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The primary mirror diameter of affordable space telescopes is limited by mass and manufacturing cost. Currently planned optical/near-infrared space telescopes use a segmented primary mirror with relatively few segments and make limited use of real-time position control. However, control can be used as an enabler for a fundamentally different, very highly segmented architecture, leading to a significant reduction in areal density, and hence a significant increase in the realistically achievable diameter of a space telescope. Weight can be reduced by minimizing the structure that supports mirror segments and instead relying on control for overall stiffness. Furthermore, smaller segments can be thinner (hence, lighter) while still providing sufficient internal rigidity. However, with these architectural changes, the control problem involves not only thousands of actuators and sensors but also many lightly damped modes within the control bandwidth. The objective here is to demonstrate that this control problem is solvable by applying a local control approach. This is illustrated for a 30-m-diam primary mirror composed of 12,000 0.3-m-diam segments.

We present a time-domain technique for correlating the control inputs given to hovering, small-scale helicopters with their corresponding accelerations. The resulting correlations give a simple plant model that can be used for proportional-integral-derivative (PID) controller gain tuning, helicopter trimming, and simulations to test low-level controllers. We have collected our data in the Autonomous Controls Environment (ACE), an indoor cooperative control test bed for small, unmanned rotorcraft and ground vehicles. The data collection utilizes pre-existing low-level controllers and the data logs automatically generated by those controllers, so no special system identification arrangements need to be made. We also present two applications of the plant model that we have implemented on the ACE test bed, namely PID gain tuning and automatic in-flight trimming. Nomenclature ai(t) = acceleration in the direction corresponding to channel i ci = proportionality constant relating acceleration to control voltage on channel i di = proportionality constant relating force to control voltage on channel i ei(t) = position error in the direction corresponding to channel i Ei(s) = Laplace Transform of ei(t) Fi(t) = net force in the direction corresponding to channel i i = controller channel corresponding to thrust, roll, pitch, or yaw k = generic PID gain kiP = gain for proportional term of PID controller on channel i kiI = gain for integral term of PID controller on channel i kiD = gain for derivative term of PID controller on channel i Li(s) = open loop transfer function for helicopter and PID controller R 2 = correlation coefficient for line fits td = time delay between control voltage Vi(t) and helicopter kinematics ai(t) or Fi(t) Ti(s) = closed loop transfer function for helicopter and PID controller V0i = reference voltage for trimmed flight on channel i Vi(t) = control input on channel i expressed as a voltage set in the RC helicopter’s transmitter Vi(s) = Laplace Transform of Vi(t) Vtrim,i = value of Vi(t) when there is no acceleration x = Cartesian body frame coordinate corresponding to the pitch direction y = Cartesian body frame coordinate corresponding to the roll direction Yi(s) = Laplace Transform of the output on channel i, namely a yaw angle or position Ydi = Laplace Transform of the desired output on channel i z = Cartesian body frame coordinate corresponding to the thrust direction

A Rijke tube is used to demonstrate model-based control of a combustion instability, where controller design is based on measurement of the unstable system. The Rijke tube used was of length 0.75m and had a grid-stabilised laminar flame in its lower half. A microphone was used as a sensor and a loudspeaker as an actuator for active control. The open loop transfer function (OLTF) required for controller design was that from the actuator to the sensor. This was measured experimentally by sending a signal with two components to the actuator. The first was a control component from an empirically designed controller, which was used to stabilise the system, thus eliminating the non-linear limit cycle. The second was a high bandwidth signal for identification of the OLTF. This approach to measuring the OLTF is generic and can be applied to large-scale combustors. The measured OLTF showed that only the fundamental mode of the tube was unstable; this was consistent with the OLTF predicted by a mathematical model of the tube, involving 1-D linear acoustic waves and a time delay heat release model. Based on the measured OLTF, a controller to stabilise the instability was designed using Nyquist techniques. This was implemented and was seen to result in an 80dB reduction in the microphone pressure spectrum. A robustness study was performed by adding an additional length to the top of the Rijke tobe. The controller was found to achieve control up to an increase in tube length of 19%. This compared favourably with the empirical controller, which lost control for an increase in tube length of less than 3%.

