# Relationship between controllability and stability running

Dec 15, The controllability and stability of the automobile refers to ability that the automobile is able to run following the way given by the driver through quality characteristic parameter, and link it to the body and the under frame of. Nov 1, Some problems, what values of aerodynamic characteristics are appropriate or increasing stability and controllability at high speed running. Thanks to the Kreiss matrix theorem, the robust stability measures give insight into the . Running times of the new algorithm with the divide-and- conquer . The ratio αϵ/ϵ is plotted as a function of log10ϵ for the Grcar matrix on the .

Effect of Weight on Stability and Controllability Overloading effects stability. An aircraft that is stable and controllable when loaded normally may have very different flight characteristics when overloaded.

The stability of many certificated aircraft is completely unsatisfactory if the gross weight is exceeded. Nose-up trim involves setting the tail surfaces to produce a greater down load on the aft portion of the fuselage, which adds to the wing loading and the total lift required from the wing if altitude is to be maintained.

This requires a higher AOA Angle of Attack of the wing, which results in more drag and, in turn, produces a higher stalling speed. The recovery from a stall in any aircraft becomes progressively more difficult as its CG moves aft.

A flat spin is one in which centrifugal force, acting through a CG located well to the rear, pulls the tail of the aircraft out away from the axis of the spin, making it impossible to get the nose down and recover. An aircraft loaded to the rear limit of its permissible CG range handles differently in turns and stall maneuvers and has different landing characteristics than when it is loaded near the forward limit.

The forward CG limit is determined by a number of considerations. As a safety measure, it is required that the trimming device, whether tab or adjustable stabilizer, be capable of holding the aircraft in a normal glide with the power off. A tailwheel-type aircraft loaded excessively nose-heavy is difficult to taxi, particularly in high winds.

It can be nosed over easily by use of the brakes, and it is difficult to land without bouncing since it tends to pitch down on the wheels as it is slowed down and flared for landing. Steering difficulties on the ground may occur in nosewheel-type aircraft, particularly during the landing roll and takeoff. To summarize the effects of load distribution: The CG position influences the lift and AOA of the wing, the amount and direction of force on the tail, and the degree of deflection of the stabilizer needed to supply the proper tail force for equilibrium.

The latter is very important because of its relationship to elevator control force. The aircraft stalls at a higher speed with a forward CG location.

This is because the stalling AOA is reached at a higher speed due to increased wing loading.

### AP4ATCO - Weight and Balance - SKYbrary Aviation Safety

Higher elevator control forces normally exist with a forward CG location due to the increased stabilizer deflection required to balance the aircraft. The aircraft cruises faster with an aft CG location because of reduced drag.

The drag is reduced because a smaller AOA and less downward deflection of the stabilizer are required to support the aircraft and overcome the nose-down pitching tendency. The aircraft becomes less stable as the CG is moved rearward. When the point is reached that the wing and tail contributions balance, then neutral stability exists.

Any CG movement further aft results in an unstable aircraft. A forward CG location increases the need for greater back elevator pressure. The elevator may no longer be able to oppose any increase in nose-down pitching.

Adequate elevator control is needed to control the aircraft throughout the airspeed range down to the stall. System Analysis section, the eigenvalues of the system matrix,equal to the poles of the transfer function determine stability.

## Introduction: State-Space Methods for Controller Design

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: Controllability and Observability A system is controllable if there always exists a control input,that transfers any state of the system to any other state in finite time.

It can be shown that an LTI system is controllable if and only if its controllabilty matrix,has full rank i. In these cases it is necessary to estimate the values of the unknown internal state variables using only the available system outputs. A system is observable if the initial state,can be determined based on knowledge of the system input,and the system output,over some finite time interval.

### Control Tutorials for MATLAB and Simulink - Introduction: State-Space Methods for Controller Design

For LTI systems, the system is observable if and only if the observability matrix,has full rank i. A systemis controllable if and only if a systemis observable. This fact will be useful when designing an observer, as we shall see below.

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 measuring the ball's velocity, and a third measuring the current in the electromagnet.

The input is then 10 The state-space equations for the closed-loop feedback system are, therefore, 11 12 The stability and time-domain performance of the closed-loop feedback system are determined primarily by the location of the eigenvalues of the matrixwhich are equal to the closed-loop poles.

Since the matrices and are both 3x3, there will be 3 poles for the system. By choosing an appropriate state-feedback gain matrixwe can place these closed-loop poles anywhere we'd like because the system is controllable.

We can use the MATLAB function place to find the state-feedback gain,which will provide the desired closed-loop poles. Before attempting this method, we have to decide where we want to place the closed-loop poles.

The third pole we might place at to start so that it is sufficiently fast that it won't have much effect on the responseand we can change it later depending on what closed-loop behavior results.

Remove the lsim command from your m-file and everything after it, then add the following lines to your m-file: Try placing the poles further to the left to see if the transient response improves this should also make the response faster.

Consult your textbook for further suggestions on choosing the desired closed-loop poles. Compare the control effort required in both cases.

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In general, the farther you move the poles to the left, the more control effort is required. If you want to place two or more poles at the same position, place will not work.