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Pole Placement | State Space, Part 2

From the series: State Space

Brian Douglas

This video provides an intuitive understanding of pole placement, also known as full state feedback. This is a control technique that feeds back every state to guarantee closed-loop stability and is the stepping stone to other methods like LQR and H infinity.

We’ll cover the structure of the control law and why moving poles or eigenvalues around changes the dynamics of a system. We’ll also go over an example in MATLAB and touch on a few interesting comparisons to other control techniques.

Published: 11 Jan 2019

In this video, we’re going to talk about a way to develop a feedback controller for a model that’s represented using state-space equations. And we’re going to do that with a method called pole placement, or full state feedback. Now, my experience is that pole placement itself isn’t used extensively in industry; you might find that you’re using other methods like LQR or H infinity more often. However, pole placement is worth spending some time on because it’ll give you a better understanding of the general approach to feedback control using state-space equations and it’s a stepping stone to getting to those other methods. So I hope you stick around. I’m Brian, and welcome to a MATLAB Tech Talk.

To start off, we have a plant with inputs u and outputs y. And the goal is to develop a feedback control system that drives the output to some desired value. A way you might be familiar with doing this is to compare the output to a reference signal to get the control error. Then you develop a controller that uses that error term to generate the input signals into the plant with the goal of driving the error to zero. This is the structure of the feedback system that you’d see if you were developing, say, a PID controller.

But for pole placement, we’re going to approach this problem in a different way. Rather than feed back the output y, we’re going to feed back the value of every state variable in our state vector, x. We’re going to claim that we know the value of every state even though it’s not necessarily part of the output y. We’ll get to that in a bit, but for now, assume we have access to all of these values. We then take the state vector and multiply it by a matrix that is made up of a bunch of different gain values. The result is subtracted from a scaled reference signal, and this result is fed directly into our plant as the input. 

Now you’ll notice that there isn’t a block here labeled “controller” like we have in the top block diagram. In this feedback structure, this whole section is the controller. And pole placement is a method by which we can calculate the proper gain matrix to guarantee system stability, and the scaling term on the reference is used to ensure that steady state error performance is acceptable. I’ll cover both of these in this video.

In the last video, we introduced the state equation x dot = Ax + Bu. And we showed that the dynamics of a linear system are captured in this first part, Ax. The second part is how the system responds to inputs, but how the energy in the system is stored and moves is captured by the Ax term. So you might expect that there is something special about the A matrix when it comes to controller design. And there is: Any feedback controller has to modify the A matrix in order to change the dynamics of the system. This is especially true when it comes to stability.

The eigenvalues of the A matrix are the poles of the system, and the location of the poles dictates stability of a linear system. And that’s the key to pole placement: Generate the required closed-loop stability by moving the poles or the eigenvalues of the closed-loop A matrix.

I want to expand a bit more on the relationship between poles, eigenvalues, and stability before we go any further because I think it’ll help you understand exactly how pole placement works.

For this example, let’s just start with an arbitrary system and focus on the dynamics, the A matrix. We can rewrite this in non-matrix form so it’s a little bit easier to see how the state derivatives relate to the states. In general, each state can change as a function of the other states. And that’s the case here; x dot 1 changes based on x2 and x dot 2 changes based on both x1 and x2. This is perfectly acceptable, but it makes it hard to visualize how eigenvalues are contributing to the overall dynamics. So what we can do is transform the A matrix into one that uses a different set of state variables to describe the system.

This transformation is accomplished using a transform matrix whose columns are the eigenvectors of the A matrix. What we end up with after the transformation is a modified A matrix consisting of the complex eigenvalues along the diagonal and zeroes everywhere else. These two models represent the same system. They have the same eigenvalues, the same dynamics; it’s just the second one is described using a set of state variables that change independently of each other. 

With the A matrix written in diagonal form, it’s easy to see that we’re left with a set of first-order differential equations where the derivative of each state is only affected by that state and nothing else. And here’s the cool part: The solution to a differential equation like this is in the form Z = a constant times e ^ lambda t. Where lambda is the eigenvalue for that given state variable. 