In this paper, a two-stage method is developed for the closed-loop identification of the pitch angle and speed plant transfer functions of a commercial Boeing 747 transport aircraft. A PID controller is used for the pitch angle control while a PD controller is used for the speed control. To generate identification data, the continuous-time transfer functions and the continuous-time controllers are first converted to discrete-time systems. Independent zero-mean unit variance Gaussian white noise reference signal and noise disturbance signal are used to simulate the closed-loop discrete time system. In the first step of the two-stage method, a causal high-order FIR (Finite impulse response) model is used to identify the sensitivity function of the closed loop system. The estimated sensitivity function is then used to reconstruct a noise-free uncorrelated plant input signal. In the second step the open-loop plant transfer functions are identified using the uncorrelated input and output signals. The estimated plant transfer functions are compared with the actual ones in the form of Bode plots. The results obtained from the two-stage method are also compared with those obtained using the indirect identification method.

In classical approaches to control of flexible structures, system equations are usually rewritten in a state space domain, but these state space transformations often lose insight into the physics of the problem from the point of view of a structural dynamicist. On the other hand, second order compensators enable the designers to keep the system equations of motion in their second order form. In particular, acceleration feedback control, which uses second order equations, shows unconditional stability for single degree of freedom systems and collocated pairs of sensor and actuator. AFC can also be effectively used with non-collocated actuators and sensors, even thought it is not unconditionally stable. The objective of the paper is to compare two different designs of acceleration feedback control compensators. First, the technique, based on the crossover point design of the controller, is reviewed. Then, a new acceleration feedback control method based on minimizing the H2 norm of the closed loop transfer function is developed. Both these techniques are validated by numerical simulation studies. Then, an experimental program is designed to control more than one mode with a single piezoceramic actuator for a tapered cantilevered plate.

A mixed //2/floo optimal control design and its application to a flight control problem of B-l aircraft is studied. The mixed #2/ 00 optimal control design is one of finding an internally stabilizing controller that minimizes the //2/#oo performance index subject to an inequality constraint on H^ norm. The application is a linear model of longitudinal motion of B-l aircraft. A standard eigenvalue problem that involves linear matrix inequalities is formulated, and efficient interior point algorithms are used to solve this problem numerically. Results show that this mixed //2/#oo optimal design leads the designer into a tradeoff between HI and HQQ objectives. Through this method, a designer can determine the controllers that result in the desired closed-loop noise rejection properties and stability robustness.

This paper presents a robust controller design for second-order dynamic systems. The controller is model independent and is a virtual second-order dynamic system. The conditions for actuator and sensor placements are identified for controller designs that guarantee overall closed-loop stability. The dynamic controller can be viewed as a virtual passive damping system that serves to stabilize the actual dynamic system. The control gains are interpreted as virtual mass, spring, and dashpot elements that play the same roles as actual physical elements in stability analysis. Position, velocity, and acceleration feedback are considered. Simple examples are provided to illustrate the controller design. From this illustration the physical meaning of the controller design is apparent.

A robust H-infinity control design methodology and its application to a Space Station attitude and momentum control problem are presented. This new approach incorporates nonlinear multi-parameter variations in the state-space formulation of H-infinity control theory. An application of this robust H-infinity control synthesis technique to the Space Station control problem yields a remarkable result in stability robustness with respect to the moments-of-inertia variation of about 73% in one of the structured uncertainty directions. The performance and stability of this new robust H-infinity controller for the Space Station are compared to those of other controllers designed using a standard linear-quadratic-regulator synthesis technique.

Active wing/store flutter suppression systems were demonstrated in 1977 in a series of wind tunnel tests on a YF-17 scale model. In order to substantially improve the suppression system performance, new control laws were developed based on multiple feedback loops, multiple control surfaces, or both. For test safety, a flutter sensing unit and a new store, functioning as a flutter stopper, were designed and fabricated. Test monitoring programs were organized on a Hewlett-Packard 5451C Fourier Analyzer that permitted a real time assessment of the control law effectiveness. One of the monitoring programs generated the aircraft open loop transfer function and Nyquist plots in the supercritical region while the flutter suppression loop was closed. In the tests performed in late 1979, the new control laws were applied to suppress a severe flutter condition to 70% above the uncontrolled flutter dynamic pressure. Postanalysis of the test data indicated the potential to increase the dynamic pressure to an even higher level.

