . For the closed-loop system, the unknown operating point can be regarded as a step disturbance. Hence, the problem of stabilizing the unknown operating point can be cast into that of disturbance attenuation
of the closed-loop system. An important inherent property of controllers to stabilize unknown operating points is that their transfer functions have
blocking zeros at zero frequency.
Fig 2.Closed-loop system of the linearized system P(s)around the unknown operating point y in the manual control system and the proposed operator-support controller k(s)
A transfer function matrix K(s) (respectively,K(z) for discrete-time systems) is said to have a steady-state blocking zero ifK(s)=0 at s=0 (respectively,K(z)=0 at z=1). If a feedback controller K(s) with a steady-state blocking zero stabilizes the closed-loop system, the steady-state input always satisfies because, from the final value theorem :
Therefore, the biased input can be removed by any feedback controller with K(0)=0 which stabilizes the manual control system. Similarly, in discrete-time setting, blocking zeros play animportant role instabilization of an unknown fixed point of discrete-time systems. When we consider a linearized system around an unknown fixed point as
we stabilize it by a discrete-time controller K(z)with its statespace realization
If stabilizes (5) and has a steady-state blocking zero, then the steady-state input always satisfy . Because
It is well known that delayed feedback control utilizes the difference between the current output and the delayed output to eliminate the biased input in the steady state.The transfer function of the delayed feedback controller can be factored , where K(s) denotes a real rational transfer function. Hence, it has a steady-state blocking zero. In contrast to the simple control structure described here, the design procedure is complicated for practical use. To stabilize the continuous-time system with the unknown equilibrium point, a certainty equivalence adaptive control scheme was proposed. The continuous-time washout filter aided feedback controller and the discrete-time one satisfy
eqtns (8) and (9)
respectively. The washout filter is a high-pass filter which is added to a feedback controller in order to eliminate the biased input in the steady state. However, (8) and (9) are sufficient conditions for the finite-dimensional controller with a steady-state blocking zero. These conditions are very conservative.
In this paper, I propose less conservative conditions for finite-dimensional controllers with a steady-state blocking zeroA continuous-time controller with a state-space realization (2) is called a washout controller if it satisfies the conditions
A discrete-time controller with a state-space realization (6) is called a discrete-time washout controller if it satisfies the conditions
In fact, the conditions (8) and (9), respectively, are sufficient for (10) and (11).
If the feedback controller (2) is the washout controller, then it has a steady-state blocking zero. It is obvious that the feedback controller (2) with the condition (10) satisfies
at s=0 .
If the feedback controller (6) is a discrete-time washout controller, then it has the steady-state blocking zero. Since the controller (6) with the condition (11) satisfie s
FULL ORDER PARAMETERIZATION OF WASHOUT CONTROLLERS:
The term “full order” implies that the order of the controller is the same as that of the plant. For the plants, we make an assumption of controllability and observability in this section. It can be relaxed to stabilizability and detectability.
5.1 Continuous time washout controller:
Let us suppose that a state-space realization of a continuoustime linear system be given as
Then, we have the following theorem for the full-order continuous- time washout controller.
Theorem 1: There exists a continuous-time washout controller stabilizing (12) if and only if is nonsingular. Moreover, when the above condition holds, a set of stabilizing washout controllers is given by
Where eqtn (14)
and and are asymptotically stable, and is nonsingular. .
Proof: For notational brevity, we will introduce the notations as follows: If the closed-loop system with the controller (2) is well-posed (i.e., is invertible), it can be described
(Necessity) If the controller (2) stabilizes the closed-loop system and it is a washout controller, then 0 and . Hence, by using the matrix inversion lemma as follows. If , and are nonsingular matrices, then
Therefore eqtn (19)
Since the closed-loop system is asymptotically stable, does not have any zero eigenvalues. Hence, . Therefore, from (19), . (Sufficiency) Under the condition that , we will show that the controller given by (13) is a washout controller which makes (15) asymptotically stable. Let us suppose that F and L be chosen from S. Then,I + QD is nonsingular, and the feedback controller is given by
By using in (20) and the matrix inversion lemma (17), we have
Moreover, a similarity transformation of with the matrix is given by
SinceA + BF and A+LC are stable, so is . Now, we define
then it is invertible because
Then, from (21), we have
Therefore, we conclude that (13) gives a continuous-time washout controller. Since poles of the closed-loop system are eigenvalues of A+BF and A+ LCin the case of the washout controller, the pole of the closed-loop system can be arbitrarily placed by selecting matrices F and L.
5.2 Discrete-Time Washout Controller:
In this subsection, let us suppose that a state-space realization of a discrete-time linear system be given as
Then, we have the following theorem for the full-order discrete- time washout controller.