Okay, let’s dive into this equation a little bit more. Zn shows how the state changes over time given some initial condition, C. Or another way of thinking about this is that if you initialize the state with some energy, this equation shows what happens to that energy over time. And by changing lambda, you can affect how the energy is dissipated or, in the case of an unstable system, how the energy grows.

Let’s go through a few different values of lambda so you can visually see how energy changes based on the location of the eigenvalue within the complex plane.

If lambda is a negative real number, then this mode is stable since the solution is e raised to a negative number, and any initial energy will dissipate over time. If it’s positive, then it’s unstable because the energy will grow over time. And if there is a pair of imaginary eigenvalues, then the energy in the mode will oscillate, since e ^ imaginary number produces sines and cosines. And any combination of real and imaginary numbers in the eigenvalue will produce a combination of oscillations and exponential energy dissipation.

I know this was all very fast, but hopefully it made enough sense that now we can state the problem we’re trying to solve. If our plant has eigenvalues that are at undesirable locations in the complex plane, then we can use pole placement to move them somewhere else. Certainly if they’re in the right half plane it’s undesirable since they’d be unstable, but undesirable could also mean there are oscillations that you want to get rid of, or maybe just speed up or slow down the dissipation of energy in a particular mode.

With that behind us, we can now get into how pole placement moves the eigenvalues. Remember the structure of the controller that we drew at the beginning? This results in an input u = r*Kr - k*x. Where r Kr is the scaled reference, which again we’ll get to in a bit. And kx is the state vector that we’re feeding back multiplied by the gain matrix.

Here’s where the magic happens. If we plug this control input into our state equation, we are closing the loop and we get the following state equation: Notice that A and -Bk both act on the state vector so we can combine them to get modified A matrix.

This is the closed-loop A matrix and we have the ability to move the eigenvalues by choosing an appropriate K. And this is easy to do by hand for simple systems. Let’s try an example with a second-order system with a single input. We can find the eigenvalues by setting the determinant of A - lambda I to zero and then solve for lambda. And they are at -2 and +1. One of the modes will blow up to infinity because of the presence of the positive real eigenvalue and so the system is unstable. Let's use pole placement to design a feedback controller that will stabilize this system by moving the unstable pole to the left half plane.

Our closed-loop A matrix is A - BK and the gain matrix, k, is 1x2 since there is one output and two states. This results in - K1, 1 - k2, 2 and -1. We can solve for the eigenvalues of Acl like we did before and we get this characteristic equation that is a function of our two gain values.

Let’s say we want our closed-loop poles at -1 and -2. In this way, the characteristic equation needs to be L^2 + 3L + 2 = 0. So at this point, it’s straightforward to find the appropriate K1 and K2 that make these two equations equal. We just set the coefficients equal to each other and solve. And we get K1 = 2, and K2 = 1 and that’s it. If we place these two gains in the state feedback path of this system, it will be stabilized with eigenvalues at -1 and -2. 

Walking through an example by hand, I think, gives you a good understanding of pole placement; however, the math involved starts to become overwhelming for systems that have more than two states. The idea is the same; just solving the determinant becomes impractical. But we can do this exact same thing in MATLAB with pretty much a single command. 

I’ll show you quickly how to use the place command in MATLAB by recreating the same system we did by hand. I’ll define the four matrices, and then create the open-loop state-space object. I can check the eigenvalues of the open-loop A matrix just to show you that there is, in fact, that positive eigenvalue that causes this system to be unstable.

That’s no good, so let’s move the eigenvalues of the system to -2 and -1. Now solving for the gain matrix using pole placement can be done with the place command. And we get gain values 2 and 1 like we expected.

Now the new closed-loop A matrix is A - BK, and just to double check, this is what Acl looks like and it does have eigenvalues at -1 and -2. Okay, I’ll create the closed-loop system object and now we can compare the step responses for both. 

The step response of the open-loop system is predictably unstable. The step response of the closed-loop system looks much better. However, it’s not perfect. Rather than rising to 1 like we’d expect, the steady state output is only 0.5. And this is finally where the scaling on the reference comes in. So far, we’ve only been concerned with stability and have paid little attention to steady state performance. But even addressing this is pretty straightforward. If the response to the input is only half of what you expect, why don’t we just double the input? And that’s what we do. Well, not double it, but we scale the input by the inverse of the steady state value. 

