System and Disturbance Identification for Feedforward and Feedback Control Applications

This paper examines the problem of system identie cation in the presence of unknown disturbances. Specie cally, weconsiderthecasewherethedisturbanceeffect on theoutputismodeled explicitlyand variouswaysto separateit from the system disturbance-free dynamics. Available for identie cation are the excitation signals and the resultant responses, which may be corrupted by unknown and possibly dominating disturbances. We assume that no actual measurement of the disturbances themselves is available for identie cation. The case where the disturbance proe le is unknown and may be quite complicated, but its period is known, is considered e rst. Next, we consider the case where the disturbance frequencies are known only approximately, and a procedure is applied to iteratively ree ne the estimation of the disturbance frequencies for successful system identie cation. Finally, we examine the situationwheretheunknowndisturbanceisnonperiodic.Theidentie cationproducesresultsthatcanbeusedforthe synthesis of feedforward and feedback control to cancel the disturbance effect. Both simulation and experimental results will be used for illustration. The simulation is carried out with a model of a communications satellite, and the experimental results are obtained from a e exible truss structure. A companion paper addresses the system identie cation problem where the disturbance effect is modeled implicitly. HE control problem of rejecting unwanted disturbance has many applications in electrical, mechanical, aerospace, and acoustic systems. Many methods have been developed to treat this problem. If both the plant and disturbance frequencies are known, classical feedback control approaches call for the design of e lters with high gain at the disturbance frequencies to produce corre- sponding zeros in the closed-loop transfer function relating the dis- turbances to the system response. The closed-loop system is then capable of rejecting the unwanted disturbances at the designed fre- quencies. One such design is included in the attitude control sys- tems of the INMARSAT III and INTELSAT VIII spacecraft. 1 Re- jection of sinusoidal disturbances can also be achieved using the frequency-shaped cost functional method. 2 This is an adaptation of linear quadratic Gaussian (LQG) design methods that determines the control necessary to minimize a cost function expressed in the frequency domain. The cost function penalizes the response at the known disturbance frequencies, resulting in high gain feedback at these frequencies. Another method for disturbance rejection is known as disturbance accommodation control or, as it is sometimes called, disturbance modeling or disturbance estimation. 3 Itassumes an effective disturbance input at the control input location that has the same effect at the output as the actual disturbance. The same harmonic disturbance can be modeled as marginally stable modes and appended to the state-space model of the plant. An observer is designed to estimate the plant states together with the disturbance from which the control signal is computed. The disturbance ob- server approach also assumes an equivalent effective disturbance at the control input, but it uses an inverse plant model to estimate this disturbance for control. 4 Repetitive control is another approach to reject periodic disturbance where the tracking error observed in the previous periods is used to correct the control signal for the cur- rent period. 5,6 Adaptive control can be used to cancel the effects of unknown sinusoidal or periodic disturbance through the use of a sufe ciently overparameterized model so that the disturbance dy- namics can be entirely absorbed in the identie ed model. 7 With the disturbance embedded in the model, based on the internal model principle the resulting feedback control has ine nite open-loop gain at the disturbance frequencies and achieves complete cancellation. The e ltered-X least mean squares is another well-known distur- bance rejection method. 8 This method requires measurement of a disturbance-correlated signal, and together with an assumed model of the system it adaptively tunes the coefe cients of a e nite impulse response e lter driven by a disturbance-correlated reference signal to achieve disturbance cancellation. Adaptive inverse control com- bines adaptive feedforward techniques for command or model fol- lowing and adaptivefeedback techniques for disturbance rejection. 9 Artie cial neural networks can also be used to provide disturbance rejection control. 10 Neural networks are used to identify the dynam- icsfromthedisturbancesources,andthecontrolinputstothesystem outputs and adapts the control signals for disturbance cancellation. Instead of treating the disturbance-rejection problem from a con- trol system synthesis standpoint, we address the problem from a system identie cation perspective. The research e rst focuses on the system identie cation problem in the presence of unknown distur- bance inputs, and then uses the identie cation results to solve the re- lated disturbance-rejection control problem. We assume no a priori knowledge of the system and no actual measurement of the dis-