A well-known property of the reduced-order observer is exploited to obtain the controller solution of the loop transfer recovery problem. In that problem, the controller is sought that generates some desired loop shape at the plant's input or output channels. Past approaches to this problem have typically yielded controllers generating loop shapes that only converge pointwise to the desired loop shape. In the proposed approach, however, the solution (at the input) is obtained directly when the plant's first Markov parameter is full rank. In the more general case when the plant's first Markov parameter is not full rank, the solution is obtained in an analogous manner by appending a special set of input and output signals to the original set. A dual form of the reduced-order observer is shown to yield the LTR solution at the output channel.

The technique proposed in this paper gives a simple and useful procedure for solving the Bezout identity in the domain of stable rational transfer functions for finding the parameterization of all stabilizing controllers for single-input single-output control systems. This procedure leads to a solution of linear simultaneous equations involving the parameters of the solution-functions of the Bezout identity. One important consequence of this procedure is that it leads to a relatively lower-order for the controller and the compensated closed loop transfer functions. The procedure is illustrated by desi ning the longitudinal mode control systems for the aircra t YF-16 satisfying its flying qualities. Rf Introduction With the pioneering work of Bongiorno and Youla 11 in I which they parameterized the set of all stabi izing controllers, this area of research has exploded during the past decade. Using this parameterization, Zames and Francis [2] solved the problem of finding an optimal controller (for SISO System) so that the H~ norm of the sensitivity function is minimum. These results have since been generalized to multi-input-multi-output (MIMO) control systems [3]. The recent book of Vidyasagar [5] is an excellent comprehensive reference for this area. Those who have used this technique for nontrivial numerical examples would agree that this elegant approach of designing control systems for stability and performance leads to high orders for the controller and the resultant closed loop transfer functions. Recall that this approach is based on solving the Bezout identity [5]. Usually, the Bezout identity is solved either by solving a pair of Riccati equations or by resorting to some pole-placement technique. As far as we know, there are no known precise guidelines for selecting the eigenvalues of appropriate matrices involved in this process. We strongly feel that the lack of these guidelines for selecting the eigenvalues in the above procedure is one of the main reasons for large order controllers. In this paper, we propose a systematic procedure for solving the Bezout identity by representing the given proper transfer function of a plant in a suitable way. The solution of the Bezout identity turns out to be very simple but extremely useful in as much as it leads to low order controller and the resulting closed loop transfer function. In addition to this, from the form of the resulting closed loop transfer function, the choice of the free parameter becomes quite transparent for meeting performance specifications. This proposed procedure is subject to one technical constraint viz. the number of unstable poles for the plant does not exceed the number of minimum phase zeros by one. But this does not seem to be a serious constraint as most practical control systems satisfy this condition. Assistant Professor, Dept. of Electrical Systems Engineering, "Copyright o 1988 by L.R. Pujara. Published The Algorithm We follow the notation of Vidyasagar [5 . S denotes the set of proper rational functions with rea coefficients and Hurwitz denominator. 1 Consider a typical unity feedback control system represented by the following figure: Figure 1 Suppose the plant transfer function P(s) is represented as where the polynomial ni(s) corresponds to all nonminimum phase zeros of P(s), the polynomial di(s) corresponds to all unstable poles of P(s), and ni(s), di(s) are Hurwitz polynomials.

An analysis of optimal and near optimal atmospheric flight trajectories for drag modulated aeroassisted orbital transfer is presented. An explicit and adaptive closed loop guidance approach for this mode of orbit transfer is also presented with performance near the optimal nominal trajectories. The orbital transfer of interest is for return from high earth orbit to low earth orbit. Most of what is discussed in this paper concerns the aeroassisted or atmospheric segment which lowers the apogee of the high earth orbit to the apogee of the low earth orbit. Minimization of the total impulsive delta-V at this low earth orbit apogee is the optimization criterion. Control about this impulse due to a number of potential error sources in atmospheric braking is the requirement imposed on closed loop guidance.

The application of controlled wind-fixed pitch and yaw moments to control the coning angle of a spinning missile is described. The open-loop response to applied pitch and yaw moments is derived, and the closed-loop behavior of an angle-of-attack control system is analyzed. The angle-of-attack undamping due to a yaw moment is shown to be equal to that for steady roll resonance, and resonance is shown to be a limiting case of yaw moment undamping when the roll rate is equal to the critical frequency. The practical implementation of an angle-of-attack control system is described, and several applications are discussed including passive angle-ofattack damping, roll lockin prevention, and drag control.