In MATLAB, we can do this by inverting the DC gain of the system. You can see that the DC gain is 0.5, and so the inverse is 2. Now we can rebuild our closed-loop system by scaling the input by Kr. and checking the step response. No surprise; its steady state value is 1. 

And that’s pretty much what there is to basic pole placement. We feed back every state variable and multiply them by a gain matrix in such a way that moves the closed-loop eigenvalues, and then we scale the reference signal so that the steady state output is what we want.

Of course, there’s more to pole placement than what I could cover in this 12-minute video, and I don’t want to drag this on too long, but I also don’t want to leave this video without addressing a few more interesting things for you to consider. So in the interest of time, let’s blast through these final thoughts lightning-round style. Are you ready? Let’s go!

Pole placement is like fancy root locus. With root locus you have one gain that you can adjust that can only move to the poles along the locus lines. But with pole placement, we have a gain matrix that gives us the ability to move the poles anywhere in the complex plane, not just along single-dimensional lines.

A two-state pole placement controller is very similar to a PD controller. With PD, you feed back the output and generate the derivative within the controller. With pole placement, you are feeding back the derivative as a state, but the results are essentially the same: 2 gains, one for a state and one for its derivative.

Okay, we can move eigenvalues around, but where should we place them? The answer to that is a much longer video, but here are some things to think about. If you have a high-order system, consider keeping two poles much closer to the imaginary axis than the others so that the system will behave like a common second-order system. These are called the dominant poles since they are slower and tend to dominate the response of the system.

Keep in mind that if you try to move a bunch of eigenvalues really far left in order to get a super-fast response, you may find that you don’t have the speed or authority in your actuators to generate the necessary response. This is because it takes more gain, or more actuator effort, to move the eigenvalues further from their open-loop starting points.

Full state feedback is a bit of a misnomer. You are feedback every state in your mathematical model, but you don’t, and can’t, feed back every state in a real system. For just one example, at some level, all mechanical hardware is flexible, which means additional states, but you may choose to ignore those states in your model and develop your feedback controller assuming a rigid system. The important part is that you feed back all critical states to your design so that your controller will still work on the real hardware.

You have to have some kind of access to all of the critical states in order to feed them back. The output, y, might include every state, in which case you’re all set. However, if this isn’t the case, you will either need to add more sensors to your system to measure the missing states or use the existing outputs to estimate or observe the states you aren’t measuring directly. In order to observe your system, it needs to be observable, and similarly, in order to control your system it needs to controllable. We’ll talk about both of those concepts in the next video.

So that’s it for now. I hope these final few thoughts helped you understand a little more about what it means to do pole placement and how it’s part of an overall control architecture.

If you want some additional information, there are a few links in the description that are worth checking out that explain more about using pole placement with MATLAB.

If you don’t want to miss the next Tech Talk video, don’t forget to subscribe to this channel. Also, if you want to check out my channel, control system lectures, I cover more control theory topics there as well. Thanks for watching. I’ll see you next time.

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pole placement design by state feedback

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pole placement design by state feedback

Introduction: State-Space Methods for Controller Design

In this section, we will show how to design controllers and observers using state-space (or time-domain) methods.

Key MATLAB commands used in this tutorial are: eig , ss , lsim , place , acker

Related Tutorial Links

  • LQR Animation 1
  • LQR Animation 2

Related External Links

  • MATLAB State FB Video
  • State Space Intro Video

Controllability and Observability

Control design using pole placement, introducing the reference input, observer design.

There are several different ways to describe a system of linear differential equations. The state-space representation was introduced in the Introduction: System Modeling section. For a SISO LTI system, the state-space form is given below:

$$
\frac{d\mathbf{x}}{dt} = A\mathbf{x} + Bu
$$

To introduce the state-space control design method, we will use the magnetically suspended ball as an example. The current through the coils induces a magnetic force which can balance the force of gravity and cause the ball (which is made of a magnetic material) to be suspended in mid-air. The modeling of this system has been established in many control text books (including Automatic Control Systems by B. C. Kuo, the seventh edition).

pole placement design by state feedback

The equations for the system are given by:

$$
m\frac{d^2h}{dt^2} = mg - \frac{Ki^2}{h}
$$

From inspection, it can be seen that one of the poles is in the right-half plane (i.e. has positive real part), which means that the open-loop system is unstable.

