2a) Copy your program DT_sv1_servo_driver.m to a new file DT_sv2_servo_driver.m, then copy the Simulink file DT_sv1_servo.mdl to DT_sv2_servo.mdl . Modify these new files to implement both state variable feedback and an integrator control. Your programs should be able to use either place or acker to place the **closed** **loop** **poles** directly. Note that if our system has an integrator in it, there should be no prefilter. Modify the Matlab code (the **poles** and the place command) to place the **poles** of the **closed** **loop** system in such a way so that for a 15 degree step input, for the first disk:

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a) Determine a strictly proper controller so the **closed** **loop** **poles** are at , determine the **closed** **loop** transfer function, and find a constant prefilter so the steady state error for a unit step is zero. Show that the resulting **closed** **loop** transfer function (without the prefilter) is

3a) Copy your program DT_sv1_driver.m to a new file DT_sv1_observer_driver.m, then copy the Simulink file DT_sv1.mdl to DT_sv1_observer.mdl . Modify these new files to implement state variable feedback using a full order observer to estimate the states for a one degree of freedom system. Your programs should be able to use either place or acker to place the **closed** **loop** **poles** directly, or dlqr to place the **poles** using the LQR algorithm. Your programs should write all of the true states and all of the estimated states to the workspace. Note that if our system has no integrator in it, there should be a prefilter. Be sure u k ( ) is taken to be the signal just before the limiter.

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determine the transfer function when there is state variable feedback determine if k1 and k2 exist k = [ k1 k2 ] to allow us to place the closed loop poles anywhere.. If this is true, [r]

a) Implement (Simulink/Matlab) a state observer (not the transfer function) with state variable feedback for the one degree of freedom system on the web. Assume the state feedback gain is chosen so the **closed** **loop** **poles** are at p = [ -20 -30], the initial position and velocity of the true system are both zero, and the initial estimated position is 1 cm and the initial estimate velocity is -5 cm/s. You should be sure to include a prefilter. We are going to be examining the unit step response in this problem.

variable feedback to place the **closed** **loop** **poles** where ever we want to, as we will see in the next chapter. Observability means that if we know the input and measure the output of a system for n time steps, we can determine the initial state of the system, x(0). It also means that we can construct observers to estimate the state of the system. Since for state variable feedback we need knowledge of all of the state this is a very useful property. Sometimes it is much cheaper and easier to estimate the states than to try and measure the states directly. Of course, the accuracy with which we can measure the states depends to some extend on how accurate our model of the system is. However, in order to understand where the tests for controllability and observability come from, we need to ﬁrst review some concepts from linear algebra.

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Abstract— This paper presents a robust control design based on constrained optimization using Differential Evolution (DE). The feedback controller is designed based on state space model of the plant considering structured uncertainty such that the **closed**-**loop** system would have maximum stability radius. A wedge region is assigned as a constraint for desired **closed** **loop** **poles** location. The proposed control technique is applied to a two-mass system that is known as benchmark problem for robust control design. The simulation results seem to be interesting in which the robustness performance is achieved in the presence of parameter variations of the plant.

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Pole placement method is a controller design method in which the places of the **closed** **loop** **poles** are determined on the complex plane by setting a controller gain K. Placing the **poles** is ideal because the location of the **poles** corresponds directly to the Eigen values of the system, which control the characteristics and response of the system. The system must be controllable in order to implement this technique.

All plots should be neatly organized on one page • Using the state variable model on the web page, place the six closed loop poles at -10, -15, -20+10j, -20-10j, -40-20j, -40+20j • By ch[r]

• Thus, in state space, given the pair (A,B), we can always determine the K (gain), to place all the system **closed**-**loop** **poles** in the left-half of the plane if and only if the system is controllable – that is, if and only if the controllability matrix C M is of full rank.

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For stable plants whose **poles** have negative real-parts less than a pre-specified −h , we obtained a sufficient condition for existence of PID-controllers that achieve integral-action and **closed**-**loop** **poles** with real-parts less than −h . We pro- posed a systematic design procedure, which allows freedom in the choice of parameters. We showed in an example how this freedom can be used to improve a single-input single- output system’s performance. Extending the optimal parame- ter selection to MIMO systems would be a challenging goal. These results are limited to stable plants. Future direc- tions of this study will involve extension to certain classes of unstable MIMO plants. In addition, optimal parameter selections for the MIMO case will be explored.