Theorem 2: There exists a discrete-time washout controller stabilizing (22) if and only if I –A is nonsingular. Moreover, when the previous condition holds, a set of stabilizing discretetime washout controller is given by
where is given by (14), and
and are asymptotically stable,
and is nonsingular .
When and 0, is invertible, because
Then, we have
TUNING OF WASHOUT CONTROLLERS FOR
In this section, we will propose an iterative design method of washout controllers for operator-support control. Since washout controllers are implemented on digital computers, we design a discrete-time washout controller by using a discrete-time linearized model of manual control systems. To design awashout controller assisting in manual operations,we need a discrete-time linearized model of the manual control system around the operating point. In general, however, modelling of themanualcontrol system is difficult. Hence, using input/ output data observed from the manual control system, a system identification seems promising to obtain a linear model of the manual control system in the vicinity of its operating point. First, we will obtain a linear model as an initial model via open-loop identification. Note that a relatively small number of
data in the vicinity of the operating point are available for system identification since, without any operator support controller, the measured output of the manual control system oscillates significantly. Therefore, the initial model may contain large modelling errors, and such modeling errors can lead to poor performance
of the initial controller. To reduce the effect of modeling errors, closed-loop identification is implemented to refine the model of the manual control system for the control design. Since the vibration is suppressed by the washout control in closed-loop setting, there are enough data to identify the model of the manual control system. In this paper, we will adopt a closed-loop subspace identification
method, i.e., the SSARX method
6.1 SSARX Method
The SSARX method can be categorized as a direct approach to closed loop identification. In this method, it is assumed that a linear system can be described in the innovations form by the following state space realization:
(where is the innovation. Define and
, and assume that is stable. From (24), we have
Then, the state x(t) is approximated by . Moreover, when s is sufficiently large, (25) is constructed by stacking ARX models. The procedure of the SSARX method is shown as follows.
1) Estimate a high order ARX model from observed data .
2) Estimate D and K from coefficients of the estimated high order ARX model. Let D and K denote estimates of D and K, respectively.
3) From (25), we have
By performing canonical correlation analysis on and we obtain which is the estimate of L.
4) Estimate(A,B, C,D,K) and the innovation e(k) from the estimated state
6.2 Experiment with inverted pendulum
To demonstrate the effectiveness of the proposed technique, we applied it to manual control of the inverted pendulum system on the rail inclined at an unknown angle ? from the horizon as illustrated in Fig. 4. The task of a human operator in the manual control system was to stabilize the pendulum by means of moving the cart with the mouse Note that not only the inherent instability of the inverted pendulum in open loop but also the use of the mouse as the input device and the incline of the rail at the unknown ? make it difficult for the human operator to stand the inverted pendulum. The length from the joint to the gravity center of the pendulum is 0.5 m, the mass of the pendulum m is 0.056 kg, the mass of the cart M is 0.235 kg, and the angle of the rail ? is 0.18 rad. In the experiment, these parameters are assumed to be unknown. In this system, the observed output is the angle of the pendulum O(t) and the operating point y is equal to the angle of the rail . Moreover, the sampling time is 20 ms, and the operator-support controller is implemented on a digital computer.
Fig. 3 shows the time responses of the angle of the pendulum O(t) the control input by the human operator v(t), and the control input by the washout controller(t) . Fig. 3(a) is a result obtained with only manual control, whereas Fig. 3(b) has the results
for manual control with the initial washout controller, and Fig. 3© has the results for manual control with the controller ? after tuning. In the experiment, the washout controller was redesigned only once. Although the upright state of the pendulum is maintained, as can be seen from Fig. 3(a), vibration occurs. Moreover, there is a great deal of vibration in the control input due to manual manipulation. On the other hand, the washout controller suppresses these vibrations [see Fig. 3(b) and ©]. Therefore, by using our method, the control input in manual manipulation is suppressed and the load for manual operationis reduced. Moreover, the washout
controller after tuning can suppress the vibration in the manual control system to be more effective than the initial controller.
Fig 4. Inverted pendulum system.
In this paper, I have proposed a new operator-support control scheme for suppressing harmful vibration in manual control systems without disturbing the human operator’s manipulation. As support controllers for human operators, we have proposed a washout controller which is a finite-dimensional feedback control method with steady-state blocking zeros, and showed that such a controller can suppress undesirable vibration in a manual control system. Moreover, we have proposed a tuning technique of washout control for manual operations via closed-loop identification.The proposed washout controller is effective for construction
of a support system for the human operator.
A future issue is to deal with manual control systems with a time-varying operating point since the proposed scheme assumes that the operating point is constant.
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