To observe what happens to this unstable system when there is a non-zero initial condition, add the following lines to your m-file and run it again:

pole placement design by state feedback

It looks like the distance between the ball and the electromagnet will go to infinity, but probably the ball hits the table or the floor first (and also probably goes out of the range where our linearization is valid).

$u(t)$

Let's build a controller for this system using a pole placement approach. The schematic of a full-state feedback system is shown below. By full-state, we mean that all state variables are known to the controller at all times. For this system, we would need a sensor measuring the ball's position, another measuring the ball's velocity, and a third measuring the current in the electromagnet.

pole placement design by state feedback

The state-space equations for the closed-loop feedback system are, therefore,

$$
\dot{\mathbf{x}} = A\mathbf{x} + B(-K\mathbf{x}) = (A-BK)\mathbf{x}
$$

From inspection, we can see the overshoot is too large (there are also zeros in the transfer function which can increase the overshoot; you do not explicitly see the zeros in the state-space formulation). Try placing the poles further to the left to see if the transient response improves (this should also make the response faster).

pole placement design by state feedback

This time the overshoot is smaller. Consult your textbook for further suggestions on choosing the desired closed-loop poles.

Note: If you want to place two or more poles at the same position, place will not work. You can use a function called acker which achieves the same goal (but can be less numerically well-conditioned):

K = acker(A,B,[p1 p2 p3])

Now, we will take the control system as defined above and apply a step input (we choose a small value for the step, so we remain in the region where our linearization is valid). Replace t , u , and lsim in your m-file with the following:

pole placement design by state feedback

The system does not track the step well at all; not only is the magnitude not one, but it is negative instead of positive!

$K\mathbf{x}$

and now a step can be tracked reasonably well. Note, our calculation of the scaling factor requires good knowledge of the system. If our model is in error, then we will scale the input an incorrect amount. An alternative, similar to what was introduced with PID control, is to add a state variable for the integral of the output error. This has the effect of adding an integral term to our controller which is known to reduce steady-state error.

$y = C\mathbf{x}$

From the above, we can see that the observer estimates converge to the actual state variables quickly and track the state variables well in steady-state.

Published with MATLAB® 9.2

pole placement design by state feedback

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9.0: Prelude to Controllers for State Variable Models

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The state variable models of dynamic systems comprises first-order differential equations that express the time derivatives of a set of state variables. For linear time-invariant (LTI) systems, these equations are commonly expressed in vector-matrix form.

The controller design for the state variable models involves feeding back all the state variables using appropriate weights to generate the error signal. State feedback allows arbitrary placement of roots of the closed-loop characteristic polynomial. It is more powerful and offers greater flexibility than the output feedback that allows only selective placement of closed-loop roots. State feedback assumes that the complete set of state variables are availabe for feedback.

The pole placement design refers to the selection of feedback gains for placing the roots of the closed-loop characteristic polynomial at the desired locations in the complex plane. The pole placement design is performed with ease when the state variable model is in the controller form. Alternately, Ackermann’s and Bass-Gura formulas, or the Sylvester’s equation can be used for this purpose.

Output regulation refers to finding a control law to asymptotically track prescribed refernce signals and/or asymptotically reject undesired disturbance inputs. It includes imparting desired degree of dynamic stability to the system through arbitrary selection of the closed-loop characteristic polynomial.

The tracking system design involves reducing the steady-state error to a given reference input to zero. Though reference signal can be used to cancel the tracking error, the design is not robust against parameter variations. A more robust design involves integrating the error signal inside the feeback loop to form an augmented system model, which can used for pole placement. The augmented model includes the differential equation describing the out put of the integrator.

The state-space design methods primarily cater to the design of multi-input multi-output (MIMO) systems. This chapter, however, introduces the state-space design methods using examples from single-input single-output (SISO) systems.