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The program will print out the corresponding locations of the closed loop poles and the correct gain kpf , as well as produce a plot of the estimated system response with state variable [r]

Preview In this Lab you will explore the use of the root locus technique in designing con- trollers. The root locus indicates the possible location of the **closed** **loop** **poles** of a system as a parameter (usually the gain k) varies from small to large values. Often we implement con- trollers/compensators to put the dominant **poles** of a system in a location that will produce a more desirable response. This assignment is to be done with Matlab’s sisitool

The main problem of state feedback control is the choice of **closed** **loop** pole locations. For multiple input systems it is not easy to relate elements of the control matrix K to the positions of the **closed** **loop** **poles**. As such, there is no unique solution K for a set of **poles**, and choosing the optimum K-values is not trivial. It is known that **poles** of the system must be chosen in the left half of s plane to insure stability. The procedure of pole placement set such that the rise time, overshoot and settling time are set in the same manner as in [11] using well known formulas (11) under the given conditions.

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To determine if the system is stable, we could compute the transfer function for the close **loop** system and look at the **poles**, but you’ll get to do that enough on next weeks homework, so , we’ll be clever and assume we actually remember something from MA 221. Whenever we compute the transfer function, the denominator is the determinant of sI − A, which means the **poles** of the **closed** **loop** system are actually equal to the eigenvalues of the A matrix. Hence, to determine the **closed** **loop** **poles** when we have state variable feedback, we need to compute the eigenvalues of A − Bk.

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In this Lab you will explore the use of the root locus technique in designing controllers. The root locus indicates the possible location of the **closed** **loop** **poles** of a system as a parameter (usually the gain k) varies from small to large values. Often we implement controllers/compensators to put the dominant **poles** of a system in a location that will produce a more desirable response. This assignment is to be done with Matlab's sisotool. Some things to keep in mind about the root locus:

TC = Set up cost for remanufacture, manufacture and recycle life cycle cost for wind energy + transportation costs + disposal cost+holding costs for remanufacture,manufacture a[r]

Open Open- -loop FRF contains closed loop FRF contains closed- -loop stability info.. 2008/09 MECH466 : Automatic Control 5[r]

The ability of hoverflies to control their head orientation with respect to their body contributes importantly to their agility and their autonomous navigation abilities. Many tasks performed by this insect during flight, especially while hovering, involve a head stabilization reflex. This reflex, which is mediated by multisensory channels, prevents the visual processing from being disturbed by motion blur and maintains a consistent perception of the visual environment. The so-called dorsal light response (DLR) is another head control reflex, which makes insects sensitive to the brightest part of the visual field. In this study, we experimentally validate and quantify the control **loop** driving the head roll with respect to the horizon in hoverflies. The new approach developed here consisted of using an upside-down horizon in a body roll paradigm. In this unusual configuration, tethered flying hoverflies surprisingly no longer use purely vision-based control for head stabilization. These results shed new light on the role of neck proprioceptor organs in head and body stabilization with respect to the horizon. Based on the responses obtained with male and female hoverflies, an improved model was then developed in which the output signals delivered by the neck proprioceptor organs are combined with the visual error in the estimated position of the body roll. An internal estimation of the body roll angle with respect to the horizon might explain the extremely accurate flight performances achieved by some hovering insects.

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4. 3. **Closed** **Loop** System **Closed** **loop** system is established to achieve a regulated output.The **closed** **loop** QBC is simulated with P, PI and PID-controller using MATLAB simulink and the results are presented. The output voltage is continuously compared to check its variation with the reference voltage using a differential amplifier. The differential signal is amplified and fed to a comparator circuit which compares it with a triangular wave. The comparator output is fed to the MOSFET switch. Another triangular wave which is phase shifted by 180 degree is compared with the same differential amplifier output and in turn of the comparator output. The signals are fed as the pulse signals to the MOSFET switch which in turn regulates the output voltage. The error signal is applied to the controller, the output of the controller is given to the gate of MOSFET.

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