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8.2.  POLE-PLACEMENT DESIGN USING LINEAR-STATE-VARIABLE FEEDBACK

Having presented methods for designing linear control systems using classical techniques, let us now look at the problem of specifying pole placement from the viewpoint of state-variable feedback [ 1 ]. In order to do this, let us first look at the basic feedback problem illustrated in Figure 8.1 . This figure illustrates the concept of feeding back the states of the process in addition to that of the output. Because a linear process can be characterized by the phase-variable canonical equations

Image

Figure 8.1   General feedback system problem illustrating feedback of the output state and the states of the process.

let us consider the configuration of Figure 8.2 . It is important to observe from this figure that the control signal is generated from a knowledge of the reference input r ( t ) and the state variables x ( t ). Note that r ( t ), u ( t ), and c ( t ) represent scalars.

In general, the control input u can be represented as

u ( t ) = f ( x ( t ), r ( t )).

Rather than considering the controller in such a broad sense, let us consider the specific condition of linear state-variable feedback where the controller weights the sum of the state variables ...

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Investigation of Spatial Control Strategies with Application to Advanced Heavy Water Reactor pp 43–60 Cite as

State Feedback Control Using Pole Placement

  • Ravindra Munje 5 ,
  • Balasaheb Patre 6 &
  • Akhilanand Tiwari 7  
  • First Online: 14 October 2017

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Part of the Energy Systems in Electrical Engineering book series (ESIEE)

In this chapter, a state feedback-based control technique is explored for spatial control of Advanced Heavy Water Reactor (AHWR). The AHWR model with 90 state, 18 output, and 5 input variables is decomposed into slow and fast subsystems of orders 73 and 17, respectively, by two-stage linear transformation. As the fast subsystem is observed to be stable, controller is designed only for the slow subsystem and then composite controller is derived for the original system. Vectorized nonlinear model of AHWR is simulated with presented composite controller and performance is tested under various transient conditions. It is noticed that xenon oscillations are effectively suppressed and performance is found to be acceptable.

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Notation of total power feedback is changed from \(\mathbf {K}\) in ( 2.48 ) to \(\mathbf {K}_G\) , in order to avoid repeatability of symbol.

Chow, J.H., Kokotovic, P.V.: A decomposition of near-optimum regulators for systems with slow and fast modes. IEEE Trans. Autom. Ctrl. 21 (5), 701–705 (1976)

Article   MathSciNet   MATH   Google Scholar  

Gajic, Z., Lim, M.-T.: Optimal Control of Singularly Perturbed Linear Systems and Applications: High Accuracy Techniques. Marcel Dekker, New York (2001)

Book   MATH   Google Scholar  

Kokotovic, P.V., O’Malley, R.E., Sannuti, P.: Singular perturbation and order reduction in control theory-an overview. Automatica 12 , 123–132 (1976)

Ladde, G.S., Siljak, D.D.: Multiparameter singular perturbations of linear systems with multiple time scales. Automatica 19 , 385–394 (1983)

Munje, R.K., Parkhe, J.G., Patre, B.M.: Spatial control of advanced heavy water reactor via two stage decomposition. Ann. Nucl. Energy 77 , 326–334 (2015)

Article   Google Scholar  

Naidu, D.S.: Singular Perturbation Methodology in Control Systems. Peter Peregrinus Ltd., London (1988)

Phillips, R.G.: A two-stage design of linear feedback controls. IEEE Trans. Autom. Control 25 , 1220–1223 (1980)

Saberi, A., Khalil, H.: Stabilization and regulation of nonlinear singularly perturbed systems-composite control. IEEE Trans. Autom. Control 30 , 739–747 (1985)

Saksena, V.R., O’Reilly, J., Kokotovic, P.V.: Singular perturbation and time-scale methods in control theory: survey 1976–1983. Automatica 20 , 273–293 (1984)

Shimjith, S.R., Tiwari, A.P., Bandyopadhyay, B.: A three-time-scale approach for design of linear state regulator for spatial control of advanced heavy water reactor. IEEE Trans. Nucl. Sci. 58 (3), 1264–1276 (2011)

Suzuki, M.: Composite controls for singularly perturbed systems. IEEE Trans. Autom. Control 26 , 505–507 (1981)

Syrcos, G., Sannuti, P.: Singular perturbation modeling of continuous and discrete physical systems. Int. J. Control 37 , 1007–1022 (1983)

Article   MATH   Google Scholar  

Syrmos, V.L., Abdallah, C.T., Dorato, P., Grigoriadis, K.: Static output feedback-a survey. Automatica 33 , 125–137 (1997)

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Department of Electrical Engineering, K. K. Wagh Institute of Engineering Education and Research, Nashik, Maharashtra, India

Ravindra Munje

Shri Guru Gobind Singhji Institute of Engineering and Technology, Nanded, Maharashtra, India

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Bhabha Atomic Research Centre, Mumbai, Maharashtra, India

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Munje, R., Patre, B., Tiwari, A. (2018). State Feedback Control Using Pole Placement. In: Investigation of Spatial Control Strategies with Application to Advanced Heavy Water Reactor. Energy Systems in Electrical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-10-3014-7_3

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IMAGES

  1. Pole placement by state feedback method

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  2. State space feedback 2

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  3. Pole Placement with Integral Feedback Simulink Diagram.

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  4. Pole placement design

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  5. Pole Placement and State feedback

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  6. Full state feedback control-pole placement and LQR.

    pole placement design by state feedback

VIDEO

  1. The Concept of Pole Placement in Classical and Modern Control, 30/3/2016

  2. L18 State regulator design by pole placement via state variable feedback

  3. L19 Numerical example on pole placement

  4. Pole placement design part 2

  5. Pole placement design part 4

  6. Pole placement design part 3

COMMENTS

  1. PDF Pole Placement Design Technique 8.2 State Feedback and Pole Placement

    Pole Placement Design Technique 8.2 State Feedback and Pole Placement Consider a linear dynamic system in the state space form In some cases one is able to achieve the goal (e.g. stabilizing the system or improving its transient response) by using the full state feedback, which represents a linear combination of the state variables, that is

  2. Pole placement design

    Pole Placement Design for Second-Order System. Open Live Script. For this example, consider a simple second-order system with the following state-space matrices: ... N.K. Nichols, and P. Van Dooren, "Robust Pole Assignment in Linear State Feedback," International Journal of Control, 41 (1985), pp. 1129-1155. [2] Laub, A.J. and M. Wette ...

  3. 9.1: Controller Design in Sate-Space

    Pole placement design refers to the selection of the feedback gain vector that places the poles of the characteristic polynomial at the desired locations. The control law for the pole placement design is expressed as: \[u(t)=-{\bf k}^{T} {\bf x}(t)+r(t), \nonumber \] ... pole placement using state feedback is a generalization of proportional ...

  4. PDF 16.30 Topic 11: Full-state feedback control

    Full state feedback process is quite simple as it can be automated in Matlab using acker and/or place. With more than 1 actuator, we have more than n degrees of freedom in the control → we can change the eigenvectors as desired, as well as the poles. The real issue now is where to put the poles. . .

  5. What is Pole Placement (Full State Feedback)

    Check out the other videos in the series: https://youtube.com/playlist?list=PLn8PRpmsu08podBgFw66-IavqU2SqPg_wPart 1 - The state space equations: https://you...

  6. Pole Placement

    This design technique is known as pole placement, which differs from root locus in the following ways: Using pole placement techniques, you can design dynamic compensators. Pole placement techniques are applicable to MIMO systems. ... A state-feedback controller gain K using inputs 1, 2, and 4 of the plant as control inputs . A state ...

  7. Pole Placement using State Feedback

    We discuss why state feedback allows the closed loop poles to be freely assigned.

  8. PDF Pole placement

    CHAPTER 4. POLE PLACEMENT server design for LTI systems. 4.2 Pole assignment by state feedback We shall present a design method commonly called pole placement. We assume that all state variables are measurable and available for feedback. If the system is completely state controllable, i.e., the controllability matrix has full row rank, the

  9. Pole Placement

    This video provides an intuitive understanding of pole placement, also known as full state feedback. This is a control technique that feeds back every state to guarantee closed-loop stability and is the stepping stone to other methods like LQR. ... Let's use pole placement to design a feedback controller that will stabilize this system by ...

  10. Pole Placement by State Feedback

    In this chapter we discuss an important control design question: that of choosing a control law such that the closed loop system is stable (stabilization) or, more generally, such that it has a certain degree of stability reflected, for example, in a requirement on the location of the closed loop poles (pole placement). Keywords. Close Loop ...

  11. Introduction: State-Space Methods for Controller Design

    Control Design Using Pole Placement. Let's build a controller for this system using a pole placement approach. The schematic of a full-state feedback system is shown below. By full-state, we mean that all state variables are known to the controller at all times. For this system, we would need a sensor measuring the ball's position, another ...

  12. State Feedback & Pole Placement (Lecture 16)

    In this video, I explain the basics and design procedure of state-feedback controller via pole placement technique. This video's content is based on Lecture ...

  13. Full state feedback

    Full state feedback (FSF), or pole placement, is a method employed in feedback control system theory to place the closed-loop poles of a plant in pre-determined locations in the s-plane. Placing poles is desirable because the location of the poles corresponds directly to the eigenvalues of the system, which control the characteristics of the response of the system.

  14. PDF Controller design by pole placement

    524 Controller design by pole placement the use of state feedback u(k) = -Kx(k) is sometimes of interest to provide reference cases and is sometimes implementable, as in the case of a motor with both shaft position and rotation velocity measured. In such cases, all n = dim (x) system poles can be placed arbitrarily by

  15. 10.2: Controllers for Discrete State Variable Models

    Pole Placement Design of Digital Controller Given a discrete state variable model \(\left\{A_{\rm d},\ B_{\rm d}\right\}\), and a desired pulse characteristic polynomial \(\Delta _{\rm des} (z)\), a state feedback controller for the system can be designed using pole placement similar to that of the continuous-time system (Sec. 9.1.1).

  16. Design of state and output feedback pole placement controller in the

    Pole placement state feedback with feedforward controller is proposed so that both SRTM and conventional fast-rate output can track their step reference input. This controller comprises a periodically time-varying gain and an observer to estimate the slow-rate instantaneous state variable at the sampling instances.

  17. 9.0: Prelude to Controllers for State Variable Models

    State feedback assumes that the complete set of state variables are availabe for feedback. The pole placement design refers to the selection of feedback gains for placing the roots of the closed-loop characteristic polynomial at the desired locations in the complex plane. The pole placement design is performed with ease when the state variable ...

  18. Pole Placement by State Feedback (Part-I)

    In this lecture, we discuss the concept of pole placement, design of state feedback controller using pole placement approach. Further, controller design is i...

  19. 8.2. Pole-Placement Design using Linear-State-Variable Feedback

    8.2. POLE-PLACEMENT DESIGN USING LINEAR-STATE-VARIABLE FEEDBACK. Having presented methods for designing linear control systems using classical techniques, let us now look at the problem of specifying pole placement from the viewpoint of state-variable feedback [].In order to do this, let us first look at the basic feedback problem illustrated in Figure 8.1.

  20. state feedback design MIMO

    ٦. Note that if the system is not completely controllable, matrix K cannot be determined. (No solution exists.) ٧. The system uses the state feedback control u=-Kx. Let us choose the desired closed-loop poles at. Determine the state feedback gain matrix K. ٨. By defining the desired state feedback gain matrix K as.

  21. State Feedback Control Using Pole Placement

    Feedback design may then proceed for each subsystem and results are combined to yield a composite feedback control for original system. Here, state feedback control employing two-stage decomposition is designed for AHWR model. ... B., Tiwari, A. (2018). State Feedback Control Using Pole Placement. In: Investigation of Spatial Control Strategies ...

  22. L18 State regulator design by pole placement via state variable feedback

    This video explores the concept of state regulation, pole placement and state variable feedback. It covers the design of State regulator by pole placement vi...

  23. PDF State Feedback controller design using Pole-placement method and its

    Some more results on pole placement using different approaches can be seen in [8] and [4]. However in best of our knowledge there is no study on State feedback controller design using MATLAB. This paper has provided the generalized method and technique for solving pole placement problem by given algorithm which is much less